How Do You Calculate Mechanical Energy Lost Due to Friction on a Slide?

[bbreezy]

Homework Statement

A 27.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 17.00 m. When she is partway down the slide, at a height h2 of 7.00 m, she is moving at a speed of 7.50 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.).

Homework Equations

I used mg(h1)-mg(h2)+.5mv^2

The Attempt at a Solution

I inputted 27(9.81)17-27(9.81)(7) and got 2648.7 and added it to .5(27)(7.5^2) which was 759.375 and came up with the answer 3408.075 J.. this seems to be wrong.. What am I doing wrong here?

 

[tedbradly]

Homework Statement

A 27.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 17.00 m. When she is partway down the slide, at a height h2 of 7.00 m, she is moving at a speed of 7.50 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.).

Homework Equations

I used mg(h1)-mg(h2)+.5mv^2

The Attempt at a Solution

I inputted 27(9.81)17-27(9.81)(7) and got 2648.7 and added it to .5(27)(7.5^2) which was 759.375 and came up with the answer 3408.075 J.. this seems to be wrong.. What am I doing wrong here?

Let K be kinetic energy and U be potential energy. In a perfect world, we have

$$K_1 + U_1 = K_2 + U_2$$

But in an imperfect world, there will be a change in the sum of kinetic and potential energy, and a simple way to account for that change is to blame it on friction. Thus,

$$W_{FO} = K_2 - K_1 + U_2 - U_1 = \Delta K + \Delta U$$

with W_{FO} being the work of friction done to the object. It will be negative, but your answer should be positive due to the phrasing, so change its sign.

You seem to be doing K_2 - K_1 and U_1 - U_2, causing your error.