Question

Elmira, New York boasts of having the fastest carousel ride in the world. The merry-go-round at Eldridge Park takes riders on a spin at 18 mi/hr (8.0 m/s). The radius of the circle about which the outside riders move is approximately 7.4 m. a. Determine the time for outside riders to make one complete circle. b. Determine the acceleration of the riders.

Answer 1

The time taken is 5.81 s and the acceleration is 8.64 m/s².

Explanation:

a) The time taken by the riders to make one complete cycle can be determined easily from the ratio of circumference of the circular path to the speed with which the riders are moving.

$Speed=\frac{Distance}{Time}$

Distance traveled by the riders will be equal to the circumference of the circle as they are moving in circular motion.

So the speed with which they are moving is 8 m/s and the distance traveled by them to complete one circle will be the circumference of the circle.

$Distance= Circumference = 2 *3.14 * radius$

As the radius of the circle is given as 7.4 m, the distance will be

$Distance = 2*3.14*7.4 = 46.5 m$

So the time taken by the riders to cover 46.5 m with speed of 8 m/s is

$Time taken = \frac{Distance}{Speed} = \frac{46.5}{8} = 5.81 s$

Thus, 5.81 s is required by the riders to complete one cycle with 8 m/s speed.

b) The acceleration of the riders can be found by finding the ratio of speed square to the radius.

$Acceleration =\frac{\text {velocity}^{2}}{\text {radius}}$

$Acceleration =\frac{\text {8}^{2}}{\text {7.4}}= 8.64\ m/s^{2}$

So the acceleration of the riders is 1.38 m/s².

Thus, the time taken is 5.81 s and the acceleration is 1.38 m/s².