A 4.0-kg block and a 2.0-kg block are connected to opposite ends of a relaxed sp

Question

A 4.0-kg block and a 2.0-kg block are connected to opposite ends of a relaxed spring of spring constant 300 N/m. The blocks are pushed toward each other for 0.5 s. The 4.0-kg block is pushed with a force of 50 N , and the 2.0-kg block is pushed with a force of 20 N. Ignore the inertia of the spring.

Part A

What is the acceleration of the center of mass of the two-block system while this pushing is going on? Assume that the positive direction is from 4.0-kg block to2.0-kg block.

Part B

When the blocks are released, what is the velocity of the 0.20-kg block if the 4.0-kg block is moving toward it at 2.0 m/s in the Earth reference frame? Assume that the positive direction is from 4.0-kg block to 2.0-kg block.

Explanation / Answer

A) 50 N is from 4kg to 2kg

and 20N is from 2kg to 4kg

Fnet = 50 - 20 = 30 N

a = Fnet / m = 30 / (4+2) = 5 m/s^2

B) velocity of centre of mass after 0.5 s

v = u + at = 0. + 5x0.5 = 2.5 m/s

Vcm = m1v1 + m2v2 / (m1+m2)

2.5 = [ 4x2 + 2v ] / 6

8 + 2v = 15

v = 3.5 m/s

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