An automobile steering wheel is shown. what is the ideal mechanical advantage? if the ama is 8, what is the efficiency of the steering wheel?

1. Ideal Mechanical Advantage (IMA): 9

Explanation:

For a wheel and axle system like the steering wheel, the IMA is given by:

where

is the radius of the wheel

is the radius of the axle

For the steering wheel of the problem, we see that and , so the IMA is

2. Efficiency: 88.9%

Explanation:

The efficiency of a system is defined as the ratio between the AMA (actual mechanical advantage) and the IMA:

In this problem, AMA=8 and IMA=9, so the efficiency is

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft