[20 points] The Figure below shows a two-ended \"rocket\" that is initially stat

Question

[20 points] 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 2.00 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. 2. Here is the sequence: (1) At time t 0, block L is shot to the left with a speed of 3.0 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 3.00 m/s relative to the velocity that block C then has. Att 2.80s What are the velocity of block C and the position of its center? a. b.

Explanation / Answer

2. given M = 6 kg

m = 2 kg

i. at t = 0, L is shot from the left with u = 3 m/s relative to the velocity of the rest of the rocket

ii. at t = 0.8 s, R is shot to the right with u = 3 m/s relative to the velocity of block C

a. so, let speed of block C at t = 0 after explosion be v1

then

in inertial frame

speed of u towards left = (u - v1)

speed of C towards right = v1

hence from conservation of momentum

m(u - v1) = (M + m)v1

2(3 - v1) = 8v1

v1 = 0.6 m/s to the right

position of the C at t = 0.8 s, r = 0.6*0.8 = 0.48 m

now, after second explosion, speed of C = v2 to the left

speed of R = u to the right wrt to the C

hence

from in inertial frame

speed of R = (u - v2)

hence from conservationfo momentum

6v2 = 2(3 - v1)

v2 = 0.8 m/s to the left

position of center at this time = 0.48 m

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