Two masses (combined m=8kg) are placed on a vertical spring, compressed by a dis

Question

Two masses (combined m=8kg) are placed on a vertical spring, compressed by a distance of ?y=0.2m. The spring is released, and the masses are launched upwards, reaching a maximum height of 12m above the equilibrium position of the spring. (In this problem, equilibrium of the spring refers to equilibrium with the masses on the spring) a) (5 pts) What is the spring constant (k) of the spring? b) (5pts) What is the velocity of the masses as they leave the spring? c) (5 pts) Using the work-energy principle and your answer for (b), calculate the work done on the masses by the spring. d) (5pts) Calculate the work done by gravity on the masses from the time they leave the spring to the time they reach the peak of their trajectory. e) (5pts) Suppose I catch one of the masses (which weighs 2kg) at the top of its trajectory. The other mass falls back onto the spring. How much is the spring compressed by the remaining mass?

Explanation / Answer

F = kx, F = mg kx= mg k = 392 b) 1/2mv^2 = mgh .5*8*v^2 =8*9.8*12 v= 15.33 c) work done on the masses = 392*.2 = 78.4J

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