The figure below shows a two-ended \"rocket\" that is initially stationary on a

Question

The figure below shows a two-ended "rocket" that is initially stationary on a frictionless floor, with its center at the origin of an x axis. The rocket consists of a central block C (of mass M = 6.00 kg) and blocks L and R (each of mass m = 2.60 kg) on the left and right sides. Small explosions can shoot either of the side blocks away from block C and along the x axis. Here is the sequence: (1) At time t = 0, block L is shot to the left with a speed of 3.60 m/s relative to the velocity that the explosion gives the rest of the rocket. (2) Next, at time t = 0.80 s, block R is shot to the right with a speed of 3.60 m/s relative to the velocity that the explosion gives to block C?

(a) What is the velocity of blockCatt= 2.80 s?

(b) What is the position of blockC's center at that time?

Explanation / Answer

at t=0, V(c+r) + Vl = 3.6 also, (M+m)V(c+r) = mVl MV(c+r) +mV(c+r) = m(3.6-V(c+r)) 6V + 2.6V = 9.36 - 2.6V V = 0.836 m/s to right Vl = 2.764 m/s to left at t=0.8 s, Vr-Vc = 3.6 8.6 x 0.836 = 6Vc + 2.6Vr 7.2 = 6Vc+2.6(3.6+Vc) 8.6Vc = - 2.16 Vc = - 0.2511 m/s Vr = 3.355 m/s a)Vc at 2.8 s = 0.2511 m/s towards left b) Vcm = [(-2.764+3.355)2.6 - 6x0.2511]11.2 = 0 (approx)

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