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 0.235 m from a nonstretched 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?

Explanation / Answer

Part A

Current potential energy = 0.5 * k * x2 = 0.5 * 35 * 0.235 * 0.235 = 0.966 J

He needs = 17 J

Let new spring constant be a

0.5 * a *  0.235 * 0.235 = 17

a = 615.66 N/m

Therefore, he needs to increase the spring constant by a factor of = 615.66 / 35 = 17.5

Part B

let new elongation be b

0.5 * 35 * b2 = 17

b = 0.98 m

Therefore, he sholud pull further by 0.98 / 0.235 times or 4.19 times

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.