Question

A gondola can carry 20 skiers, with a total mass of up to 2000 kg . The gondola ascends at a constant speed from the base of a mountain, at 2250 m , to the summit at 3765 m .

I need help with part C

Part A

How much work does the motor do in moving a full gondola up the mountain? 2.97×10⁷ J

Part B

How much work does gravity do on the gondola? −2.97×10⁷ J

Part C

If the motor is capable of generating 10 % more work than found in A, what is the acceleration of the gondola? (in m/s)

Answer 1

A)

m = total mass = 2000 kg

h_i = initial height = 2250 m

h_f = final height = 3765 m

work done = W = change in gravitational potential energy

W = mg (h_f - h_i)

W = (2000) (9.8) (3765 - 2250) = 2.97 x 10⁷ J

B)

W_g = work done by gravity = - mg (h_f - h_i)

W_g = - (2000) (9.8) (3765 - 2250) = - 2.97 x 10⁷ J

C)

W_extra = 10% of W = 0.1 x 2.97 x 10⁷ J = 2.97 x 10⁶ J

F_net = net force

d = distance travelled = 3765 - 2250 = 1515 m

using the equation

W_extra = F_net d

2.97 x 10⁶ = F_net (1515)

F_net = 1960.4 N

ma = 1960.4

2000 a = 1960.4

a = 0.98 m/s²