A vertical ideal spring is mounted on the floor and has a springconstant of 124

Question

A vertical ideal spring is mounted on the floor and has a springconstant of 124 N/m. A 0.50-kg block is placed on the spring in twodifferent ways. (a) In one case, the block isplaced on the spring and not released until it rests stationary onthe spring in its equilibrium position. Determine the amount(magnitude only) by which the spring is compressed.(b) In a second situation, the block is releasedfrom rest immediately after being placed on the spring and fallsdownward until it comes to a momentary halt. Determine the amount(magnitude only) by which the spring is now compressed.

Explanation / Answer

(a) When stationary, the spring force holds up the block F=-kx=mg where k is the spring constant, x is the compression, m the mass,and g=9.8ms-2 . x = -mg/k x = -0.0395 m So the magnitude is 3.95 cm (b) Here we use conservation of energy Ei = (1/2)kxi2 +mgxi Ef = (1/2)kxf2 +mgxf There is no kinetic energy at the start as it is released fromrest. For Ef , the block is momentarily stationary, sokinetic energy is again zero. xi = 0 Ei = 0 so (1/2)kxf2 = -mgxf or (1/2)kxf = -mg or xf = -2mg/k therefore xf = -0.0790 the magnitude now is 7.9cm Notice how it oscillates about the position found in (a)

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