3 blocks shown are identical. A & C are moving together at 12 m/s. B is at rest when A hits B as shown. Collision is perfectly inelastic. The friction coefficient between A & C is same as that between B and C and is equal to 0.2. Finally C is on top of B and all are moving together with same speed. What is the length of each block (in m) ? Ground is smooth.
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pi = pf
= m × 12 × 2 = 3 mv
v = 8 m/s
m × 12 = 2mv1
v1 = 6 m/s
Just after collision, C moves with 12 m/s but A and B move with 6 m/s. So friction acts between them
mac = –µmg
2maB+A = +µmg
ac = –µg, aA+B = +µg/2
finally, vrel = 0
02 = urel2 + 2arel srel
02 = 62 – 2 × 3 × ℓ
ℓ = 6m