Work done against friction and air resistance on a ski run

[nikelberry]

calculating workdone due to friction and air resistance...HELP!

Homework Statement

this is my 1st post and i don't really no if i should put the whole question, so i will...just to make sure i get some help!

A skier of mass 72kg, initially at rest, reached a speed of 32ms/1 at the bottom of the ski run length of 1500m that was 120m lower at the bottom than the top.
calculate:
the loss of potential energy
the gain of kinetic energy of the skier
the work done against fiction and air resistance
the average force opposing the motion of the skier

Its mainly the last 2 questions that I am having trouble with.

Homework Equations

The Attempt at a Solution

i tried the 1st two questions and when i came to the next two i got stuck.
1st of all i tried Work done= force * distance moved
and but in order to get the force i then used the equation F=m*a, and in order to get 'a' then used SUVAT equation v²=u²+2as
and its around here in which i got stuck becasue of all the numbers!
Please help me!
thanks in advanced!

 

[kuruman]

Hi nikelberry, welcome to PF.The skier starts with a certain numbers of Joules at the top. When the skier gets to the bottom, some of these Joules got to kinetic energy and the rest goes to friction, a number you can figure out. That is the "work done against friction and air resistance" in question 3. Once you have that, use Work done = force*distance to find "force". You don't need F = ma.

 

[nikelberry]

but the thing is i need help on working out question 3 "work done against friction and air resistance" because i can't remember how to work this sort of question out! :(

 

[kuruman]

As I said, the initial number of Joules at the top is split into two kinds of Joules at the bottom

Initial potential energy = Final Kinetic energy + Work done against friction

You know two of these quantities. Can you find the third?

 

[nikelberry]

Kuruman! i just worked it out!
Thanks a million for the help and a quick relpy!

 

[tigor]

start with energy - select reference point - the bottom

thus the energy at the top is M*G*H= 72 *G*120
the energy stays the same therefore

MGH=MV^2/2 + Work of Friction and drag
Work of Friction and drug = MGH - MV^2/2

I suppose the 4th task is simple to use W=F*X formula... otherwise you'll have to create function for air drag (since it was mention here) and then to integrate this function. And F(drag) is going to be complicated with 2 functions within - p(air densitity) and V(velocity) - that seem way to complicated comparing to the rest of your tasks