Question

"If the end of the crutch is a circle of radius 1.2 cm without the tip, and the rubber tip is a circle of radius 2.3 cm , by what factor does the tip reduce the pressure exerted by the crutch?"

Answer 1

The pressure exerted by the crutch is reduced factor by 0.72.

Step-by-step explanation:

Given that,

Radius of crutch = 1.2 cm

Radius of tip = 2.3 cm

We need to calculate the pressure without tip

Using formula of pressure

`P=(F)/(A)`

`P_(1)=(F)/(\pi r^2)`

Put the value into the formula

`P_(1)=(F)/(\pi*(1.2*10^(-2))^2)`....(I)

We need to calculate the pressure with tip

Using formula of pressure

`P_(2)=(F)/(\pi r^2)`

`P_(2)=(F)/(\pi*(2.3*10^(-2))^2)`....(II)

We need to calculate the reduction factor

Using formula of reduction factor

`\text{reduction factor}=(P_(1)-P_(2))/(P_(1))`

Put the value into the formula

`\text{reduction factor}=((F)/(\pi*(1.2*10^(-2))^2)-(F)/(\pi*(2.3*10^(-2))^2))/((F)/(\pi*(1.2*10^(-2))^2))`

Here, F is the same

`\text{reduction factor}=((1)/((1.2*10^(-2))^2)-(1)/((2.3*10^(-2))^2))/((1)/((1.2*10^(-2))^2))`

`\text{reduction factor}=0.72`

The pressure exerted by the crutch is reduced by 72%.

Hence, The pressure exerted by the crutch is reduced factor by 0.72.