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A hydraulic brake system of a car of mas...

A hydraulic brake system of a car of mass 1000 kg having speed of 50 km/h, has a cylindrical piston of radius of 0.5 cm. The slave cylinder has a radius of 2.5 cm. If a constant force of 100 N is applied on the brake what distance the car will travel before coming to stop?

Text Solution

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Given, `F_(1) = 100 N, A_(1) = pi (0.5xx10^(-2))^(2) m^(2), A_(2) = pi (2.5xx10^(-2))^(2) m^(2), F_(2) = ?`
By Pascal.s Principle,
`(F_(2))/(A_(2))=(F_(1))/(A_(1))`
`F_(2)=(100xxpi (2.5xx10^(-2))^(2))/(pi (0.5xx10^(-2))^(2))=2500 N`
Acceleration of the car = `a = F_(2)//m =2500//1000=2.5" m/s"^(2)`. Using Newton,s equation of motion,
`v^(2) =u^(2)-2as` where final velocity `v=0, u = 50` km/h
`s=((50xx1000)/(3600))^(2) xx(1)/((2xx2.5))=38.58 m`
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