a knife of mass m is at a height x from a large wooden block . the knife is allowed to fall freely , strikes the block and comes to rest after penetrating distance y . find the work done by the block to stop the knife
Answers
Knife stops at a depth of y (the level where total energy can be assumed = 0) inside the block,
total p.e stored in the object = mg(x + y)------------------------> [ h = x + y)]
potential energy lost as it falls to reach the surface of the wooden block = mgx ---------------------> [p.e = mgh, h = height]
distance it penetrates is y
this loss in p.e is all converted to kinetic energy till the moment the penetration begins in the block.
once the penetration begins the k.e = mgx is spent in doing negative work (loss of energy) against the deaccelerating force of the block.
once it comes to rest the object has lost all its k.e(mgx) and a further mgy of p.e.
due to law of conservation of energy total energy lost = negative work done against the wooden block deaccelerating force.
=> mg(x +y) = negative work.
Hence the work done by wooden block to stop knife is - mg(x +y)
Answer: -mg(x+y)
Explanation:
