Question

A block is attached to an ideal spring. The spring is laid out horizontally along the x-axis, and the block is on a frictionless surface. When the block is at x = 0, the spring is at its natural length. The block is given an initial kinetic energy of 9.00 J, when the block is at x = 0, with the initial velocity directed in the positive x-direction. That kinetic energy is enough to cause the block to move out to x = +d before reversing direction. How much kinetic energy would the block have to have at x = 0 for the reversal of direction to occur at x = +2d, instead of x = +d? _______ J

Answer 1

Answer:

K = 36 J

Explanation:

In this exercise we must use the conservation of mechanical energy at two points at initial x = 0 and the end point of maximum compression of the spring

Initial x = 0

    Em₀ = K = ½ m v²

Final point of maximum compression

    $Em_{f}$ = Ke = ½ k x²

    Em₀ = $Em_{f}$

    K = ½ k x²

We put the kinetic energy because it is a data, let's look for the spring constant

     k = 2 K / x²

     k = 2 9 / d²

     k = 18 / d²

Let's calculate the kinetic energy, so that the compression is x = 2d

    K = ½ k x²

    K = ½ (18 / d²) (2d)²

    K = ½ 18/d²  4d²

    K = 36 J