The velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s. When a force act on it for 2 seconds, find :
(a) What is the momentum before the force act?
(b) What is the momentum after the force act?
(c) What is the momentum gain in momentum per sec?
(d) What is the value of force?

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2015-06-06T03:58:00+05:30

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Initial velocity (u) = 4 m/s
Final velocity (v) = 8 m/s
Mass (m) = 10 kg
Time (t) = 2 seconds
Initial momentum (p₁) = m × u
Final momentum (p₂) = m × v

(a) 
Momentum before the force act = Initial momentum 
                                               = m × u
                                               = 10 × 4
                                               = 40 kg.m/s
(b)
Momentum after the force act = Final momentum
                                            = m × v
                                            = 10 × 8
                                            = 80 kg.m/s
(c)
Momentum gain = Final momentum - Initial momentum 
                        = 80 - 40 = 40 kg.m/s
Momentum gain in momentum per second = Momentum gain / time
                                                              = 40 / 2 = 20 kg.m/s
(d)
Force = mass × acceleration
         = m × (v - u) / t           ( as, acceleration is change in velocity per time)
         = 10 × (8 - 4) / 2
         = 10 × 2
         = 20 N
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