Find the potential, kinetic, and mechanical energy

In summary, the conversation discusses a problem involving a 1.40 kg block sliding on a frictionless surface until encountering a spring with a force constant of 637 N/m. The block compresses the spring by 4.15 cm and comes to rest. The conversation then delves into finding the spring potential energy, kinetic energy, and total mechanical energy for various compressions, with a focus on part B where the incorrect use of units is corrected. It is explained that as the spring is compressed, some of the block's kinetic energy transforms into potential energy of the spring, resulting in a decrease in the total energy of the system. The concept of conservation of energy is also discussed.
  • #1
Angela_vaal
59
1

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?
 
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  • #2
Angela_vaal said:
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.)
 
  • #3
Angela_vaal said:
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.
 
  • #4
TSny said:
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.
 
  • #5
Angela_vaal said:
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.
 
  • #6
TSny said:
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!
 
  • #7
TSny said:
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?
 
  • #8
Angela_vaal said:
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?
 
  • #9
Doc Al said:
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.)

Can you please explain further...
 
  • #10
TSny said:
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.
 
  • #11
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.
 
  • #12
Angela_vaal said:
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).

Angela_vaal said:
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.)
 
  • #13
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
 
  • #14
Angela_vaal said:
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?
 
  • #15
TSny said:
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 :(
 
  • #16
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)?
 
  • #17
TSny said:
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.
 
  • #18
Angela_vaal said:
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.
 
  • #19
I would use total energy=PE+KE ?
 
  • #20
Angela_vaal said:
I would use total energy=PE+KE ?
Yes.
 
  • #21
how do I know the value of the total energy?
 
  • #22
Angela_vaal said:
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?)
 
  • #23
I figured it out. Thanks for all your help!
 

1. What is the difference between potential, kinetic, and mechanical energy?

Potential energy is the energy an object possesses due to its position or configuration. Kinetic energy is the energy an object possesses due to its motion. Mechanical energy is the sum of potential and kinetic energy in a system.

2. How do you calculate potential energy?

Potential energy can be calculated by multiplying the mass of an object by the acceleration due to gravity (9.8 m/s^2) and the height of the object above the ground (PE = mgh).

3. What is the formula for kinetic energy?

Kinetic energy can be calculated by multiplying the mass of an object by its velocity squared and dividing by 2 (KE = 1/2 mv^2).

4. What is an example of mechanical energy?

An example of mechanical energy is a roller coaster at the top of a hill. At this point, it has a high amount of potential energy. As it goes down the hill, it converts this potential energy into kinetic energy, resulting in mechanical energy.

5. How does energy conservation apply to potential, kinetic, and mechanical energy?

According to the law of conservation of energy, energy cannot be created or destroyed, only transferred or converted. This applies to potential, kinetic, and mechanical energy as they can be converted into each other but the total amount of energy remains constant.

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