# Solve Work-Energy Theorem Problems with Expert Help

In summary: How can you use that information to find the maximum speed of the child?In summary, the conversation discusses a problem involving the Work-Energy theorem, specifically the concepts of Kinetic Energy, Potential Energy, and Work. The first question involves finding the maximum speed of a child on a swing based on the height above the ground, and the answer is approximately 5.4 m/s. The second question involves finding the average force exerted by an ax when it penetrates a log, and the answer is 180 kN. The conversation ends with a request for help in understanding the solutions to these problems.
I am currently working on a problem that I do not know how to solve. It is on the Work-Energy theorem. I would really appreciate it if you could help. :D

Kinetic Energy = 1/2 mv^2
Potential Energy = mgh
Work = Fd
KE(initial) + PE(initial) = KE(final) + PE(final)

The height above the ground of a child on a swing varies from 50 cm at the lowest point to 200 cm at the highest point. The maximum speed of the child is?

D. dependent on the child's mass

The answer for this question is A, and I do not understand how they got it.

I also have one more question.

The 2.0-kg head of an ax is moving at 60 m/s when it strikes the log. If the blade of the ax penetrates 20 mm into the log, the average force it exerts is

A. 3 kN
B. 90 kN
C. 72 kN
D. 180 kN

I have no idea where to start for these problems. Help would really be appreciated!

For the first question:

KE(initial) + PE(initial) = KE(final) + PE(final)

You have the correct equation. You only have to evaluate it. Don't forget about gravity.

Hint for axe problem:

What energy does the axe use to cleave into the log? Does it do work on the log?

Hint for first question: Think of when the child is at his/her lowest point as 0 cm instead of 50 cm. What does that make his/her highest point equal to?

I would be happy to assist you with these problems. The first step in solving these problems is to understand the concepts of work, energy, and the work-energy theorem. Work is the force applied over a distance, and it can be calculated by multiplying the force by the distance traveled. Energy is the ability to do work, and it can be divided into two forms - kinetic energy, which is the energy of motion, and potential energy, which is the energy stored in an object due to its position or state. The work-energy theorem states that the total work done on an object is equal to the change in its kinetic and potential energy.

Now, let's apply these concepts to the first problem about the child on a swing. We know that at the lowest point, the child's potential energy is equal to mgh = 0.5 * m * 9.8 * 0.5 = 2.45 mJ. At the highest point, the potential energy is mgh = 0.5 * m * 9.8 * 2 = 9.8 mJ. We also know that at the highest point, all of the child's potential energy is converted into kinetic energy, which is calculated by KE = 0.5 * m * v^2. Therefore, we can set up the equation 2.45 mJ + 0.5 * m * v^2 = 9.8 mJ and solve for v to get the maximum speed of the child, which is approximately 5.4 m/s.

For the second problem, we can use the work-energy theorem again. The initial kinetic energy of the ax head is 0.5 * 2.0 kg * (60 m/s)^2 = 3.6 kJ. When it strikes the log, the kinetic energy is converted into work done on the log, which is equal to the force applied (unknown) multiplied by the distance traveled (0.02 m). Therefore, we can set up the equation 3.6 kJ = F * 0.02 m and solve for F to get approximately 180 kN.

I hope this explanation helps you understand how to approach and solve work-energy theorem problems. If you have any further questions, please do not hesitate to ask. Good luck with your studies!

## 1. What is the work-energy theorem?

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. In simpler terms, it explains the relationship between the work done on an object and its resulting change in motion.

## 2. How do I solve work-energy theorem problems?

To solve work-energy theorem problems, you will need to identify the initial and final velocities of the object, as well as the external forces acting on it. Then, you can use the formula W = ΔKE = ½m(vf² - vi²) to calculate the net work done on the object.

## 3. What is expert help and how can it assist with solving work-energy theorem problems?

Expert help refers to the assistance and guidance provided by professionals or experienced individuals in a particular field. In the case of work-energy theorem problems, expert help can provide you with a thorough understanding of the concept and offer step-by-step guidance on how to solve specific problems.

## 4. Can expert help improve my understanding of the work-energy theorem?

Yes, expert help can greatly improve your understanding of the work-energy theorem. By working with someone who is knowledgeable and experienced in the subject, you can gain a deeper understanding of the concept and learn how to apply it to different scenarios and problem-solving methods.

## 5. Where can I find expert help for solving work-energy theorem problems?

You can find expert help for solving work-energy theorem problems through various sources such as tutoring services, online forums, or by working with a physics teacher or professor. You can also seek help from a physics textbook or online resources that provide step-by-step solutions to work-energy theorem problems.

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