Conservation of Energy w/ Frictional Forces

[maxhersch]

Homework Statement

During a rockslide, a 710 kg rock slides from rest down a hillside that is 500 m long and 300 m high. The coefficient of kinetic friction between the rock and the hill surface is 0.23.
https://physicsforums-bernhardtmediall.netdna-ssl.com/data/attachments/57/57890-5a3321dd6b8a58eb42038e3fc5bbe5e1.jpg
(a) If the gravitational potential energy U of the rock-Earth system is set to zero at the bottom of the hill, what is the value of U just before the slide?
(b) How much energy is transferred to thermal energy during the slide?
(c) What is the kinetic energy of the rock as it reaches the bottom of the hill?

Homework Equations

U[/B]=mgh
N=mgcosθ
F_ƒ=μN
W_ƒ=F_ƒdcosθ

The Attempt at a Solution

a)[/B] Easy. U_ο=(710)(9.8)(300)=2087400 J (Accepted as correct answer)

b) θ=tan^-1(300/500)=31°
N=(710)(9.8)cos(31)=5964.2 N
F_ƒ=(.23)(5964.2)=1371.8 N
W_ƒ=(1371.8)(583.1)cos(180°)=-799896.6 J (This was not accepted as correct answer)

(c) U_ο+K_ο=U_f+K_f+W_ƒ
2087400+0=0+K_f+799896.6
K_f=1287503.4 J (Also not accepted as correct answer)Please let me know where I went wrong.

 

[haruspex]

W_ƒ=(1371.8)(583.1)cos(180°)=-799896.6 J

Where did the 583.1 come from?
Should the answer be positive or negative?

 

[maxhersch]

Where did the 583.1 come from?
Should the answer be positive or negative?

583.1 is the distance the rock slides found by the Pythagorean Theorem √300²+500². I tried both positive and negative with those answers. I assume the work done by friction is always negative since it is opposite the motion. and the kinetic energy should be positive because the velocity would be in the positive x-direction.

 

[Chestermiller]

You misinterpreted the problem. The 500 is the hypotenuse.

Chet

 

[haruspex]

You misinterpreted the problem. The 500 is the hypotenuse.

Chet

... which means this is also wrong:

θ=tan^-1(300/500)​

 

[maxhersch]

You misinterpreted the problem. The 500 is the hypotenuse.

Chet

Ahh knew I missed something basic. Thanks a lot.