A block of mass m=0.1 kg is connected to a spring of unknown spring constant k

• Work Energy

A block of mass m=0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance (x/2) from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity 3 ms^-1. The total initial energy of the spring is:

1. 1.5 J
2. 0.6 J
3. 0.3 J
4. 0.8 J

Solution

Apply principle of conservation of momentum and energy

Momentum before collision = momentum after collision

0.1u + m*0 = 0.1*0 + m*3

½*0.1*u² = ½*m*3²

Solving these two equations, u = 3

½kx² = ½k(x/2)² + ½*0.1*3²

3/4 kx² = 0.9

½kx² = 0.6 J

The correct option is B.