Question

A ski starts from rest and slides down a 30 ∘ incline 70 m long.

a) If the coefficient of friction is 0.095, what is the ski's speed at the base of the incline?

b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.

Answer 1

From conservation of energy, we can write

Total change in energy = Loss of energy due to the friction ..........................(1)

And Loss of energy due to friction = negative work done by the friction

Form the diagram,

  

(a) Given, length of ramp = 70 m

the force of friction is given by

So, workdone by force of friction is

   (as the direction of force is in opposite direction of motion)

Initially:

  Energy of the system = mgh = m x 9.8 x 35 = 343m J

Finally (i.e. at the base of incline):

Energy of the system = 05mv²

So, change in energy = 0.5mv² - 343m

Now from equation (1),we have

or,   

or,   

(b) Now the ski will slide untill the total energy at the base of the incline will be consumed (or lost) by the force of friction.

In this situation (as there is no inclination), the force of the friction will be

Let the ski travel S distance before it stops.

So, workdone will be

  

Now applying work energy theorem, we get

  

or,   

or,

or,  

For any doubt please comment.