Two blocks move towards each other on a frietionless surface, the one on the lef

Question

Two blocks move towards each other on a frietionless surface, the one on the left having a velocity of v-and mass10ky, the one on the right having a velocity of v-13 and mass m 13kg. However the one on the left has a spring attached to it of spring constant 1577. The figure shows the initial configuration of the system in pusple. The blocks in the middle (green and red) are the same two blocks but at a later time. This configuration shows the pring at maximum compression when theyre in contact. What is the initial total momentum? kg m s At the instant when the spring is at maximum compression, the two blocks are moving at the same velocity. What is their velocity at this instant? Since the surface is frictionless, you can assume conservation of momentum m/'s What is the maximum compression from equilibrium of the spring? Assume conservation of energy.

Explanation / Answer

initial momentum

pi = (10 x 6) + (13 x - 13)

pi = -109 kg m/s ..........Ans

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pf = pi

(10 + 13) v = - 109

v = -4.72 m/s ...........Ans

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Applying energy conservation,

KEi + PEi = PEf + KEf

(10 x 6^2 /2 ) + (13 x 13^2 / 2) = (1577) (x^2)/2 + (10 + 13)(4.72)^2 / 2

x = 1.14 m .....Ans

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