# Find the potential, kinetic, and mechanical energy

## Homework Statement

A 1.40 kg block slides with a speed of 0.885 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 637 N/m . The block comes to rest after compressing the spring 4.15 cm.

Part A
Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 0 cm.
Part B
Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 1.00 cm.
Part C
Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 2.00 cm.
Part D
Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 3.00 cm.
Part E
Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 4.00 cm.

## Homework Equations

Potential energy= 1/2Kx2
Kinetic energy=1/2mv2
Mechanical energy=KE+PE

## The Attempt at a Solution

I got the first answer correct using these equations. However, when I use these equations for part B I get them wrong. For example, this is what I did.
part B) PE=(.5)(.01m)(.0415m)2 =8.6x10-6J
KE= (.5)(1.40kg)(.885m/s)2 = .548 J
ME= .548J+8.6x10-6 = .548 J
I don't know what I am doing wrong if someone can please explain I would appreciate it! Also, I have seen in other examples that the KE is supposed to change with each compression. How? if the mass and the velocity remain the same?

Doc Al
Mentor
How? if the mass and the velocity remain the same?
The velocity does not remain the same!

As the spring is compressed, some of the block's KE transforms into the spring's PE. (Plug in the given compression for B, not .0415m.)

TSny
Homework Helper
Gold Member
I got the first answer correct using these equations. However, when I use these equations for part B I get them wrong. For example, this is what I did.
part B) PE=(.5)(.01m)(.0415m)2
Why the factor of .01 m here. If you combine the units on the on the right-hand side, do you get the correct units for energy?

As Doc Al points out, you have not use the correct amount of compression for the spring here.

Why the factor of .01 m here. If you combine the units on the on the right-hand side, do you get the correct units for energy?
I thought it had to be in meters not cm.

TSny
Homework Helper
Gold Member
I thought it had to be in meters not cm.
You know the formula for potential energy of a spring is (1/2)kx2. It looks like you used .01 m for k.

You know the formula for potential energy of a spring is (1/2)kx2. It looks like you used .01 m for k.

I'm just confused about it all! It looks like I am pluggining in the wrong numbers!

Why the factor of .01 m here. If you combine the units on the on the right-hand side, do you get the correct units for energy?

As Doc Al points out, you have not use the correct amount of compression for the spring here.
isn't that the compression of 1cm?

TSny
Homework Helper
Gold Member
I'm just confused about it all! It looks like I am pluggining in the wrong numbers!
Yes. What does k stand for? What is the value of k as given in the problem?
What does x stand for? What is the value of x for part B?

The velocity does not remain the same!

As the spring is compressed, some of the block's KE transforms into the spring's PE. (Plug in the given compression for B, not .0415m.)

Yes. What does k stand for? What is the value of k as given in the problem?
What does x stand for? What is the value of x for part B?

I thought x represented distance, so I assumed it was the 4.15 cm in the beginning of the problem. I thought K was the value that was given for the compression.

TSny
Homework Helper
Gold Member
You need to review the formula for PE of a spring in your class notes or your textbook. The meaning of the symbols should be explained there.

Doc Al
Mentor
I thought x represented distance, so I assumed it was the 4.15 cm in the beginning of the problem.
That 4.15 cm is the compression when the block comes to rest (momentarily).

I thought K was the value that was given for the compression.
K stands for the spring constant. (What is called "force constant" in the problem statement.)

I just reviewed it in my textbook and I was so wrong with the units.
Going back to part B I got,

PE: (.5)(637N/m)(.01m)2=.03185J

I still don't understand how the velocity changes with each compression. would I solve for a new velocity and use the ΔKE to find the new velocity?

ΔKE= 1/2mvf2-1/2mvi2

TSny
Homework Helper
Gold Member
I just reviewed it in my textbook and I was so wrong with the units.
Going back to part B I got,

PE: (.5)(637N/m)(.01m)2=.03185J
That looks good!

Think about the total energy E of the system when the spring is compressed .01 m. How does that total energy compare to the initial total energy E in part A?

That looks good!

Think about the total energy E of the system when the spring is compressed .01 m. How does that total energy compare to the initial total energy E in part A?

I'm not sure :(

TSny
Homework Helper
Gold Member
As the block compresses the spring, what happens to the PE of the spring? Does it increase, decrease, or remain constant?
As the block compresses the spring, what happens to the KE of the block? Does it increase, decrease or remain constant?
What happens to the total energy, E? Does it increase, decrease, or remain constant (conserved)?

As the block compresses the spring, what happens to the PE of the spring? Does it increase, decrease, or remain constant?
As the block compresses the spring, what happens to the KE of the block? Does it increase, decrease or remain constant?
What happens to the total energy, E? Does it increase, decrease, or remain constant (conserved)?

wouldn't the potential energy increase and kinetic energy decrease? the total energy should remain conserved.

TSny
Homework Helper
Gold Member
wouldn't the potential energy increase and kinetic energy decrease? the total energy should remain conserved.
Yes. Use the fact that the total energy is conserved to help find the KE for part B.

I would use total energy=PE+KE ?

TSny
Homework Helper
Gold Member
I would use total energy=PE+KE ?
Yes.

how do I know the value of the total energy?

Doc Al
Mentor
how do I know the value of the total energy?
Use the information given in the problem statement to calculate it. (What's the energy before it hits the spring?)

I figured it out. Thanks for all your help!!