Physics Question?

Question

Please explain how you come to the conclusion because I really need to know this stuff.
Thanks in advance.

A snowboard starts at rest and slides down a 15 degree incline that is 60 m long. The coefficient of friction is 0.090. Use energy methods to solve problems.

A. What is the snowboard's speed at the base of the incline?


B. If the snow is level at the base of the incline and has the same coefficient of friction, how far will the snowboard travel along the level ground?

Answer 1

a) P=w h (potential energy)
w=mg (weight
h=60 x sin(15)
P= m x g x 60 x sin(15)
(note that amount of energy on top of the incline is equal to the amount of work done in moving the object along th incline)
P=W=m x g x sin(15) x 60
Taking force of friction into consideration
W'=P-Wf= (wi-f)
W'=(m x g x sin(15) -u m x g xcos(15) )x 60
W'=m x g (sin(15)-ucos(15))x 60
u- coefficient of friction

b) P(on top)=Ke (on the bottom)
Wit friction however
Ke=W'
Ke=0.5mv^2 (Kinetic energy.)
v=sqrt(2 Ke / m)
v=sqrt(2 W' /m)
v=sqrt(2 m x g x 60 x sin(15)/m)
and finally
v=sqrt(2 g x 60 x sin(15))

c) Work done by friction force
Wf=uwS= Ke
w=mg
finally the distance S= Ke/(umg)

I hope it helps