Question

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?

Answer 1

1. Ideal Mechanical Advantage (IMA): 9

Explanation:

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

$IMA=\frac{r_w}{r_a}$

where

$r_w$ is the radius of the wheel

$r_a$ is the radius of the axle

For the steering wheel of the problem, we see that $r_w = 18 cm$ and $r_a=2 cm$, so the IMA is

$IMA=\frac{18 cm}{2 cm}=9$

2. Efficiency: 88.9%

Explanation:

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

$\eta=\frac{AMA}{IMA}\cdot 100$

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

$\eta=\frac{8}{9}\cdot 100=88.9\%$