A body initially at rest explodes into three fragments of masses m, 2m and 3m. The m-fragment moves with velocity (12, 0) m/s and the 2m-fragment moves with velocity (0, 6) m/s. If the speed of the 3m-fragment is 4√N m/s, find N.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
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Question

A body initially at rest explodes into three fragments of masses m, 2m and 3m. The m-fragment moves with velocity (12, 0) m/s and the 2m-fragment moves with velocity (0, 6) m/s. If the speed of the 3m-fragment is 4√N m/s, find N.

Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum

G1 Physics · Accepted Answer

Since the body was initially at rest, total initial momentum is zero. Momentum of the first fragment is p₁ = m(12, 0) = (12m, 0). Momentum of the second fragment is p₂ = 2m(0, 6) = (0, 12m). Therefore p₃ = −(p₁+p₂) = (−12m, −12m). Its magnitude is |p₃| = 12m√2. Since the third fragment has mass 3m, its speed is v₃ = 12m√2/(3m) = 4√2 m/s. Hence N = 2.