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

9, and 89%

Step-by-step explanation:

Answer 2

1. Ideal Mechanical Advantage (IMA): 9

Step-by-step explanation:

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

`IMA=(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=(18 cm)/(2 cm)=9`

2. Efficiency: 88.9%

Step-by-step explanation:

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

`\eta=(AMA)/(IMA)\cdot 100`

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

`\eta=(8)/(9)\cdot 100=88.9\%`