Work of a child going down a slide

[delecticious]

Homework Statement

A 28.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 24.00 m. When she is partway down the slide, at a height h2 of 15.00 m, she is moving at a speed of 8.00 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.).

Homework Equations

non conservative work = (final KE + final PE) - (initial KE + initial PE)

The Attempt at a Solution

initial KE cancels since the child starts from rest so it'll be the sum of the final kinetic energy and potential energy minus the initial potential energy. I worked that out and got -1573.6 J but when I go to check the answer it's wrong and I keep reworking and getting the same answer, but for some reason it's wrong. Anyone know what I'm doing wrong?

 

[Chi Meson]

non conservative work = (final KE + final PE) - (initial KE + initial PE)

I never liked that "non-conservative work" forumula. It makes it harder to understand than it is.

The Attempt at a Solution

initial KE cancels since the child starts from rest so it'll be the sum of the final kinetic energy and potential energy minus the initial potential energy. I worked that out and got -1573.6 J but when I go to check the answer it's wrong and I keep reworking and getting the same answer, but for some reason it's wrong. Anyone know what I'm doing wrong?

HOw about this:

How much mechanical energy did the girl start with (KE + PE at the top)?

How much mechanical energy does the girl have part way down (KE + PE in the middle)?

How much mechanical energy went missing?

I get the same answer as you, by the way, but when you view it as I described, you can see that you are correct. If you are submitting homework online, then it's probably rejecting your sig figs (1574 J or 1570 J depending on how much of a sig fig stickler the prof is) or maybe it doesn't want the negative sign. Who knows? I can't stand online homework either.

 

[m2003]

I would like to first commend you for attempting to solve this problem and for seeking help when you encountered difficulties. It shows a great dedication to learning and understanding the concepts involved.

In order to solve this problem, we need to consider the conservation of energy principle. The total mechanical energy of the system (consisting of the child and the slide) remains constant throughout the motion, assuming no external forces act on the system.

At the top of the slide, the child has only potential energy (PE = mgh1), and no kinetic energy (KE = 0). At the point where the child is moving at a speed of 8.00 m/s, she has both kinetic energy (KE = (1/2)mv^2) and potential energy (PE = mgh2). Therefore, the total mechanical energy at this point is:

E = KE + PE = (1/2)mv^2 + mgh2

Now, since there is no external work being done on the system, the total mechanical energy at the top (E = mgh1) must be equal to the total mechanical energy at the point where the child is moving (E = (1/2)mv^2 + mgh2). Therefore, we can write the following equation:

mgh1 = (1/2)mv^2 + mgh2

Solving for the height h2, we get:

h2 = (h1 - (1/2)v^2)/g

Plugging in the given values, we get:

h2 = (24.00 m - (1/2)(8.00 m/s)^2)/9.8 m/s^2 = 15.49 m

Now, to calculate the mechanical energy lost due to friction, we need to find the difference between the initial and final mechanical energies. Therefore, the mechanical energy lost is:

E_lost = mgh1 - (1/2)mv^2 - mgh2 = (28.0 kg)(9.8 m/s^2)(24.00 m) - (1/2)(28.0 kg)(8.00 m/s)^2 - (28.0 kg)(9.8 m/s^2)(15.49 m) = -1612.4 J

Note that the negative sign indicates that the energy was lost, as expected. Therefore, the mechanical energy lost due to friction in this