Calculate the change in mechanical energy during collision

[berrytea]

Homework Statement

A 15 kg block is attached to a very light horizontal spring of force constant 5000.0 N/m and is resting on a frictionless table. It is struck by a 3.00 kg stone at 8.00 m/s to the right, then rebounds at 2.00 m/s to the left.

Homework Equations

ΔE = ΔK + ΔU

The Attempt at a Solution

I have been stuck on this part of this problem for a while now, and I'm not sure which formula to use, or if I am plugging in the wrong numbers.

 

[kuruman]

Hi berrytea and welcome to PF>

It would help if you showed us what exactly you did under "The attempt at a solution". It would also be more useful if you formulated a strategy instead of looking for a formula. How do you think yo should proceed to find the change in mechanical energy? You have a "Relevant equation". That's a good beginning. What must you do to implement it?

 

[berrytea]

Hi berrytea and welcome to PF>

It would help if you showed us what exactly you did under "The attempt at a solution". It would also be more useful if you formulated a strategy instead of looking for a formula. How do you think yo should proceed to find the change in mechanical energy? You have a "Relevant equation". That's a good beginning. What must you do to implement it?

Hello, and thanks!

My attempt was to find the change in kinetic and potential energies and add them. What is confusing to me, is a friend of mine got -52 J for this solution. I calculated ΔPE = -30.25 J and I got simply ΔE = 30 J, which gives me -0.25 as ΔKE. So I am not sure what I'm doing wrong or which answer is correct.

 

[kuruman]

Hello, and thanks!

My attempt was to find the change in kinetic and potential energies and add them. What is confusing to me, is a friend of mine got -52 J for this solution. I calculated ΔPE = -30.25 J and I got simply ΔE = 30 J, which gives me -0.25 as ΔKE. So I am not sure what I'm doing wrong or which answer is correct.

Never mind your friend. We are interested in what you did and what it means. First of all what is the system for which you want to calculate the change in mechanical energy? Is it just the block or the block and ball together?

 

[berrytea]

Never mind your friend. We are interested in what you did and what it means. First of all what is the system for which you want to calculate the change in mechanical energy? Is it just the block or the block and ball together?

I am unsure, but I assume it is the block and the ball together as the question does not specify.

 

[haruspex]

It is struck by a 3.00 kg stone at 8.00 m/s to the right, then rebounds at 2.00 m/s to the left.

Do you mean the stone comes from the right or moves to the right?
What rebounds at 2m/s? Do you mean the block moves off left at 2m/s, or the stone rebounds from the collision at 2m/s?

Where does the spring come into this? Is the rebound immediate or after some spring compression and expansion? Or are there more parts to the question?

 

[haruspex]

I assume it is the block and the ball together

Ball? Stone?

 

[kuruman]

I am unsure, but I assume it is the block and the ball together as the question does not specify.

I would say it is the block and ball stone together. First things first. What do you think ΔU is in this case?

 

[berrytea]

Do you mean the stone comes from the right or moves to the right?
What rebounds at 2m/s? Do you mean the block moves off left at 2m/s, or the stone rebounds from the collision at 2m/s?

Where does the spring come into this? Is the rebound immediate or after some spring compression and expansion? Or are there more parts to the question?

The stone is traveling to the right and it (the stone) rebounds at 2.00 m/s to the left.

There are other parts to the question that I have answered which are:
the maximum compression of the spring = 0.11m
the speed of the block after the collision being 2 m/s
the work done by the spring during compression is = -30.25 J
.

 

[berrytea]

I would say it is the block and ball stone together. First things first. What do you think ΔU is in this case?

I think ΔU = 30.35 J

 

[kuruman]

I think ΔU = 30.35 J

Can you explain what are the two points between which you are asked to calculate the change in mechanical energy? Is it from the start of the collision to when the spring is fully compressed?

 

[berrytea]

This is what I have gotten so far:
ΔE = ΔK + ΔU
I previously calculated the ΔU to be 30.25 J
ΔK = K_i- K_f
= 1/2m₁v₁²- 1/2m₁v₁²+1/2m₂v₂²
= 1/2(15.0)(8.00)^2 - 1/2(15)(8.00)^2+1/2(15.0)(2)^2 = 480 - 510 = -30
ΔE = ΔK + ΔU
ΔE = -30 + 30.25 = 0.25 ??

I am super confused at this point and don't know how to continue.
What am I doing wrong?

 

[berrytea]

Can you explain what are the two points between which you are asked to calculate the change in mechanical energy? Is it from the start of the collision to when the spring is fully compressed?

Yes, it is during the collision, so from the start to the end when the spring is fully compressed.

 

[kuruman]

This is what I have gotten so far:
ΔE = ΔK + ΔU
I previously calculated the ΔU to be 30.25 J
ΔK = K_i- K_f
= 1/2m₁v₁²- 1/2m₁v₁²+1/2m₂v₂²
= 1/2(15.0)(8.00)^2 - 1/2(15)(8.00)^2+1/2(15.0)(2)^2 = 480 - 510 = -30
ΔE = ΔK + ΔU
ΔE = -30 + 30.25 = 0.25 ??

I am super confused at this point and don't know how to continue.
What am I doing wrong?

At maximum compression the blocks are moving together with speed V which you have not found yet. Then ΔK=½(m₁+m₂)V²-½m₁v₁² where v₁ = initial speed of the stone.

 

[berrytea]

At maximum compression the blocks are moving together with speed V which you have not found yet. Then ΔK=½(m₁+m₂)V²-½m₁v₁² where v₁ = initial speed of the stone.

Blocks? There is only one block and one stone though. So, in your equation what would m₂ be?

 

[haruspex]

At maximum compression the blocks are moving together

It is still not crystal clear, but as I read post #9 the stone rebounds at 2m/s immediately after the collision. The bodies do not coalesce.

 

[kuruman]

Blocks? There is only one block and one stone though. So, in your equation what would m₂ be?

Sorry, it was way past my bedtime when I posted this. I meant block m₂ and stone m₁.

It is still not crystal clear, but as I read post #9 the stone rebounds at 2m/s immediately after the collision. The bodies do not coalesce.

Yes, the stone rebounds at 2 m/s after the collision is complete. It is not crystal clear what the starting and ending points of the change in ME are. My initial interpretation was from the onset of the collision to after its completion. In post #9 OP revealed that there is more to the problem statement than initially posted. Then in #13 OP confirmed that the change in ME is from the onset to maximum compression. Perhaps if OP posted the entire problem statement as was given, it might become crystal clear what we are looking for.