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Forces come in pairs When an object collides with another object, the two objects exert an equal and opposite force on each other for the same length of time. Force = change in momentum Time Force x time = change in momentum So the change in momentum of one body is the same as the change in momentum of the other body, in the opposite direction

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Momentum is conserved In any collision or explosion momentum is always conserved total momentum after = total momentum before m 1 v 1 + m 2 v 2 = m 1 u 1 + m 2 u 2 This can be used to analyse the collision of two objects

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5 kg3 kg5 kg3 kg 4 m/s2 m/s ? m/s Before After total momentum after = total momentum before m1v1 + m2v2 = m1u1 + m2u2 5v + 3 v = (5 x 4) + (3 x 2) 8v = 26 v = 26 / 8 = 3.25 m/s

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The conservation of momentum explains the recoil of a gun A stationary tank of mass 10 000 kg fires a 250 kg shell at a velocity of 200 m/s. Calculate the recoil velocity of the tank. total momentum after = total momentum before m1v1 + m2v2 = m1u1 + m2u2 10 000 v1 + 250 x 200 = 10 000 x 0 + 250 x 0 10 000 v1 + 50 000 = 0 10 000 v1 = - 50 000 v1 = - 5 m/s Recoil velocity of the tank is 5 m/s in the opposite direction

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Rockets A rocket or jet moves forward because the exhaust gases go backwards. The momentum of the rocket forward= momentum of the gases backwards

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9.2 Conservation of Momentum

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