Blocks and Spring: Two blocks, one with mass 1.00 kg and the other with mass 3.0
ID: 776483 • Letter: B
Question
Blocks and Spring: Two blocks, one with mass 1.00 kg and the other with mass 3.00 kg, are forced together, compressing a spring 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 a force constant of 720 N/m and initially compressed 0.225 m from its original length. For each block, what is (a) the acceleration just after the blocks are released; (b) the final speed after the blocks leave the spring? [LO 21, LO 25, LO 34, LO 38, LO 39, LO 46, LO 48)Explanation / Answer
Given,
m1 = 1 kg ; m2 = 3 kg ; k = 720 N/m ; x = 0.225 m
a)We know that,
F = kx ; F = ma
ma = kx => a = kx/m
a1 = 720 x 0.225/1 = 162 m/s^2
Hence, a1 = 162 m/s^2
a2 = 720 x 0.225/3 = 54 m/s^2
Hence, a2 = 54 m/s^2
b)from conservation of energy
1/2 m v^2 = 1/2 k x^2
v = x sqrt (k/m)
v1 = 0.225 sqrt(720/1) = 6.04 m/s
v2 = 0.225 sqrt(720/3) = 3.49 m/s
Hence, v1 = 6.04 m/s ; v2 = 3.49 m/s