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 55.0 N / m . When he pulls the slingshot back 0.235 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 . 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

Answer 1

Answer:

He needs to increase the spring constant by a factor of 11.2

Explanation:

Given the present spring constant of k = 55N/m and stretching distance of x = 0.235m, he must make a slingshot of new spring constant if he must achieve his goal of aiming for 17J slingshot.

E = 1/2×kx²

k= 2E /x² = 2×17/(0.235)² = 34/0.0552 = 616N/m

This new value for I compare to the old one is 616/55 = 11.2

So the new slingshot must have a spring constant 11.2 time as great as the former one.