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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.65.0 N/m. When he pulls the slingshot back 0.235 m0.235 m from a nonstretched position, it just does not 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 J.17.0 J. 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 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?

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.65.0 N/m. When he pulls the slingshot back 0.235 m0.235 m from a nonstretched position, it just does not 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 J.17.0 J. 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 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?

check_circleAnswer
Step 1

Given:

Spring constant of the spring = 65 N/m

Required elastic potential energy = 17 J

Initial stretch in the length of the spring = 0.235 m

Step 2

Calculating how many time more he should stretch in o...

Required elastic potential energy, P.E=k*
=17J
Susbtitute k
65 N/m
(65N/m)xx17J
34J
- 0.523
65N/ m
= f0.523 = 0.723m
Initial stretch in the spring = 0.235 m
0./253.07 3
0.235
Required ratio
That means he must strecth 3 times more than he stretched
in the beginning in order to achieve desired elastie energy
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Required elastic potential energy, P.E=k* =17J Susbtitute k 65 N/m (65N/m)xx17J 34J - 0.523 65N/ m = f0.523 = 0.723m Initial stretch in the spring = 0.235 m 0./253.07 3 0.235 Required ratio That means he must strecth 3 times more than he stretched in the beginning in order to achieve desired elastie energy

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