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 35.0 N/m. When he pulls the slingshot back 0.445 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?

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? O They Are Equal O Increased Pullback Distance O Increased Spring Constant

Explanation / Answer

As spring potential energy, P.E. = 0.5*k*x2

Where k = spring constant

x = distance by which spring is pulled from non stretched position.

And as per requirement

0.5*k*x2 = 17

0.5*k*(0.445)2 = 17

k = 171.695 N/m

Hence spring constant must be increased by 171.695/35 = 4.9056 times

Also if he want to stretch it more then, let x’ is the distance by which it is stretched and

0.5*k’*x’2 = 17

x’2 = 34/35

x’ = 0.9856 m

Hence he must pull the slingshot back, 0.9856/0.445 = 2.215 times.

In first case force, F = kx = 171.695*0.445 = 76.404 N

In second case force, F = kx = 35*0.0.9856 = 34.496 N

So he has to pull harder for increased spring constant case.

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