An object of mass 2.0 kg is attached to the top of a vertical spring that is anc

Question

An object of mass 2.0 kg is attached to the top of a vertical spring that is anchored to the floor. The unstressed length of the spring is 6.9 cm and the length of the spring when the object is in equilibrium is 4.9 cm. When the object is resting at its equilibrium position, it is given a sharp downward blow with a hammer so that its initial speed is 0.30 m/s. To what maximum height above the floor does the object eventually rise? How long does it take for the object to reach its maximum height for the first time? Does the spring ever become unstressed? What minimum initial speed must be given to the object for the spring to be unstressed at some time?

Explanation / Answer

a) 2*9.81=k*(0.069-0.049) k=981 N/m 0.5*2*0.3^2=0.5*981*x^2 x=1.35 cm distance above the floor=4.9+1.35=6.25 cm b)Time period T=2*pi*sqrt(m/k)=0.283 sec time to reach max height=1.5*T=0.424 sec c)no d)let the speed=v for the spring to be unstressed x=6.9-4.9=2 cm 0.5*2*v^2=0.5*981*0.02^2 v=0.44 m/s

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