After being released, the restoring force exerted by the spring performs
1/2 (5200 N/m) (0.090 m)² = 12.06 J
of work on the block. At the same time, the block's weight performs
- (0.260 kg) <em>g</em> (0.090 m) ≈ -0.229 J
of work. Then the total work done on the block is about
<em>W</em> ≈ 11.83 J
The block accelerates to a speed <em>v</em> such that, by the work-energy theorem,
<em>W</em> = ∆<em>K</em> ==> 11.83 J = 1/2 (0.260 kg) <em>v</em> ² ==> <em>v</em> ≈ 9.54 m/s
Past the equilibrium point, the spring no longer exerts a force on the block, and the only force acting on it is due to its weight, hence it has a downward acceleration of magnitude <em>g</em>. At its highest point, the block has zero velocity, so that
0² - <em>v</em> ² = -2<em>gy</em>
where <em>y</em> is the maximum height. Solving for <em>y</em> gives
<em>y</em> = <em>v</em> ²/(2<em>g</em>) ≈ 4.64 m
