Three uniform blocks are at rest side-by-side on a horizontal frictionless floor

Question

Three uniform blocks are at rest side-by-side on a horizontal frictionless floor. The outer blocks have equal masses, while the interior block's mass is different from the other two. Between each pair of blocks is a loaded massless spring. One of the springs unloads, sending two blocks in one direction and one block in the other. Then the second spring unloads, and the result is that the center block is left stationary while the outer blocks continue to move apart. Which of the following conclusions can be drawn about the status of the three block system after both springs have unloaded? a. The outer blocks are moving at the same speed, and the system center of mass is at rest at the center of the middle block. b. The outer blocks are moving at the same speed, and the system center of mass is moving. c. The outer blocks are not moving at the same speed, and the system center of mass is at rest at the center of the middle block. d. The outer blocks are not moving at the same speed, and the system center of mass is moving. e. None of the above.

Explanation / Answer

The correct choice is a)

let the mass of two equal blocks as "m" and middle block as "M"

when the first spring unlocks,

using conservation of momentum

0 = (m + M) V - m v

mv = (m + M) V                             V = speed of two blocks combination moving to left , v = speed of other block

when the second spring unlocks, using conservation of momentum

(m + M) V = mv'

from the two equations

mv' = mv

v' = v

hence two blocks moves at same speed

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