A. An object of mass 7.7 kg is in equilibrium while connected to a light spring

Question

A. An object of mass 7.7 kg is in equilibrium while connected to a light spring of constant 47 N/m that is fastened to a wall. A second object of mass 4.3 kg is slowly pushed up against mass m1, compressing the spring by the amount 0.12 m. The system is then released, causing both masses to start moving to the right on the
frictionless surface. When m1 is at the equilibrium point (see (3)), m2 loses contact with m1 and moves to the right with speed v. Find the value of v.
Answer in units of m/s. ANSWER: .2375 m/s

B. How far apart are the objects when the spring is fully stretched for the first time? Answer in units of cm.

Explanation / Answer

(1/2) m1 v2 = (1/2) k x12

0.5*7.7*(0.2375)2 = 0.5*47*x12

>>>> x1 = 9.613 cm

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it takes t seconds for the spring stretching:

t = T/4 = (2/)/4 = (2/(k/m))/4 = (/2) * ((m/k))

= (3.14/2) * ((7.7/47))

= 0.635 s

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displacement of the second mass is x2

x2 = v2 * t

     = 0.2375 * 0.635

     = 15.092 cm

>>>> x2 = 15.092 cm

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x2 - x1 = 15.092 - 9.613

           = 5.479 cm

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