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 0.515 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 17.0 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?

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?

In which of the two scenarios does Tom have to pull harder?

a.Increased Spring Constant

b.They Are Equal

c.Increased Pullback Distance

Explanation / Answer

elastic potnetial energy U = 0.5 kx^2

U1 = initial elastic potential energy = 0.5 * 65* 0.515^2

U1 = 8.6198 J

so U1/U2 = K1/K2

so K2 = 65 * 17/8.6198

K2 = 128.91

so he has use new K = 128.91 N/m    thta he has increase ( nearlt dounle the spring constnat) so as to acheive his goal

a.Increased Spring Constant

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