Physics power problem ?

Question

A T-bar tow is planned in a new ski area. At any one time, it will be required, to pull a maximum of 73 skiers up a 556-m slope inclined 15° at above the horizontal at a speed of 2.50 m/s. The coefficient of kinetic friction between the skiers skis and the snow is typically 0.055. As the manager of the facility, what motor power should you request of the construction contractor if the mass of the average skier is 74.0 kg. Assume you want to be ready for any emergency and will order a motor whose power rating is 50 percent larger than the bare minimum.

______kW

Answer 1

Let:

F be the force needed,

R be the normal reaction,

v be the towing speed,

P be the power needed,

a be the angle of inclination of the slope to the horizontal,

m be the mass of the skiers,

g be the acceleration due to gravity,

u be the coefficient of friction.

Resolving parallel and perpendicular to the slope:

F - mg sin(a) = uR ...(1)

mg cos(a) = R ...(2)

P = Fv ...(3)

Eliminating R from (1) and (2):

F = mg[ sin(a) + u cos(a) ]

Substituting for F in (3):

P = mgv[ sin(a) + u cos(a) ].

Allowing 50% extra:

P = 73 * 74.0 * 9.81 * 2.50 * 1.5 [ sin(15) + 0.055 cos(15) ] W

= 62.0 kW.