Question

Well, Professor Pearce and her friend went skiing again, and to no one's surprise, they wiped out again. Professor Pearce wants to know if she can slide her friend's ski back up the mountain to her. You could solve this question as we did before: using Newton's Laws to find the acceleration and then using kinematics. But now, let's see how to solve this same problem using energy. This time we will include the force of friction; the ski sliding up the mountain has a coefficient of kinetic friction 3.8×10−2 . Professor Pearce's friend is a distance 1.86 m above her (measured along the mountain), and the slope makes angle 7.00 ∘ with respect to the horizontal where they are. The ski has mass 1.12 kg .

Calculate the minimum speed Professor Pearce has to give the ski (when she lets go of it) for it slide up to her friend.

Answer 1

Angle of slope, = 7.0 deg

Mass of the ski, m = 1.12 kg

Coefficient of kinetic friction, = 3.8 x 10^-2 = 0.038

Total force downward the slope acting, F = m*g*sin + *m*g*cos

Therefore, downward acceleration, a = F/m = (m*g*sin + *m*g*cos) / m = g*sin + *g*cos

Put the values -

a = 9.8*sin7 + 0.038*9.8*cos7

= 1.19 + 0.37 = 1.56 m/s^2

Distance along the slope, L = 1.86 m

Suppose the initial speed given to the ski = u

Final speed of the ski, v = 0

use the expression -

v^2 = u^2 - 2*a*L

=> 0 = u^2 - 2*1.56*1.86

=> u^2 = 2*1.56*1.86

=> u = 2.41 m/s (Answer)