A block of mass m moves between two springs on a horizontal tabletop. The spring

Question

A block of mass m moves between two springs on a horizontal tabletop. The spring on the left has a strength constant of kl, and the spring on the right has a strength constant of kr. The legs on the left and right sides of the table are a distance d apart.

a) assuming that there is no friction between the block and the table top, if we compress the spring on the left by an amount (Delta x) by pushing the block against it and subsequently release the block, by how much will it compress the spring on the right?

b) How would your answer to (a) change if we repeat this activity with a block and a table between which the coefficient of kinetic friction is equal to Uk?

c) How would your answer to (b) change if we sawed  length of y off of the legs on the left side of the table

Explanation / Answer

a) when there is no friction

    1/2*kl*x^2 = 1/2*kr*y^2

    thus, y = (kl/kr)^1/2 * x

b) In case of friction, energy will be lost due to friction, W = Uk*m*g*d

   1/2*kl*x^2 = Uk*m*g*d + 1/2*kr*y^2

thus, y = {(1/2*kl*x^2 - Uk*m*g*d)*2/kr}^1/2

c) If length of leg is sawed on left, then kinetic energy would be converted to potential energy because the right side is on higher elevation, so the compression in spring would be further reduced.

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