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.

 

[kerimek]

Your attempt at a solution is correct, but there may be a mistake in your calculation. The correct answer for maximum velocity is indeed 3.42 m/s. You can double check your calculation to ensure that you are using the correct values for m, k, x, and v. Additionally, make sure you are converting all units to the correct form (e.g. kg to m/s^2). If you are still getting a different answer, please provide your calculations so I can help identify any errors.