In the figure, a block is moving at an initial speed of v0 along a horizontal frictionless surface toward an ideal spring attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of x.
Find the block's speed v as a fraction of its initial speed when it has compressed the spring only 82.3% of the maximum distance. Fill in the missing factor below.
[Hint: Start by solving the full compression" problem to find the spring constant. Then use conservation of energy to solve the partial compression" problem.]
v = _______ v0