Problem: What is the total momentum of two objects, one moving in the positive direction at 18 m/s and the other moving at 8 m/s in the negative direction? The mass of the first object is 71 kg and that of the second is 20 kg. Assuming that the two objects stick together when they collide, what then is the total mass and velocity after collision?
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Solution: The momentum of the first is ( 18 m/s)( 71 kg)= 1278 kg m/s, and that of the second is ( 8 m/s)(- 20 kg) = -160 kg m/s. The total momentum is therefore 1278 kg m/s + -160 kg m/s = - 1118 kg m/s. The total mass is easily found to be 91 kg. Since the total momentum after collision is the same as that before collision, we see that after collision we have a mass of 91 kg with momentum -1118 kg m/s. Dividing we obtain velocity ( -1118 kg m/s)/( 91 kg) = -129 m/s.
Generalized Response: The total momentum of a mass m1 moving at velocity v1 and a mass m2 moving at velocity v2 is pTot = m1 v1 + m2 v2. By Newton's Third Law and the Impulse-Momentum Theorem this momentum will remain unchanged during collision.
After collision we wil have one object of mass m1 + m2 and momentum m1 v1 + m2 v2. The object will therefore have velocity
velocity = momentum / mass = (m1 v1 + m2 v2) / (m1 + m2).
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Figure description: