Question

Use the following information to answer parts a–b. You are asked to design a rollercoaster. It will have ten attached cars, each of which will have a mass of 500 kg and carry six people with average mass of 70.0 kg. You want to design a vertical circular loop with a radius of 55.0 m. The centre of the circle would have a height of 71.0 m above the ground. Assume the track is frictionless.

a) Calculate the minimum speed the rollercoaster cars would have to have at the top of the circle in order to continue around the circle and not fall off the track.

For the remaining questions, assume the rollercoaster is designed to operate at the minimum speed at the top of the loop.

b) Calculate the mechanical energy of the cars at the top of the circle, with respect to the ground.

c) Calculate the speed of the cars when they are 40˚ below the horizontal.

d)Calculate the amount of tension on the track when the cars are 40˚ below the horizontal.

e) Calculate the maximum amount of tension that the rollercoaster track would have to withstand within the loop. Include a free body diagram of the cars and specify the location in the circle.

Answer 1