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Impulse and Impulse Force

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According to Newton's Second Law of Motion - force can be expressed as

F = dM / dt                                      (1)


F = applied force (N, lbf)

dM = change of momentum (kg m/s, lb ft/s)

dt = time taken (s)

Eq. (1) can alternatively be expressed as

  dM = F dt                                      (1b)

Change in momentum is force times acting time.

Forces that act for a very short time are called impulse forces. The product of the impulsive force and the time it acts is called the impulse. The impulse is equal to the change of momentum caused by the impulsive force and can be expressed as

I = F dt = dM                                      (2)


I = impulse (N s)

Example - resulting Velocity after an Acting Force

A force 1000 N is acting on a car with mass 1000 kg in 10 second.

The impulse - or change in momentum - can be calculated

I = dM = (1000 N) (10 s)

  = 10000 (N s, kg m/s)

Since momentum can be expressed as

M = m v                                                 (3)


M = momentum (kg m/s, lb ft/s)

m = mass (kg, lb)

v = velocity (m/s, ft/s)

then the velocity of the car after 10 s can be calculated as

v = (10000 kg m/s) / (1000 kg)

 = 10 m/s

 = 36 km/h

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