Block A has mass 1.00 kg, and block B has mass 3.00 kg. The blocks are forced to

Question

Block A has mass 1.00 kg, and block B has mass 3.00 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. The spring has force constant 733 N/m and is initially compressed 0.225 m from its original length.

A) What is the acceleration of block A just after the blocks are released?

B) What is the acceleration of block B just after the blocks are released?

C) What is the final speed of block A after the blocks leave the spring?

D) What is the final speed of block B after the blocks leave the spring?

Explanation / Answer

A) just after release ,

force due to spring = kx

so a = F /m = kx/m

so acc. of block A = aA = (733 x 0.225) / (1) = 164.92 m/s^2

B) acc. of block B = aB = (733 x 0.225) / (3) = 54.97 m/s^2

C) momentum of system will be conserved.

initial = final momentum

0 = - 1 vA   + 3vB

vA =3vB

Using energy conservation,

initial energy = final energy

kx^2 /2 = mA vA^2 /2   + mB vB^2 /2

733 x 0.225^2 /2 = 1 ( vA^2) /2    +    3(vA / 3)^2 /2

37.11 = vA^2 + vA^2 /3

vA = 5.28 m/s

D) vB = vA/3 = 1.76 m/s

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