The figure shows a two-ended The figure shows a two-ended \"rocket\" that is ini

Question

The figure shows a two-ended

The figure 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 = 5.50 kg) and blocks L and R (each of mass m = 2.70 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 2.80 m/s relative to the velocity that the explosion gives the rest of the rocket. (2) Next, at time t = 0.70 s, block R is shot to the right with a speed of 2.80 m/s relative to the velocity that block C then has (after the second explosion). At t = 2.70 s, what are (a) the velocity of block C (including sign) and (b) the position of its center?

Explanation / Answer

a) vL +vC   = 2.80

vL = 2.80 -vC

using momentum conservation,

0 = (5.50 + 2.70) x vC - 2.70vL

2.70 ( 2.80 -vC )   = 8.2vC

vC = 0.694 m/s

after t = 0.70 sec

vR + vCf =2.80

vR = 2.80 - vCf

using momentum conservation,

8.2 x 0.694 = 2.7vR - 5.5vCf

5.69   = 2.7 x (2.80 - vCf) - 5.5vCf

vCf = 0.228 m/s to the left

so v = - 0.228 m/s

b) there is no external force on this system, all forces are internal.

so centre of mass will not move.

final position= initial position = at origin

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