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 65.0 N/m. When he pulls the slingshot back 0.305 m from a non-stretched 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 19.5 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? During a follow up conversion. 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? In which of the two scenarios does Tom have to pull harder? They Are Equal Increased Pullback Distance Increased Spring Constant

Explanation / Answer

Total potential energy stored by spring having x displacement from its normal position= 0.5 KX2

A) let the spring constant of new spring be Knew

therefore, 19.5= 0.5 Knew 0.3052

Knew= 419.24 N/m

B) Similarly, spring needs to be stretched by Xnew

Therefore, 0.5*65*Xnew2 = 19.5

Xnew= 0.774 m

C) In both the cases user need to impart same amount of energy= 19.5J

Therefore effort required to pull are equal in both the cases

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