Block A in the figure below has a mass m A = 4.00 kg, and block B has a mass m B

Question

Block A in the figure below has a mass mA = 4.00 kg, and block B has a mass mB = 7.00 kg. The blocks are forced together, compressing a spring S between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block B acquires a speed of 1.70 m/s

(a) What is the final speed of block A?
____ m/s

(b) How much potential energy was stored in the compressed spring?
____J

Explanation / Answer

Here ,

a) as there is no external force in the system

let the speed of block A is

mA * vA - mB * vB = 0

4 * vA - 7 * 1.70 = 0

vA = 2.975 m/s

the final speed of block A is 2.975 m/s

b)

using conservation of energy

potential energy in spring = kinetic energy of blocks A and B

potential energy in spring = 0.5 * 4 * 2.975^2 + 0.5 * 7 * 1.7^2

potential energy in spring = 27.81 J

the potential energy in spring is 27.81 J

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