Question

A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center. The linear speed of a passenger on the rim is constant and equal to 9.00 m/s.

(a) What are the magnitude and direction of the passenger's acceleration as she passes through the lowest point in her circular motion?




(b) What are the magnitude and direction of the passenger's acceleration as she passes through the highest point in her circular motion?

Answer 1

Before we even worry about magnitude for question (a), whenever something's traveling in a circle, in what direction is it's acceleration?

Answer 2

inward?

Answer 3

my options are

upward toward the center
downward away from the center
tangent to the circular path

Answer 4

You're right about inward - meaning towards the centre of the circle. When the person is at the BOTTOM of the ferris wheel, what direction is towards the centre of the circle for her?

Answer 5

up

Answer 6

Right - so which of your options is the answer for acceleration?

Answer 7

ok i got the directions correct, now how do i find the magnitudes?

Answer 8

The question gives you v and r. To find the acceleration, start by looking at the net force. The acceleration is toward the centre of the circle - this is centripetal acceleration, which becomes centripetal force, F(ac) when multiplied by the mass of the person. You need to also remember that gravity, F(g), is pulling that same person down. That means the net force is the following:

\[F_{net}=F_{a_c}-F_g\]\[ma=ma_c-mg\]\[a=a_c-g\]
The net acceleration is the centripetal acceleration minus the acceleration due to gravity. You know g=9.8, and you can find a(c) using v^2/r. That means:

\[a={v^2 \over r}-g\]
Do you think you can find the magnitude of the acceleration now?

Answer 9

By the way - be very careful with the directions of your forces. What I wrote above is true for when the passenger is at the BOTTOM of the ferris wheel, because gravity is acting in the direction opposite that of the centripetal force.

At the TOP of the ferris wheel, BOTH gravity and centripetal force are acting in the same direction, so you will need to use a slightly different equation!