At a ride in an amusement park a cart, with a mass of 150 kg, rolls down a long

Question

At a ride in an amusement park a cart, with a mass of 150 kg, rolls down a long curved hill. The height of the hill is 50 m and the length of the track that the cart follows is 300 m. As the cart rolls down the hill, it experiences both a rolling frictional force and air resistance. The net effect of these two resistive forces over the run is equivalent to a constant force of 70 N, which is opposite to the cart’s velocity.

A) If the cart starts out at rest at the top of the hill, what is its speed at the bottom?

B) There is a large hydraulic piston at the bottom of the hill that engages the cart and brings it to rest by applying a constant force for 5.0 m. Neglecting all other resistive forces, what is the magnitude of the force needed to stop the cart?

Explanation / Answer

work done by friction and air resistance = 70 x 300 = 21000 J

initial potential energy at the top = mgh = 150 x 9.8 x 50 = 73500 J

kinetic energy at bottom = pE - W = 73500 - 21000 = 52500 J

V = speed at bottom

(0.5) m V2 = 52500

(0.5) (150) V2 = 52500

V = 26.5 m/s

B)

F = constant force

d = stopping distance

F d = kinetic energy at bottom

F d = 52500

F (5) = 52500

F = 10500 N

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