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Problem_of_the_Week_4_Sol

# Problem_of_the_Week_4_Sol - Problem of the Week#4 Solution...

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Problem of the Week #4 Solution A spring has a relaxed length of 12 cm. You suspend it vertically and hang a 35 gram mass from it, and you observe that with the mass hanging motionless the spring is 19 cm long. You then pull down on the mass until the spring is 22 cm long and you release the mass without giving it any initial speed. a. How long does it take the mass to make a round trip, up and back down? System: mass + spring, Surroundings: Earth When the mass is hanging motionless with the spring length 19 cm, the system is in equilibrium. Therefore the momentum of the mass-spring system is zero, and the rate of change of the mass-spring system is zero as well. With the mass-spring system motionless, the Momentum Principle gives: ! ! p = ! F net ! t = 0 Therefore the net force must equal zero. This is essentially a one-dimensional problem, so we need only consider the y-direction. ! F net = 0,( k ! y " Mg ),0 = 0,0,0 where k is the spring constant and Δ y is the displacement of the spring from its

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Problem_of_the_Week_4_Sol - Problem of the Week#4 Solution...

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