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 "" 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?

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

the answer is a 3.8cm

explanation:

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.