A block with a mass m1 = 1.5 kg is pushed by a mass m2 = 1 kg against a spring w

Question

A block with a mass m1 = 1.5 kg is pushed by a mass m2 = 1 kg against a spring with a force constant of k = 750Nm^-1. The blocks are on a frictionless table. The initial compression is 20 cm and the blocks are released at rest at a time t = 0.

a.) What is the period of the motion initially?

b.) At what position (relative to equilibrium) will mass m2 lose contact with m1? (Hint - it will lose contact when Fn = 0)

c.) What is the speed of block m2 as it leaves?

d.) What is the maximum position block m1 stretches to part equilibrium?

Sorry I cannot scan in the picture in.

Explanation / Answer

a)

w = sqrt(k/m) = sqrt(750/(1.5+1)) = 17.321 rad/s

T = 2pi/w = 2*3.1416/17.321 = 0.363 s

b)

at x = 0 m

c)

conservation of energy:

0.5 k x^2 = 0.5 (m1+m2) v^2

==> v = sqrt((k x^2)/(m1+m2)) = sqrt((750*0.20*0.20)/(1+1.5)) = 3.46 m/s

d)

conservation of energy:

0.5 k x^2 = 0.5 m1 v^2

==> x = sqrt((m1 v^2)/(k)) = sqrt(1.5*3.4641*3.4641/750) = 0.155 m

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