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A.)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 45.0 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 12.0 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? B.)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?

Respuesta :

Answer:

a) 121.19 N/m

b) x = 0.730 m

Explanation:

Given:

Spring constant of the initial slingshot, k = 45.0 N/m

Displacement of the initial spring, x = 0.445 m

Energy required, U = 12.0 J

thus,

a) To achieve the 12.0 J of potential energy, the spring constant for the new spring k' can be calculated as:

U = (1/2)k'x²

on substituting the values, we get

12.0 = (1/2)k'(0.445)²

or

k' = 121.19 N/m

b) For k = 45 N/m and U = 12.0 J

x required will be

12.0 = (1/2) × 45 × (x)²

or

x = 0.730 m

A) The factor that Tom needs to increase the spring constant to hit his potential energy goal is; 2.67

B) The distance that Tom pulled the slingshot back to hit the potential energy goal with the original spring constant is; 0.73 m

A) We are given;

Spring Constant; K = 45 N/m

Distance of spring stretch; x = 0.445 m

The formula for the initial elastic potential energy of the spring is given by:

U = ¹/₂kx²

Thus;

U = ¹/₂ × 45 × 0.445²

U = 4.456 J

We are told that the physics professor "helps" by telling him to aim for an elastic potential energy of 12.0 Joules. To know what factor does Tom need to increase the spring constant to hit his potential energy goal;

Let us make k the subject of the formula;

k = 2U/x²

Thus, at U' = 12 J, we have;

k' = (2 × 12)/0.445²

k' = 121.2 N/m

Thus, factor = k'/k = 121.2/45

factor = 2.67

B) We are told he wants to leave the spring constant unchanged at k = 45 N/m.

Thus; 12 = ¹/₂(45)x²

x² = 24/45

x = √0.5333

x = 0.73 m

Read more at; https://brainly.com/question/13617569

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