Question

You are trying to fimd the average frictional force on a skier while being pulled by a tow rope up a ski slope. An average skier has a mass of 85kg with all the skiing equipment and starts from rest at the bottom of a ski slope. The tow rope pulls the skier up a 14 degree slope that is 103m long. For the average skier, they are moving at 3m/s at the top of the hill at the end of the pull. The rope pulls the skiers with a force of 275N.

a. What is the kinetic energy of the skier at the bottom of the hill and at the top of the hill?

b. What is the change in gravitional potential energy in the skier/gravity system between the bottom and the top of the hill? Indicate if the potential energy is increasing or decreasing as the skier rises to the top of the hill?

c. What is the average frictional force on the skier during the duration of the pull up the hill?

Answer 1

a) at the bottom of the hill, KEi = (1/2)*m*vi^2

= 0 J (since vi = 0 ) <<<<<<<<--------------Answer

at the top of the hill, KEf = (1/2)*m*vf^2

= (1/2)*85*3^2

= 382.5 J <<<<<<<<--------------Answer

b) change in gravitational potential energy = Uf - Ui

= m*g*h - 0

= m*g*h

= m*g*d*sin(theta)

= 85*9.8*103*sin(14)

= 20757 J <<<<<<<<--------------Answer

potential energy is increasing.

c) workdone by friction and rope = change in mechanical energy

fk*d*cos(80) + F*d*cos(0) = 20757 + 382.5

-fk*d + 275*103 = 20757 + 382.5

-fk*103 = 20757 + 382.5 - 275*103

fk = -(20757 + 382.5 - 275*103)/103

= 69.8 N <<<<<<<<--------------Answer