Finding initial speed of block

Question

A 350 g block moving vertically upward colllides with a light verticle spring and compresses it 4.50 cm before coming to rest. If the spring constant is 50.0 N/m what was the initial speed of the block?

The correct answer is 1.8 m/s I just can't get the right eqaution to get the right answer.

Answer 1

First, find the energy stored in the spring, (which came from the kinetic energy of the block):

U = 0.5 * k * x^2

U = 0.5 * 50 * 0.045^2

U = 0.050625 J

Now find the work done on the block by gravity over the same 4.5cm distance:

W = mgh

W = 0.35 * 9.81 * 0.045

W = 0.1545075 J

The kinetic energy of the block immediately before compressing the spring is:

KE = U + W

KE = 0.050625 + 0.1545075

KE = 0.2051325 J

Therefore:

KE = 0.5 * m * v^2

0.2051325 = 0.5 * 0.35 * v^2

v^2 = 1.1721857...

v = 1.082675

v = 1.08 m/s

You said the answer is 1.8 m/s, however I'm not so sure it is. Did you miss a 0 out, or is 1.8 the answer that someone else got?

Incidentally, the velocity would be 1.8 m/s at a point 6 cm below the spring.