Physics, asked by felistaakonaay7465, 9 months ago

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?

Answers

Answered by knjroopa
30

Explanation:

Given 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?

  • So mass m = 1000 kg
  • Speed v = 50 km / hr = 50 x 5/ 18 = 250 / 18 m/s
  • Now there is a circular piston of radius r1 = 0.5 cm = 0.5 x 10^-2 m
  • Now the larger area slave cylinder whose radius r2 = 2.5 cm = 2.5 x 10^-2 m
  • Since this is circular in shape we have area A1 = π r1^2
  •                                                                           = π x (0.5 x 10^-2)^2
  •                                                                        
  •                                             Also area A2 = πr2^2
  •                                                               = π x (2.5 x 10^-2)^2
  • Now a constant force of 100 N is applied on the brake
  •                                                  So F1 = 100 N
  • Now we need to find F2 that is the force applied to stop.
  • So we have F2 = F1 x  A 2 / A1
  •                           = 100 x π x (2.5 x 10^-2)^2 / π x (0.5 x 10^-2)^2
  •                          = 100 x 6.25 x 10^-4 / 0.25 x 10^-4
  •                          = 25 x 100
  •                     F2 = 2500 N
  •   So now the retarding acceleration a = F / m
  •                                                        So a = 2500 / 1000
  •                                                       Or a = 2.5 m /s^2
  • Now the equation of motion will be  
  •                                              So v^2 = u^2 – 2as (since retarding)
  •                                           So      0 = (250 / 18)^2 – 2 (2.5) s
  •                                          So s = 250 / 18 x 250 / 18 x 1/5
  •                                         Or s = 38.58 m

Reference link will be

https://brainly.in/question/13970541

Answered by srushtigaikwad16
7

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