1a)A block of mass, m, is pushed up against a spring, compressing it a distance

Question

1a)A block of mass, m, is pushed up against a spring, compressing it a distance x, and is then released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v. The same spring projects a second block of mass 4m, giving it a speed 3v. What distance was the spring compressed in the second case?

1b)Initially a body moves in one direction and has kinetic energy K. Then it moves in the opposite direction with three times its initial speed. What is the kinetic energy now?

Explanation / Answer

a)    As, 1/2mv2 = 1/2kx2

=>     9/2 *4m * v2 = 1/2kx'2

=>    36x2 = x'2

=>    distance was the spring compressed in the second case = 6x

b)    the kinetic energy now =   9K

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