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 0.375 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 22.0 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? factor of spring constant increase: 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? factor of pullback distance increase: In which of the two scenarios does Tom have to pull harder? they are equal increased pullback distance increased spring constant

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Chapter1: Units, Trigonometry. And Vectors
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**Educational Content: Physics Problem on Elastic Potential Energy with a Slingshot**

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 0.375 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 22.0 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?

**Factor of Spring Constant Increase:** [Input Field]

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?

**Factor of Pullback Distance Increase:** [Input Field]

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

- [ ] They are equal
- [ ] Increased pullback distance
- [ ] Increased spring constant

**Explanation of Diagrams or Graphs:**

There are no diagrams or graphs included in the text to explain. This scenario focuses on theoretical calculations related to spring constants and potential energy formulas.
Transcribed Image Text:**Educational Content: Physics Problem on Elastic Potential Energy with a Slingshot** 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 0.375 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 22.0 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? **Factor of Spring Constant Increase:** [Input Field] 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? **Factor of Pullback Distance Increase:** [Input Field] In which of the two scenarios does Tom have to pull harder? - [ ] They are equal - [ ] Increased pullback distance - [ ] Increased spring constant **Explanation of Diagrams or Graphs:** There are no diagrams or graphs included in the text to explain. This scenario focuses on theoretical calculations related to spring constants and potential energy formulas.
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