Two objects of masses m 1 = 0.50 kg and m 2 = 0.86 kg are placed on a horizontal

Question

Two objects of massesm1=0.50kg andm2=0.86kg are placed on a horizontal frictionless surface and a compressed spring of force constantk=270N/m is placed between them as in figure (a) shown below. Neglect the mass of the spring. The spring is not attached to either object and is compressed a distance of9.6cm. If the objects are released from rest, find the final velocity of each object as shown in figure (b). (Let the positive direction be to the right. Indicate the direction with the sign of your answer.)

Explanation / Answer

let the block m1 is compressed by distance 'x'. then the block m2 is compressed by 0.096-x meters.

by conservation of momentum for the two blocks,

0 = m1v1 + m2v2

m1v1 = -m2v2

v1 = 1.732 * v2 <===1

by conservation of energy,

1/2 k x^2 = 1/2 m1v1^2

1/2 k (0.096-x)^2 = 1/2 m2v2^2

x = 0.054m

kx^2 = m1v1^2

v1 = 1.254 m/s

v2 = 0.7244 m/s

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