A spring is compressed with a plunger so that is is 15 cmshorter thanh it is uns

Question

A spring is compressed with a plunger so that is is 15 cmshorter thanh it is unstretched length. When the plunger isreleased it strikes a steel ball transferring all of the energy ofthe spring to the ball. The ball is immediately captured by acup on the end of pendulum arm. The arm swings upward andstops when it reaches an angle of 20 degrees. Assume allenergy of the spring is transferred to the ball and that the balldoes not lose energy as it is captured by the cup. The pendulum andthe cup are much lighter than the ball and their mass can beignored in the problem. If the mass of the ball is 500g what is thespring constant?

Explanation / Answer

I'm assuming we can represent the length of the pendulum's armsymbolically as L since you don't give it in the problem. . All of the energy in the system is potential energy when thependulum reaches it's maximum height. This is the amount ofenergy that would have to have been stored by the spring when itwas compressed 15 cm = .15 m . PE of gravity for an object of mass m held at a heighth: = m*g*h . PE of compressed spring compressed a distance x: 1/2 kx2 . 500g = .5kg . .5 g*h = .5* g*(L - Cos(20)*L) = .5*g*L*(1-Cos(20)) = 1/2 k *.152 . . Solving for the spring constant after equating theenergies, . k = g * L * (1 - Cos(20)) / .152 . L is the length of the pendulum arm, g is the acceleration dueto gravity 9.8 m/s/s L is the length of the pendulum arm, g is the acceleration dueto gravity 9.8 m/s/s

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