Question

Passengers in a carnival ride move at constant speed in a circle of radius 5.0 m, making a complete revolution in 4.0 s. As they spin, they feel their backs pressing against the wall holding them in the ride. A. What is the direction of the passengers' acceleration? a. No direction (zero acceleration) b. Directed towards center c. Directed away from center d. Directed tangentially B. What is the passengers' linear speed in m/s? C. What is the magnitude of their acceleration in m/s^2? D. What is their angular speed in rad/s?

Answer 1

A. b) Directed towards center

B.
`v = 7.854\ m/s`

C.
`a_c = 12.337\ m/s^2`

D.
`w = 1.57\ rad/s`

Step-by-step explanation:

The "force" that they feel pressing their backs against the wall is because the reaction to the centripetal acceleration .

A.

This acceleration has its direction towards the center of the circle. (option b)

B.

Their linear speed can be calculated with the equation:

`v = (\theta/t)*r`

Where
`\theta` is the total angular position moved in radians (
`1\ rev = 2\pi\ radians`), 't' is the time elapsed for the angular position moved and 'r' is the radius. So we have that:

`v = (2\pi/4)*5 = 7.854\ m/s`

C.

The centripetal acceleration is given by the equation:

`a_c = v^2/r`

`a_c = 7.854^2/5`

`a_c = 12.337\ m/s^2`

D.

Their angular speed is given by the equation:

`w = \theta/t = 2\pi/4 = \pi/2 = 1.57 \ rad/s`