What is the maximum velocity of a block in a spring mechanics problem?

[ronaldor9]

Homework Statement

A block of mass m1 = 8 kg hangs from the ceiling on an ideal, massless spring with spring constant k = 65 N/m. With the block hanging on the spring, the total length of the spring is L = 3.5 m. When a second block with an identical mass of m2 = 8 kg is tied to the first with a massless string, the spring stretches an additional h0 = 1.5 m.

The string is cut so that mass m2 falls away. What is the maximum velocity of mass m1?

The Attempt at a Solution

$$\frac{kx^2}{2}=\frac{mv^2}{2}$$
x=1.5 and solving for v gives 4.3
but the answer is 3.42?

 

[tiny-tim]

Hi ronaldor9!

… With the block hanging on the spring, the total length of the spring is L = 3.5 m. When a second block with an identical mass of m2 = 8 kg is tied to the first with a massless string, the spring stretches an additional h0 = 1.5 m.
…
x=1.5 and solving for v gives 4.3
but the answer is 3.42?

1.5 isn't x …

you have to (find and) add on the bit of x that's already in the 3.5.