An analysis of the effects of an impact between two bodies
OverviewIf a body of weight overtakes a body of weight and their velocities are before impact and Then if the reaction between the bodies is R and the impulse lasts a short time r:-
- One end of a chain of length 2l is fixed. The other end is held level with it and then let go. If the weight of the whole chain is W, find the tension at the lowest point when the free end has dropped a distance x. Also find the the tension at the fixed end when the whole chain has just become straight. Explain how it is possible for this to be greater than W. In a time the free end drops a distance and so a length near the lowest point of the chain, which was moving at velocity at the beginning of , comes to rest at the end of . Since the weight of a length is . It loses momentum ( to the first order) in a time Therefore momentum is destroyed at the following rate:-
- A Pile Driver has a hammer of weight W an it is used to drive a pile of weight w. The hammer is dropped a distance H and the pile is driven a distance h. Find the average resistance of the ground, assuming that the pile and hammer have the same velocity after the impact. Calculate the loss of energy at the impact.
The velocity of the hammer just before impact is . If the velocity of the hammer and pile after impact is v then by the principle of the conservation of Momentum.