Physics problem help....power problem involving a ski lift... help please!!?

Question

Consider a ski lift of length 5.1 km. Assume it takes about 60 min for a gondola to travel all the way up. If there are 12 gondolas going up at once, each of mass 535 kg, and the angle of ascent was 30°, estimate the power P of the engine needed to operate the ski lift.

____ kW

Answer 1

Let:

F be the force needed,

v be the 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.

Resolving parallel to the slope:

F = mg sin(a)

P = Fv

Eliminating F:

P = mgv sin(a).

P = 12 * 535 * 9.81(5.1 * 10^3 / 3600) sin(30) W

= 44.6 kW.