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Mechanics

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 Practice Problems for the Mechanical Engineering PE Exam: A Companion to the Mechanical Engineering Reference Manual   Mechanical Engineering   Problems and Solutions in Introductory Mechanics  Integral Methods in Science and Engineering   Quantum Mechanics

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Examples

Linear Motion: A car travels at a uniform velocity of 20 m/s for 5s. The brakes are then applied and the car comes to rest with uniform retardation in a further 8s. How far does the car travel after the brakes are applied?

Initial Velocity = u = 20 m/s
Time traveled after brakes = t = 8s
Distance traveled after brakes = s

  
Applying  v = u + at  (where a is the retardation)  
                    0 = 20 + 8a
                     8a = -20
                       a = -20/8
                          = -2.5 m/s2 
(note the minus sign for retardation)
      Applying   s = ut + at2  (for the distance traveled after braking)
 
 
                      s = (20)(8) + (-2.5)(8)2
                            = 160 - (64)(5)/4
                              = 160 - 80
                               
 = 80 m 


Linear Motion: 
A motorist, traveling at 90 km/h, applies his brakes and comes to rest with uniform retardation in 20s.
Calculate the retardation in m/s2.

 Initial Velocity = u = 90 km/h = (90 X 1000)/3600 m/s = 25
                 Final Velocity = v = 0
                    Time taken = t = 20s
                      Retardation = a
                         
 Applying   v = u + at
                                        0 = 25 + 20a
                                   - 20a = 25
                                         a = -25/20
                                            
= -1.25 m/s2

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