Mass 2 with an attached rmassless spring sits at rest on a frictionless surface

Question

Mass 2 with an attached rmassless spring sits at rest on a frictionless surface when it is struck by Mass 1. The spring is momentarily compressed, after which the masses separate and move away from each other. Regard this collision as elastic and use the data in the diagram to answer the following questions A) What is the maximum compression of the spring? B) Find the final velocities of each mass after the collision. Do not take the arrows for the final velocities literally. Before: m, = 4kg m2 = 6 kg k = 400 N/m (h); =? After: ( =? Find:() and

Explanation / Answer

A] By momentum conservation, velocity when at maximum conservation,

v = m1vi1/[m1+m2] = 4*5/[4+6] = 2 m/s

By energy conservation, 0.5kx^2 = 0.5m1vi1^2 - 0.5(m1+m2)v^2 = 0.5*4*5^2 - 0.5*10*2^2 = 30

x = sqrt(60/400) = 0.387 m. answer

B] By energy conservation, 0.5*m1*vf1^2 + 0.5*m2*vf2^2 = 50

or 4vf1^2 + 6vf2^2 = 100

also vf1 + vf2 = 5

vf1 = 1 m/s and vf2 = 4 m/s answer

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