Conservation of Energy question

[brittkub1291]

During a rockslide, a 340 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 0.24.

(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?

(d) What is its speed then?

For letter a i found the gravitational potential energy using the formula Eg=mgy. This gave me 999600 J. I'm not sure how to find the thermal energy though, i thought that i could just multiply the gravitational energy by the coefficient of friction, but that didn't work.

 

[tiny-tim]

Hi brittkub1291!

During a rockslide, a 340 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 0.24.
…
(b) How much energy is transferred to thermal energy during the slide?
…
I'm not sure how to find the thermal energy though, i thought that i could just multiply the gravitational energy by the coefficient of friction, but that didn't work.

Nooo …

Thermal energy is heat. What generates heat ? Friction!

So the thermal energy is the work done by the friction force.

 

[brittkub1291]

Okay, i tried finding the friction force by using F=ma but i don't know if acceleration is constant or not.

 

[tiny-tim]

Okay, i tried finding the friction force by using F=ma but i don't know if acceleration is constant or not.

uhh?

Kinetic friction force = normal force times µ_k

 

[brittkub1291]

Yeah, i just realized that. So the normal force is mgcos(x), the friction force should just be (.24)(mgcos(x)) right? It keeps coming out wrong. When the question say the hill is 500 m long would that be the hypotenuse of the triangle? I was thinking that it wouldn't be..

 

[tiny-tim]

During a rockslide, a 340 kg rock slides from rest down a hillside that is 500 m long and 300 m high.

I don't see what else it can mean … high is vertically, so what can long be if it isn't the hypotenuse?

 

[brittkub1291]

Okay, i got it. I just was doing the problem as if they gave me the height and the length, and i used pathagoreans theorem to find the hypotenuse so it was making my answers wrong.