How Much Mechanical Energy Does the Skier Lose?

[bkl4life]

Homework Statement

A 60 kg skier slides from rest down a 30 m slope that makes an angle of 26 degrees with the horizontal. Assume the coefficient of friction of the slope is .2.

How much mechanical energy does the skier lose while skiing down the hill?
What is the velocity of the skier lose while skiing down the hill?

Homework Equations

w=mgh

The Attempt at a Solution

m=(60)(9.8)(30)=17640 J

I'm not sure what to do after this.

 

[mgb_phys]

H isn't 30m, the slope is 30m long (ie along the hypotonuse) you have to work out from the 26deg how high the slope is.

 

[bkl4life]

Okay, so I do

(60)(9.8)(cos26)

Is it possible to take that answer and set it up to find the velocity? Do I need part A to find part B. I'm just really confused.

 

[mgb_phys]

What units does 'mgh' have, what units does your equation have?
Always put in the units - it let's you spot mistakes.
The vertical height is 30 sin(26) m

You know how muhc potential energy the skier loses, and this equals the kinetic energy they gain less the frictional losses.
The energy lost to friction is force*distance, so the length of the slope * the frictional force along the slope

 

[bkl4life]

Thanks! This makes sense. I always mess up my units!