A massless spring with spring constant k is placed between a block of mass m and

Question

A massless spring with spring constant k is placed between a block of mass m and a block of mass 3m. Initially the blocks are at rest on a frictionless surface and they are held together so that the spring between them is compressed by an amount D from its equilibrium length. The blocks are then released and the spring pushes them off in opposite directions.

Find the speeds of the two blocks when they detach from the spring.

Express your answers in terms of the variables D, k and m.

v3m,vm=

Item 10 Part A A massless spring with spring constant k is placed between a block of mass m and a block of mass 3m. Initially the blocks are at rest on a frictionless surface and they are held together so that the spring between them is compressed by an amount D from its equilibrium length. The blocks are then released and the spring pushes them off in opposite directions. Find the speeds of the two blocks when they detach from the spring Express your answers in terms of the variables D, k and m , or x" xb b 3m, Um Submit My Answers Give Up

Explanation / Answer

From conservation of momentum

m1u1+m2v2 =m1v1+m2v2

0 = m1v1+3mv2

v2 = -v1/3 ...(1)

From conservation of energy

Potentila enrgy in spring = kinetic energy of blocks

(1/2)kD2 = (1/2)m v12 +(1/2)3m v22

(1/2)kD2 = (1/2)m v12 +(1/2)3m (-v1/3)2

kD2 = 4m v12 /3

v12 = 3kD2/4m

vm =v1 =[3kD2/4m]1/2

From (1) v2 = -v1/3 = -[3kD2/4m]1/2/3

v3m = v2= -[kD2/12m]1/2

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