# Homework Help: 2 blocks and a spring

1. Aug 9, 2015

### naianator

1. The problem statement, all variables and given/known data
A system consists of two blocks, of masses m and 2m, attached to the ends of a massless spring with a force constant k. The system is placed on a horizontal frictionless surface. Initially, the spring is relaxed. The blocks are then pulled apart an “extra” distance x and simultaneously released from the state of rest.

Find the speed v1 of the block of mass m at the instant the spring is relaxed again. Answer in terms of m, k, and x.

2. Relevant equations
U_spring = 1/2*k*x^2
K = 1/2*m*v^2
m_1*v_1+m_2*v_2 = m_1*v_1' + m_2*v_2'

3. The attempt at a solution
Momentum is conserved and initially 0 so

m*v_1 = 2m*v_2

and

v_1 = 2v_2

Potential energy in the compressed spring is equal to 1/2*k*x^2 and when the spring reaches equilibrium the potential is 0 and the kinetic energy is equal to 1/2*m*v_1^2+1/2*(2m)*(2v_1)^2 so

1/2*k*x^2 = 1/2*m*v_1^2+4*m*v_1^2

= k*x^2 = m*v_1^2+8*m*v_1^2

= k*x^2 = 9*m*v_1^2

and finally

v_1 = sqrt(k*x^2/(9*m))

Where am I going wrong?

2. Aug 9, 2015

### olivermsun

If $v_1 = 2v_2$, then why is $\frac{1}{2}kx^2 = \frac{1}{2} mv_1^2+4mv_1^2$?

3. Aug 9, 2015

### AlephNumbers

You substituted 2v1 for v2.

4. Aug 9, 2015

### naianator

Yes!!! Thank you