Finding change in thermal energy Work and Energy problem

[Ly444999]

Homework Statement

A 26.2 kg child rides a 1.00 kg potato sack down a 2.05 m high slide. If the child starts from rest and has a speed of 1.60 m/s at the bottom of the slide, what is the change in thermal energy of the child on their potato sack and the slide?

Homework Equations

KE = (1/2)mv²
PE = mgh

The Attempt at a Solution

PE = KE + E_th
mgh = (1/2)mv²+E_th
(27.2 kg)*(9.8 m/s²)*(2.05 m) = (1/2)*(27.2 kg)*(1.60 m/s)+E_th
E_th= 511.632 J

Was I supposed to add the mass of the child and potato sack together? Also was my answer, 511.632 J, correct or is there more I have to do to find the change in thermal energy? or is this whole approach wrong?

 

[Simon Bridge]

Was I supposed to add the mass of the child and potato sack together?

Reason it out... what is the reasoning you used for not doing it this way?
Were you, for eg, asked for the change in thermal energy on the potato sack and the child together or for the child alone?
How would the thermal energy likely be divided between the child and the sack anyway? (What is the mechanism that turns grav PE into thermal energy?)

Also was my answer, 511.632 J, correct or is there more I have to do to find the change in thermal energy? or is this whole approach wrong?

You are doing fine in your approach - just take care to identify the processes involved.
You correctly identify the source of the energy as gravitational PE that decreases ... this has to go to kinetic energy, and also to other stuff ... heat, sound, squashing potatoes, fraying the sack etc. By writing PE = KE + E(therm) you are saying you think all the PE that does not end up as motion goes to thermal stuff.
That seems fair in context.

As t if your answer is correct: depends what you mean by "correct". It looks consistent with your reasoning, the algebra and arithmetic seem to check out. Does that mean it is correct?
Maybe take another look at your reasoning. If you started from a false assumption, your result may not mean what you think it does.
A good test is to write out the answer in a sentence that rewords the question in the problem statement.

In this case the question is:

...what is the change in thermal energy of the child on their potato sack and the slide?

You want to be able to write:
"The change in thermal energy of the child on their potato sack and the slide is 511.632J."
... now: is that sentence true?

Aside: how many sig fig / dp should you keep in your numerical answer?

 

[Ly444999]

Reason it out... what is the reasoning you used for not doing it this way?
Were you, for eg, asked for the change in thermal energy on the potato sack and the child together or for the child alone?
How would the thermal energy likely be divided between the child and the sack anyway? (What is the mechanism that turns grav PE into thermal energy?)

You are doing fine in your approach - just take care to identify the processes involved.
You correctly identify the source of the energy as gravitational PE that decreases ... this has to go to kinetic energy, and also to other stuff ... heat, sound, squashing potatoes, fraying the sack etc. By writing PE = KE + E(therm) you are saying you think all the PE that does not end up as motion goes to thermal stuff.
That seems fair in context.

As t if your answer is correct: depends what you mean by "correct". It looks consistent with your reasoning, the algebra and arithmetic seem to check out. Does that mean it is correct?
Maybe take another look at your reasoning. If you started from a false assumption, your result may not mean what you think it does.
A good test is to write out the answer in a sentence that rewords the question in the problem statement.

In this case the question is:You want to be able to write:
"The change in thermal energy of the child on their potato sack and the slide is 511.632J."
... now: is that sentence true?

Aside: how many sig fig / dp should you keep in your numerical answer?

I just wanted a second opinion on whether or not my thinking was correct, since I was not sure if my reasoning and calculations was wrong in any way. Also 3 sig figs should be kept so the answer is really 512 J. Thank you very much though.

 

[Simon Bridge]

I'm not sure the question you answered is the one you were asked. Check.
Does it make a difference if you add the masses?

Note: what I am trying to do is show you how to work out if your thinking is correct, for yourself.
You are training to be able to solve problems nobody knows how to do - who will you ask then, and how will you know their thinking is correct?

 

[Ly444999]

I'm not sure the question you answered is the one you were asked. Check.
Does it make a difference if you add the masses?

Note: what I am trying to do is show you how to work out if your thinking is correct, for yourself.
You are training to be able to solve problems nobody knows how to do - who will you ask then, and how will you know their thinking is correct?

I already added the masses in the calculations in my post but calculating the thermal energy with just the mass of the child I end up with 492 J.

 

[Simon Bridge]

Which answers the question better?

 

[Ly444999]

Which answers the question better?

I'm fairly certain the 512 J considering the question asked about the child in the potato sack and this is calculated by using the mass of the child and the potato sack.