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.