problem solving samples about forces

v = 0 m/s

v = 88.3 m/s

( 112 m/s) 2 = (0 m/s) 2 + 2*(a)*(398 m)

12544 m 2 /s 2 = 0 m 2 /s 2 + (796 m)*a

12544 m 2 /s 2 = (796 m)*a

(12544 m 2 /s 2 )/(796 m) = a

a = 15.8 m/s 2

Return to Problem 19

v f 2 = v i 2 + 2*a*d

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(91.5 m)

0 m 2 /s 2 = v i 2 - 1793 m 2 /s 2

1793 m 2 /s 2 = v i 2

v i = 42.3 m/s

Now convert from m/s to mi/hr:

v i = 42.3 m/s * (2.23 mi/hr)/(1 m/s)

v i = 94.4 mi/hr

Return to Problem 20

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Free-Body Diagrams: Solved Problems

In this article, you can learn more about free-body diagrams using the problems-solutions approach. 

Free-Body Diagrams: Introduction

In solving any dynamic problem, it is useful to identify all forces acting on an object and then illustrate them in a single diagram, called a free-body diagram. 

In these diagrams, the object is depicted as a particle in a suitable coordinate system. 

Free-Body Diagrams: Problems

The tactics for drawing any free-body diagram are as follows:

(a) Identify all forces acting on the object. (b) Draw a suitable coordinate system. ''Suitable'' means that, for example, for an object along an inclined plane, a tilted coordinate system with the x-axis parallel to the slope is the best option.  (c) Draw each force on the diagram according to its magnitude. 

Problem (1):  A block of mass 10 kg is placed on a rough horizontal surface. Draw the free-body diagram for the block when it is at rest.

Solution : First, let's identify the forces acting on the block. 

1. Weight ($\vec{w}$): The weight of the block acts vertically downward and is equal to the mass of the block multiplied by the acceleration due to gravity ($\rm 9.8\, m/s^2$). 

2. Normal force ($\vec{N}$): The normal force acts perpendicular to the surface and counteracts the weight of the block. Since the block is at rest on a horizontal surface, the normal force will be equal in magnitude and opposite in direction to the weight of the block. 

3. Frictional force ($F_f$): The frictional force acts parallel to the surface and opposes any tendency of motion between two surfaces in contact. The block is at rest on level ground, so there is no frictional force. 

Note that the block is at rest on the surface, so the net force $\vec{F}_{net}$ acting on the block must be zero. As a result, all forces identified above must be drawn in equal magnitude.

Now that we have identified all forces acting on the block and their magnitudes qualitatively, we can draw a free-body diagram:

Note : It's important to remember that free-body diagrams are simplified representations of the forces acting on an object. They do not include other factors such as air resistance or internal forces within the object. 

Problem (2): A car of mass 1000 kg is moving with a constant velocity on a horizontal road. Draw the free-body diagram for the car.

Solution : To draw the free-body diagram for the car, we need to consider all the forces acting on it. In this case, since the car is moving with a constant velocity on a horizontal road, there are three main forces to consider:

1. Weight (W): This force is always acting vertically downwards. The weight can be represented by an arrow pointing downward from the center of the car.

2. Normal force ($N$): This force acts perpendicular to the surface of contact between the car and the road. Since the car is not accelerating vertically, the normal force must be equal in magnitude and opposite in direction to the weight. Therefore, it can be represented by an arrow pointing upward from the center of the car.

3. Frictional force ($f$): This force acts parallel to the surface of contact between the car and the road and opposes its motion. Since the car is moving at a constant velocity, this frictional force must be equal in magnitude and opposite in direction to any external forces that may try to slow down or speed up the car. The frictional force can be represented by an arrow pointing in a direction opposite to that of motion.

4. External force: in this case, the force produced by the engine is the one responsible for pushing the car forward. Here, we have denoted it by $F_{engine}$. 

Overall, your free-body diagram for a car moving with constant velocity on a horizontal road should look like this:

Problem (3): A person is standing on a weighing scale inside an elevator that is accelerating upwards at 2 m/s². Draw the free-body diagram for the person.

Solution : To draw the free-body diagram, we need to consider all the external forces acting on the person.

1. Weight ($\vec{w}=m\vec{g}$): The weight of the person acts vertically downward.

2. Normal force ($\vec{F}_N$): The normal force acts perpendicular to the surface of contact between the person and the weighing scale. It counteracts the weight of the person and prevents them from sinking into or falling through the scale. In this case, since there is an upward acceleration, the normal force will be greater (longer arrow) than just balancing out gravity (smaller arrow).

The elevator is accelerating upward, so according to Newton's second law of motion, there must be an upward net force. Hence, the magnitude of $\vec{F}_N$ will be greater than $\vec{w}$ due to upward acceleration, resulting in a net upward force on the person. 

The free body diagram for a person standing on a weighing scale inside an elevator accelerating upwards would look like this:

Problem (4): In a rotating vertical cylinder (Rotor rider), a person feels as though they are being pressed against the wall with their back. Draw a free-body diagram for this case.

Solution : The forces acting on the person include the downward weight force ($\vec{w}$), the normal force ($\vec{F}_N$) directed away from the wall toward the center rotation, and the force of friction parallel to the wall and directed upward (opposing the downward weight force). 

To create a clear representation of these forces, we can assemble them into a coordinate system, as shown in the figure below. This diagram is known as a free-body diagram for a rotating vertical wall.

Problem (5): A ball of mass 0.5 kg is thrown vertically upward with an initial velocity of 10 m/s. Draw the free-body diagram for the ball at its highest point.

Solution : At the highest point of its trajectory, the ball is momentarily at rest. Therefore, the only force acting on it is the force of gravity pulling it downward.

In all free-falling problems in which objects are tossed straight up into the air (with negligible air resistance), the only external force that is exerted on the object is the weight force, $\vec{w}$, downward. Therefore, the free-body diagram for this case is depicted below.

Problem (6): A box of mass 20 kg is standing on an inclined plane with an angle of inclination θ = 37°. Draw the free-body diagram for the box.

Solution : To solve this problem, it is better to adopt a tilted coordinate system with the $x$-axis parallel to the inclined plane, whereas the positive $y$-axis is perpendicular to the incline. The free-body diagram would include the following forces: 

1. Weight ($\vec{w}$): This force acts vertically downward, not along our chosen negative $y$-axis.

2. Normal force ($\vec{F}_N$): This force acts perpendicular to the surface of the inclined plane as shown in the figure below.

3. Friction force ($\vec{f}$): In this scenario, the static friction between the slope and the box prevents it from sliding down. If this type of friction did not exist, the box would slide down the slope. Therefore, static friction must be directed up the slope to counteract the component of weight force down the slope, resulting in the box remaining at rest.

Problem (7): A rocket is launched vertically upwards from the Earth's surface with an acceleration of 20 m/s² due to its engines. Draw the free-body diagram for the rocket at its highest point.

Solution : At the highest point of its trajectory, the rocket momentarily comes to rest before it starts to fall back down. Therefore, the only force acting on it is the Earth's gravity, which pulls it downward towards the center of the Earth. 

The free-body diagram for a rocket at the highest point of its trajectory is the same free-body diagram as an object thrown vertically upward.

Note : If we were asked to determine the forces acting on the satellite at any point except at the highest point of its trajectory, we would also need to include the thrust force that propels (pushes) the satellite forward. 

Additionally, we must consider the air drag force, which opposes the direction of motion and arises from interactions between the satellite and air molecules. Consequently, the free-body diagram would include these additional forces.

Problem (8): A pendulum bob of mass 2 kg is swinging back and forth in simple harmonic motion with no air resistance present. Draw the free-body diagram for the bob at its maximum displacement.

Solution : In a back-and-forth motion, like that of a pendulum bob, the maximum displacement of the object occurs when it is instantly at rest. (Recall that in harmonic motion problems, this distance is referred to as the amplitude of the oscillations.)

First, let's identify all the forces acting on the bob as it moves back and forth. 

The tension force $\vec{T}$ of the string attached to the bob pulls it toward the center of the semi-circular path along the string. The other force acting on it is the weight force $\vec{w}$, which acts vertically downward. 

Since there is no air resistance present, there are no other forces acting on the bob.

Therefore, we can depict the free-body diagram for this case as shown in the figure below. 

Problem (9): A satellite is orbiting around Earth in a circular path at a constant speed. Draw the free-body diagram for the satellite.

Solution : For a satellite moving in a circular orbit, the gravitational force $F_g$ is the only force acting on it. 

The satellite is attracted to the center of the Earth due to gravity. This force acts towards the center of the circular path and is responsible for keeping the satellite in orbit. This force is called the gravitational force.

Therefore, we can draw a free-body diagram for the satellite as follows:

Problem (10): Two blocks, one of mass 5 kg and another of mass 10 kg, are connected by a string passing over a pulley, as shown in the figure below. Draw separate free-body diagrams for each block.

Solution : In cases where two blocks or bodies are connected by a string (or rope), it is better to cut the rope at a certain point and then indicate the direction of the tension in each rope with two incoming arrows. 

The forces acting on the $5\,\rm kg$ block are as follows: 

The downward weight force $\vec{w}$, and the tension force of the rope that keeps the block hanging directed upward. 

Similarly, the forces acting on the $10\,\rm kg$ block are also the downward weight force, the tension in the rope, directed rightward, and the normal force $\vec{F}_N$, directed perpendicular to the surface. 

Since the two objects are connected by a string, the tension force for each block is the same. 

Therefore, the free-body diagram for this system is as follows: 

Problem (11): A cyclist is riding his bike up a hill inclined at an angle θ = 15° to the horizontal, experiencing a constant force of gravity and a frictional force. Draw the free-body diagram for the cyclist.

Solution : Similar to all free-body diagram problems, first identify all forces acting on the object. The object is moving along an inclined plane, so it is better to consider a tilted coordinate system with its $x$-axis parallel to the slope, as shown in the figure. 

The weight force $\vec{w}$ pulls the object vertically downward, not along our chosen negative $y$-axis. 

The slope's floor also exerts a force perpendicular to the surface, called the normal force $\vec{F}_N$, directed to our chosen tilted positive $y$-axis. 

As the cyclist is riding uphill, there is a frictional force that opposes the motion and acts downward along the negative $x$-axis, directed down the slope.

Assuming negligible air resistance, these three external forces are all the forces acting on the cyclist moving over an inclined plane. 

Problem (12): A person is pushing a crate weighing 50 kg across a rough surface with a constant velocity. Draw the free-body diagram for the crate.

Solution : The free-body diagram for the crate would include the following forces:

1. Downward weight force, $\vec{w}$.  2. The normal force exerted by the surface on the crate, $\vec{F}_N$. 3. The force of friction opposing the motion, $\vec{f}$.

4. The external force that the person is exerting on the crate, $\vec{F}$.

All these forces are assembled into a free-body diagram as shown in the figure below:

Problem (13): A block of mass 2 kg is placed on a rough surface with a coefficient of friction μ = 0.3 and connected to another block of mass 3 kg by a string passing over a pulley as shown in Figure Y (provide figure). Draw separate free-body diagrams for each block.

Solution : To solve this question, we need to draw separate free-body diagrams for each block and then analyze the forces acting on them.

First, let's draw the free body diagram for the $2\,\rm kg$ block. Since it is placed on a rough surface, there are two main forces acting on it:

1. Weight ($\vec{w}$): This is the force due to gravity and can be calculated using the formula $W=mg$.

2. Normal force ($\vec{F}_N$): This is the force exerted by the surface on the block perpendicular to it. It acts in the upward direction and has the same magnitude as weight but in the opposite direction.

Additionally, there is a frictional force acting on block $m_2=2\,\rm kg$ due to its contact with the rough surface:

3. Frictional force (f): This force opposes the motion, and its magnitude can be calculated using $f=\mu N$, where $\mu$ is the coefficient of friction (0.3) and $N$ is the normal force.

4. Tension force ($\vec{T}$)

Now let's draw the free body diagram for the $\rm 3 kg$ block connected by a string passing over a pulley. The downward weight force and upward tension force are the forces acting on this block.

Since both blocks are connected by a string passing over a pulley, they experience equal magnitudes of tension force ($T$). 

These free-body diagrams help us understand the forces acting on each block and will be useful in solving further questions related to this system.

Problem (14): A ball weighing 0.2 kg is thrown horizontally with an initial velocity of 15 m/s from the top of a building. Draw the free body diagram for the ball just after it leaves the thrower's hand.

Solution : The only external force that acts on the ball just after it leaves the thrower's hand is the ball's weight force. 

Weight ($\vec{w}$): This force acts vertically downwards and is equal to the mass of the ball (0.2 kg) multiplied by the acceleration due to gravity ($\rm 9.8 m/s^2$).

Since the ball is not in contact with any surface, there is no normal force acting on it. On the other hand, assuming air resistance is negligible, this force can also be ignored.

Therefore, the free body diagram would show only one force acting on the ball, which is its weight (mg) pointing downwards.

Keep in mind that in all projectile motion problems, the weight force is the only force acting on the body, if air resistance is negligible. 

Problem (15): A person is standing on an elevator that is moving upward at a constant velocity. Draw the free-body diagram for the person.

Solution : The elevator is moving upward at a constant velocity, which means that its acceleration is zero. As a result, the net force (or the resultant of forces) on the person is also zero, $F_{net}=0$. As always, the weight force acts vertically downward, representing the gravitational pull on the person's mass.

There is contact between the person's feet and the elevator's floor, so a normal force $\vec{F}_N$ must also be present to support the person's weight. 

Since the elevator is moving at a constant velocity, both of these forces must be depicted in a free-body diagram with equal magnitudes but opposite directions. 

Author : Dr. Ali Nemati Date Published: July 28, 2023

© 2015 All rights reserved. by Physexams.com

Chapter: 11th Physics : UNIT 4 : Work, Energy and Power

Solved example problems for work and work done by a force, solved example problems for work, example 4.1.

A box is pulled with a force of 25 N to produce a displacement of 15 m. If the angle between the force and displacement is 30 o , find the work done by the force.

Force, F = 25 N

Displacement, dr = 15 m

Angle between F and dr, θ = 30 o

Work done ,  W  =  Fdr cos θ

Solved Example Problems for Work done by a constant force

Example 4.2

An object of mass 2 kg falls from a height of 5 m to the ground. What is the work done by the gravitational force on the object? (Neglect air resistance; Take g = 10 m s -2 )

Work done by gravitational force is

The work done by the gravitational force on the object is positive.

Example 4.3

An object of mass  m = 1 kg is sliding from top to bottom in the frictionless inclined plane of inclination angle θ = 30 o  and the length of inclined plane is 10 m as shown in the figure. Calculate the work done by gravitational force and normal force on the object. Assume acceleration due to gravity, g = 10 m s -2

We calculated in the previous chapter that the acceleration experienced by the object in the inclined plane as g sin θ  .

According to Newton’s second law, the force acting on the mass along the inclined plane F  =  mg sin θ . Note that this force is constant throughout the motion of the mass.

The work done by the parallel component of gravitational force  (  mg sin θ )  is given by

Example 4.4

If an object of mass 2 kg is thrown up from the ground reaches a height of 5 m and falls back to the Earth (neglect the air resistance). Calculate

a) The work done by gravity when the  object reaches 5 m height

b) The work done by gravity when the   object comes back to Earth

c) Total work done by gravity both in  upward and downward motion and mention the physical significance of the result.

When the object goes up, the displacement points in the upward direction whereas the gravitational force acting on the object points in downward direction. Therefore, the angle between gravitational force and displacement of the object is 180°.

a. The work done by gravitational force in the upward motion.

Given that ∆r =5 m and F mg

b. When the object falls back, both the gravitational force and displacement of the object are in the same direction. This implies that the angle between gravitational force and displacement of the object is 0°.

c. The total work done by gravity in the entire trip (upward and downward motion)

It implies that the gravity does not transfer any energy to the object. When the object is thrown upwards, the energy is transferred to the object by the external agency, which means that the object gains some energy. As soon as it comes back and hits the Earth, the energy gained by the object is transferred to the surface of the Earth (i.e., dissipated to the Earth).

Example 4.5

A weight lifter lifts a mass of 250 kg with a force 5000 N to the height of 5 m.

a. What is the workdone by the weight lifter?

b. What is the workdone by the gravity?

c. What is the net workdone on the object?

a. When the weight lifter lifts the mass, force and displacement are in the same direction, which means that the angle between them θ = 0 0 . Therefore, the work done by the weight lifter,

b. When the weight lifter lifts the mass, the gravity acts downwards which means that the force and displacement are in opposite direction. Therefore, the angle between them θ = 180 0

c. The net workdone (or total work done) on the object

Solved Example Problems for Work done by a variable force

Example 4.6.

A variable force  F   =  k x 2  acts on a particle which is initially at rest. Calculate the work done by the force during the displacement of the particle from  x   =  0 m to  x   =  4 m. (Assume the constant  k   = 1 N m -2 )

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26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

 A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter. 

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

• Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
• Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
• Tailor your interview answer with the specific skills and qualifications outlined in the job description.
• Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills? 

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

• Critical thinking
• Analytical skills
• Decision making
• Research skills
• Technical skills
• Communication skills
• Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow. 

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve. 

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams. 

Examples of Problem-Solving in the Workplace

• Correcting a mistake at work, whether it was made by you or someone else
• Overcoming a delay at work through problem solving and communication
• Resolving an issue with a difficult or upset customer
• Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
• Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
• Troubleshooting and resolving technical issues
• Handling and resolving a conflict with a coworker
• Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
• Taking initiative when another team member overlooked or missed something important
• Taking initiative to meet with your superior to discuss a problem before it became potentially worse
• Solving a safety issue at work or reporting the issue to those who could solve it
• Using problem solving abilities to reduce/eliminate a company expense
• Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
• Changing how a process, team, or task is organized to make it more efficient
• Using creative thinking to come up with a solution that the company hasn’t used before
• Performing research to collect data and information to find a new solution to a problem
• Boosting a company or team’s performance by improving some aspect of communication among employees
• Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

• Coordinating work between team members in a class project
• Reassigning a missing team member’s work to other group members in a class project
• Adjusting your workflow on a project to accommodate a tight deadline
• Speaking to your professor to get help when you were struggling or unsure about a project
• Asking classmates, peers, or professors for help in an area of struggle
• Talking to your academic advisor to brainstorm solutions to a problem you were facing
• Researching solutions to an academic problem online, via Google or other methods
• Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. 

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description. 

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities. 

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution. 

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”  

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce. 

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence 

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

 When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

• 3 Answers to “How Do You Handle Stress?”
• How to Answer “How Do You Handle Conflict?” (Interview Question)
• Sample Answers to “Tell Me About a Time You Failed”

About the Author

Biron Clark is a former executive recruiter who has worked individually with hundreds of job seekers, reviewed thousands of resumes and LinkedIn profiles, and recruited for top venture-backed startups and Fortune 500 companies. He has been advising job seekers since 2012 to think differently in their job search and land high-paying, competitive positions. Follow on Twitter and LinkedIn .

Read more articles by Biron Clark

About the Contributor

Kyle Elliott , career coach and mental health advocate, transforms his side hustle into a notable practice, aiding Silicon Valley professionals in maximizing potential. Follow Kyle on LinkedIn .

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4.6: Problem-Solving Strategies

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Learning Objectives

By the end of this section, you will be able to:

• Understand and apply a problem-solving procedure to solve problems using Newton’s laws of motion.

Success in problem solving is obviously necessary to understand and apply physical principles, not to mention the more immediate need of passing exams. The basics of problem solving, presented earlier in this text, are followed here, but specific strategies useful in applying Newton’s laws of motion are emphasized. These techniques also reinforce concepts that are useful in many other areas of physics. Many problem-solving strategies are stated outright in the worked examples, and so the following techniques should reinforce skills you have already begun to develop.

Problem-Solving Strategy for Newton’s Laws of Motion

Step 1. As usual, it is first necessary to identify the physical principles involved. Once it is determined that Newton’s laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation . Such a sketch is shown in Figure (a). Then, as in Figure (b), use arrows to represent all forces, label them carefully, and make their lengths and directions correspond to the forces they represent (whenever sufficient information exists).

Step 2. Identify what needs to be determined and what is known or can be inferred from the problem as stated. That is, make a list of knowns and unknowns. Then carefully determine the system of interest . This decision is a crucial step, since Newton’s second law involves only external forces. Once the system of interest has been identified, it becomes possible to determine which forces are external and which are internal, a necessary step to employ Newton’s second law. (See Figure (c).) Newton’s third law may be used to identify whether forces are exerted between components of a system (internal) or between the system and something outside (external). As illustrated earlier in this chapter, the system of interest depends on what question we need to answer. This choice becomes easier with practice, eventually developing into an almost unconscious process. Skill in clearly defining systems will be beneficial in later chapters as well.

A diagram showing the system of interest and all of the external forces is called a free-body diagram . Only forces are shown on free-body diagrams, not acceleration or velocity. We have drawn several of these in worked examples. Figure (c) shows a free-body diagram for the system of interest. Note that no internal forces are shown in a free-body diagram.

Step 3. Once a free-body diagram is drawn, Newton’s second law can be applied to solve the problem . This is done in Figure (d) for a particular situation. In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples. If the problem is one-dimensional—that is, if all forces are parallel—then they add like scalars. If the problem is two-dimensional, then it must be broken down into a pair of one-dimensional problems. This is done by projecting the force vectors onto a set of axes chosen for convenience. As seen in previous examples, the choice of axes can simplify the problem. For example, when an incline is involved, a set of axes with one axis parallel to the incline and one perpendicular to it is most convenient. It is almost always convenient to make one axis parallel to the direction of motion, if this is known.

APPLYING NEWTON'S SECOND LAW

Before you write net force equations, it is critical to determine whether the system is accelerating in a particular direction. If the acceleration is zero in a particular direction, then the net force is zero in that direction. Similarly, if the acceleration is nonzero in a particular direction, then the net force is described by the equation: \(F_{net} = ma\)

For example, if the system is accelerating in the horizontal direction, but it is not accelerating in the vertical direction, then you will have the following conclusions: \[ F_{net \, x} = ma \]

\[ F_{net \, y} = 0 \]

You will need this information in order to determine unknown forces acting in a system.

Step 4. As always, check the solution to see whether it is reasonable . In some cases, this is obvious. For example, it is reasonable to find that friction causes an object to slide down an incline more slowly than when no friction exists. In practice, intuition develops gradually through problem solving, and with experience it becomes progressively easier to judge whether an answer is reasonable. Another way to check your solution is to check the units. If you are solving for force and end up with units of m/s, then you have made a mistake.

• To solve problems involving Newton’s laws of motion, follow the procedure described:
• Draw a sketch of the problem.
• Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, and the forces are represented by vectors extending in different directions from the dot. If vectors act in directions that are not horizontal or vertical, resolve the vectors into horizontal and vertical components and draw them on the free-body diagram.
• Write Newton’s second law in the horizontal and vertical directions and add the forces acting on the object. If the object does not accelerate in a particular direction (for example, the \(x\)-direction) then \(F_{net \, x} = 0 \). If the object does accelerate in that direction, \(F_{net \, x} = ma \).
• Check your answer. Is the answer reasonable? Are the units correct?

What Are Soft Skills at Work?

What are soft skills examples, why are soft skills important, what soft skills do employers look for, how to improve your soft skills, including soft skills on a resume, what careers are right for you, based on your soft skills quiz, what are soft skills definition and examples.

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Soft skills are non-technical skills that describe how you work and interact with others. Unlike hard skills , they’re not necessarily something you’ll learn in a course, like data analytics or programming skills . Instead, they’re something you often build through experience. Soft skills reflect your communication style, work ethic , and work style. 

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Soft skills are interpersonal skills that describe how you work and interact with other people. These skills apply to all kinds of jobs and careers. For example, a professor and an investment manager can both be great communicators and have exceptional leadership skills, although how those skills translate into their professions can look quite different. No matter what field you’re interested in, these skills won’t just come in handy — they’ll be integral to your success at a company.

These skills generally fall into a few different categories:

• Communication skills
• Leadership skills
• Teamwork skills
• Problem-solving skills
• Critical thinking skills
• Time management skills

Communication Skills

Communication skills describe how you interact with the people you work with — from your boss to your friendly colleague to an important client. These skills are vital in getting your ideas across in a meeting, sharing status updates on a project, or effectively negotiating with a coworker about how to move forward. Some soft communication skills include:

• Public speaking
• Negotiation
• Conflict resolution
• Verbal communication
• Friendliness
• Empathetic listening

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Leadership Skills

Leadership skills are essential in all types of roles, even if you’re not directly managing someone. Adding these skills to a resume shows your potential employer that you’re confident in taking charge and leading by example. Some soft leadership skills include:

• Decision-making
• Adaptability
• Team-building
• Reliability

Teamwork Skills

No one works in a silo, even if they’re on a team of one. Teamwork skills are critical in any job to work harmoniously with stakeholders across projects, teams, and departments. These skills aren’t just about getting along, though. It’s also essential to know when to disagree and push back to get the best result. Some soft teamwork skills include:

• Rapport-building
• Respectfulness

Problem-Solving Skills

Companies hire people to help them solve problems and find the best solutions. No matter what role you’re taking on, you’ll need to think creatively, analytically, and logically to understand why problems are happening and how to solve the issue.

Whether it’s understanding why there’s not enough traffic to a website or how to raise students’ test scores, problems in the workplace are everywhere, and companies want new hires to bring fresh and innovative ways to solve them. Problem-solving skills include:

• Communication
• Creative thinking

Critical Thinking Skills

These skills help people identify the root cause of an issue. Critical thinkers analyze, research, identify, and think outside the box to make sense of information. At work, critical thinking helps people solve problems and challenge preconceived notions to help create the best path forward. Some soft critical thinking skills include:

• Analytical skills
• Questioning

Time Management Skills

Time management skills ensure employees perform their jobs efficiently and productively. While time management is essential to any role, these skills are critical in hybrid and remote work environments. Employers want to know they can trust employees to get things done even if they’re not physically in an office with them. Some time management skills include:

• Prioritization
• Detail-oriented

“We all have soft skills because they are part of who we are,” Sabrina Cortes, resume writer, says. “Top soft skills are teamwork, attention to detail , time management, organization, verbal and written communication, leadership, emotional intelligence, adaptability/flexibility, problem-solving/conflict resolution, and interpersonal skills. … Unfortunately, all too often, these personality traits are overlooked [by applicants]. But they play a role in each job out there.”

Of course, some skills are more applicable to specific jobs than others. Here are some examples of how soft skills can be applied to specific industries:

Soft skills are important because they make you a successful employee and a helpful team member — and they’re a crucial part of helping you land a job. 

“Employers want to see how well [potential employees] work with people and can think beyond their learning,” Joanne Rosen, Chief Operations Officer at Write Choice Resumes, explains.

Employers look for soft skills because these skills are helpful indicators of how successful a new hire will be. According to a Leadership IQ study, 89% of new hire failures were a result of poor soft skills, not a lack of technical failures. New hires were more likely to fail because they lacked soft skills like coachability, emotional intelligence, and motivation. Only 11% of new hire failures were a result of technical incompetence. 

This trend especially rings true for entry-level hires. Because entry-level applicants don’t have advanced technical skills yet, having good soft skills can set you apart from the competition.

>>MORE: Learn what careers are right for you based on your skillset with our career aptitude test .

Not all soft skills are created equal in employers’ eyes. According to a 2023 survey conducted by the National Association of Colleges and Employers (NACE), the top skills employers look for are problem-solving skills and the ability to work in a team.  

“In my experience, it’s valuable [for students] to convey these three key soft skills: time management, communications, and customer service,” 5X Certified Resume Writer Virginia Franco says. “They are most relevant to entry-level success across diverse industries and job functions.”

Now you know — soft skills are a major way to stand out in the job search when you’re just starting out. But how do you start to improve yours?

Go Out of Your Way to Work With Others

If you’re like me, group projects are the bane of your academic career. Yet they’re a valuable way to build soft skills and experience that you can talk about in interviews. Proactively seek out group settings when working on projects, whether you’re in the classroom or for an extracurricular. Even if the project takes a little longer than it would have on your own, you’ll practice skills like problem-solving, collaboration, communication, and feedback. If you’re lucky, you’ll even build conflict resolution skills !

Practice Responsive Soft Skills

Soft skills aren’t just what you bring to the working world, but how you respond to it. Start with how you communicate with others. It’s not just about what you’re saying to another person, but how you listen and process what they’re saying back to you. 

Instead of just hearing the words someone is saying, make a conscious effort to truly understand their perspective, emotions, and underlying needs. Give them your full attention, maintain eye contact, and provide verbal and non-verbal cues to show that you are engaged in the conversation. By actively listening , you can develop a deeper understanding of others, build trust, and respond in a more thoughtful and empathetic manner.

Self-Reflect

Finally, the best way to work on your soft skills is to reflect on your progress. Soft skills can be a lot harder to measure than hard skills because they’re often unquantifiable. Instead, you can track your progress by thinking of examples of when you have (or haven’t!) used your soft skills when working on a school project, or in an internship , volunteer opportunity, part-time job, extracurricular, or any other experience you might talk about in an interview. Where are your gaps? Could you have been a more effective communicator? Were you a great negotiator? What can you do differently next time?

Because employers are looking for soft skills in the entry-level hiring process, it’s crucial for you not only to include them, but to know the right ones to include.

What Soft Skills Should I Include on My Resume?

One of the best ways to know what skills to include on your resume is to look at the job description. Just as you’d include hard skills based on a job description’s requirements, reading what a company is looking for can help determine what soft skills to include. 

>>Forage find: Unlike hard skills, the exact soft skills an employer is looking for might not be as spelled out. Look for clues on what kinds of workers they’re looking for — Team players? Independent? Self-motivated? — to understand what skills to include.

Is the company looking for someone who can handle communicating big ideas with customers and clients? Demonstrate those communication skills. Does it want someone strategic who can tackle big issues? Show that you’re an excellent problem-solver.

How to Include Soft Skills on a Resume

Resume experts agree that you don’t necessarily need a dedicated skills section to flaunt your soft skills on a resume.

“Soft skills need to be demonstrated, not listed,” Rosen says. “Example: Rescued at-risk account by communicating with the client about needs and creating innovative customer-facing solutions.”

By using the phrases “communicating” and” “creating innovative, customer-facing solutions,” the candidate shows off their communication skills and problem-solving skills.

>>MORE: How to Write a Resume

You can also use a professional summary to flex these skills.

“I like to mix soft skills with hard skills,” Wendi Weiner , attorney and resume expert, says. “You can include a sentence in your professional summary that speaks to some of your soft skills. Example: ‘Record of leading projects from concept to completion through strong problem solving, team building, and solid time management.’ The hard skill in this sentence is project management, and it’s leveraged by the soft skills of problem-solving, team building, and time management.”

If you do include a skills section on your resume, you can use the same section to list both hard and soft skills . It’s a great way to save on space while sharing a well-rounded picture of your abilities.

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Causes and Effects of Climate Change

Fossil fuels – coal, oil and gas – are by far the largest contributor to global climate change, accounting for over 75 per cent of global greenhouse gas emissions and nearly 90 per cent of all carbon dioxide emissions.

As greenhouse gas emissions blanket the Earth, they trap the sun’s heat. This leads to global warming and climate change. The world is now warming faster than at any point in recorded history. Warmer temperatures over time are changing weather patterns and disrupting the usual balance of nature. This poses many risks to human beings and all other forms of life on Earth.

Causes of Climate Change

Generating power

Generating electricity and heat by burning fossil fuels causes a large chunk of global emissions. Most electricity is still generated by burning coal, oil, or gas, which produces carbon dioxide and nitrous oxide – powerful greenhouse gases that blanket the Earth and trap the sun’s heat. Globally, a bit more than a quarter of electricity comes from wind, solar and other renewable sources which, as opposed to fossil fuels, emit little to no greenhouse gases or pollutants into the air.

Manufacturing goods

Manufacturing and industry produce emissions, mostly from burning fossil fuels to produce energy for making things like cement, iron, steel, electronics, plastics, clothes, and other goods. Mining and other industrial processes also release gases, as does the construction industry. Machines used in the manufacturing process often run on coal, oil, or gas; and some materials, like plastics, are made from chemicals sourced from fossil fuels. The manufacturing industry is one of the largest contributors to greenhouse gas emissions worldwide.

Cutting down forests

Cutting down forests to create farms or pastures, or for other reasons, causes emissions, since trees, when they are cut, release the carbon they have been storing. Each year approximately 12 million hectares of forest are destroyed. Since forests absorb carbon dioxide, destroying them also limits nature’s ability to keep emissions out of the atmosphere. Deforestation, together with agriculture and other land use changes, is responsible for roughly a quarter of global greenhouse gas emissions.

Using transportation

Most cars, trucks, ships, and planes run on fossil fuels. That makes transportation a major contributor of greenhouse gases, especially carbon-dioxide emissions. Road vehicles account for the largest part, due to the combustion of petroleum-based products, like gasoline, in internal combustion engines. But emissions from ships and planes continue to grow. Transport accounts for nearly one quarter of global energy-related carbon-dioxide emissions. And trends point to a significant increase in energy use for transport over the coming years.

Producing food

Producing food causes emissions of carbon dioxide, methane, and other greenhouse gases in various ways, including through deforestation and clearing of land for agriculture and grazing, digestion by cows and sheep, the production and use of fertilizers and manure for growing crops, and the use of energy to run farm equipment or fishing boats, usually with fossil fuels. All this makes food production a major contributor to climate change. And greenhouse gas emissions also come from packaging and distributing food.

Powering buildings

Globally, residential and commercial buildings consume over half of all electricity. As they continue to draw on coal, oil, and natural gas for heating and cooling, they emit significant quantities of greenhouse gas emissions. Growing energy demand for heating and cooling, with rising air-conditioner ownership, as well as increased electricity consumption for lighting, appliances, and connected devices, has contributed to a rise in energy-related carbon-dioxide emissions from buildings in recent years.

Consuming too much

Your home and use of power, how you move around, what you eat and how much you throw away all contribute to greenhouse gas emissions. So does the consumption of goods such as clothing, electronics, and plastics. A large chunk of global greenhouse gas emissions are linked to private households. Our lifestyles have a profound impact on our planet. The wealthiest bear the greatest responsibility: the richest 1 per cent of the global population combined account for more greenhouse gas emissions than the poorest 50 per cent.

Based on various UN sources

Effects of Climate Change

Hotter temperatures

As greenhouse gas concentrations rise, so does the global surface temperature. The last decade, 2011-2020, is the warmest on record. Since the 1980s, each decade has been warmer than the previous one. Nearly all land areas are seeing more hot days and heat waves. Higher temperatures increase heat-related illnesses and make working outdoors more difficult. Wildfires start more easily and spread more rapidly when conditions are hotter. Temperatures in the Arctic have warmed at least twice as fast as the global average.

More severe storms

Destructive storms have become more intense and more frequent in many regions. As temperatures rise, more moisture evaporates, which exacerbates extreme rainfall and flooding, causing more destructive storms. The frequency and extent of tropical storms is also affected by the warming ocean. Cyclones, hurricanes, and typhoons feed on warm waters at the ocean surface. Such storms often destroy homes and communities, causing deaths and huge economic losses.

Increased drought

Climate change is changing water availability, making it scarcer in more regions. Global warming exacerbates water shortages in already water-stressed regions and is leading to an increased risk of agricultural droughts affecting crops, and ecological droughts increasing the vulnerability of ecosystems. Droughts can also stir destructive sand and dust storms that can move billions of tons of sand across continents. Deserts are expanding, reducing land for growing food. Many people now face the threat of not having enough water on a regular basis.

A warming, rising ocean

The ocean soaks up most of the heat from global warming. The rate at which the ocean is warming strongly increased over the past two decades, across all depths of the ocean. As the ocean warms, its volume increases since water expands as it gets warmer. Melting ice sheets also cause sea levels to rise, threatening coastal and island communities. In addition, the ocean absorbs carbon dioxide, keeping it from the atmosphere. But more carbon dioxide makes the ocean more acidic, which endangers marine life and coral reefs.

Loss of species

Climate change poses risks to the survival of species on land and in the ocean. These risks increase as temperatures climb. Exacerbated by climate change, the world is losing species at a rate 1,000 times greater than at any other time in recorded human history. One million species are at risk of becoming extinct within the next few decades. Forest fires, extreme weather, and invasive pests and diseases are among many threats related to climate change. Some species will be able to relocate and survive, but others will not.

Not enough food

Changes in the climate and increases in extreme weather events are among the reasons behind a global rise in hunger and poor nutrition. Fisheries, crops, and livestock may be destroyed or become less productive. With the ocean becoming more acidic, marine resources that feed billions of people are at risk. Changes in snow and ice cover in many Arctic regions have disrupted food supplies from herding, hunting, and fishing. Heat stress can diminish water and grasslands for grazing, causing declining crop yields and affecting livestock.

More health risks

Climate change is the single biggest health threat facing humanity. Climate impacts are already harming health, through air pollution, disease, extreme weather events, forced displacement, pressures on mental health, and increased hunger and poor nutrition in places where people cannot grow or find sufficient food. Every year, environmental factors take the lives of around 13 million people. Changing weather patterns are expanding diseases, and extreme weather events increase deaths and make it difficult for health care systems to keep up.

Poverty and displacement

Climate change increases the factors that put and keep people in poverty. Floods may sweep away urban slums, destroying homes and livelihoods. Heat can make it difficult to work in outdoor jobs. Water scarcity may affect crops. Over the past decade (2010–2019), weather-related events displaced an estimated 23.1 million people on average each year, leaving many more vulnerable to poverty. Most refugees come from countries that are most vulnerable and least ready to adapt to the impacts of climate change.

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