Rotational Energy and Roller Coaster Designer

[costric]

Homework Statement

Homework Equations

The Attempt at a Solution

Ride Designer

A local carnival owner wants you to design a ride for him. Riders are strapped inside a rolling car which rolls down the track shown below. (sorry i can't copy the diagram)

H=50m with 2 loops and then it stops at the end.

Focus groups of riders have determined that the riders want the car to roll as fast as possible, but also expect the ride to be very popular. Evaluate the following designs.

Car A: The Barrel, R=3m, I=½MR^2, Seats 6

Car B: The Ball, R=3m, I=0.4MR^2, Seats 2

Car C: The Hoop, R=4m, I=MR^2, Seats 8


What will be the maximum speed during the ride? Where will it occur? Which car would you choose for the ride and why?

 

[NateD]

The maximum speed of the ride will depend on the mass and shape of the car, as well as the track. The kinetic energy of the car is related to its mass and velocity through the equation KE = ½mv^2, where m is the mass of the car and v is the velocity of the car. As the car moves down the track, it gains potential energy from the height of the track and converts it into kinetic energy. At the bottom of the track, the kinetic energy is at a maximum and the velocity is at its highest. The car with the highest maximum speed will be Car C, The Hoop. This is because it has the greatest moment of inertia (I=MR^2) and the largest radius (R=4m). This means that it will be able to store more potential energy, which will convert into kinetic energy as the car moves down the track. The maximum speed of the ride will occur at the bottom of the track, just before the car stops. For this ride, I would choose Car C, The Hoop. This is because it has the largest radius, which will provide the greatest amount of kinetic energy and thus the highest possible speed. It also has the highest capacity for riders (seats 8), which will make the ride very popular.