Tom has built a large slingshot, but it is not working quite right. He thinks he

Question

Tom has built a large slingshot, but it is not working quite right. He thinks he can model the slingshot like an ideal spring, with a spring constant of 75.0 N/m. When he pulls the slingshot back 0.305 m from a nonstretched position, it just doesn't launch its payload as far as he wants. His physics professor "helps" by telling him to aim for an elastic potential energy of 22.0 Joules. Tom decides he just needs elastic bands with a higher spring constant. By what factor does Tom need to increase the spring constant to hit his potential energy goal? Number During a followup conversation, Tom's physics professor suggests that he should leave the slingshot alone and try pulling the slingshot back further without changing the spring constant. How many times further than before must Tom pull the slingshot back to hit the potential energy goal with the original spring constant? Number In which of the two scenarios does Tom have to pull harder? Increased Pullback Distance Increased Spring Constant They Are Equal

Explanation / Answer

potential energy = (1/2)*Kx^2 = 22

:. (1/2)*K*0.305^2 = 22

:. K = 473

Factor at which he should increase spring constant = 473/75 = 6.30 times

(1/2)*Kx^2 = 22 where k = 75 int this case

:. (1/2)*75*x^2 = 22

:. x = 0.766m

In both the caeses Tom have to pull equally, as the potential energy in poth the cases are same, when the spring constant is less he has to stretch a longer distance and on increasing the spring constant a little bit less.

Therefore they are equal.

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