Question

The area of the piston to the master cylinder in a hydraulic braking system of a car is 0.4 square inches. If a force of 6.4 lb is applied to this piston, what is the force on the brake pad of one wheel if the area of the pad is 1.7 square inches

Answer 1

The force applied on one wheel during braking = 6.8 lb

Step-by-step explanation:

Area of the piston (A) = 0.4
`in^(2)`

Force applied on the piston(F) = 6.4 lb

Pressure on the piston (P) =
`(F)/(A)`

⇒ P =
`(6.4)/(0.4)`

⇒ P = 16
`(lb)/(in^(2) )`

This is the pressure inside the cylinder.

Let force applied on the brake pad =
`F_(1)`

Area of the brake pad (
`A_(1)`)= 1.7
`in^(2)`

Thus the pressure on the brake pad (
`P_(1)`) =
`(F_(1) )/(A_(1) )`

When brake is applied on the vehicle the pressure on the piston is equal to pressure on the brake pad.

⇒ P =
`P_(1)`

⇒ 16 =
`(F_(1) )/(A_(1) )`

⇒
`F_(1)` = 16 ×
`A_(1)`

Put the value of
`A_(1)` we get

⇒
`F_(1)` = 16 × 1.7

⇒
`F_(1)` = 27.2 lb

This the total force applied during braking.

The force applied on one wheel =
`(F_(1) )/(4)` =
`(27.2)/(4)` = 6.8 lb

⇒ The force applied on one wheel during braking.