Problem 7.28 An unstretched spring has a force constant of 1300 N/m . Part A How

ID: 249113 • Letter: P

Question

Problem 7.28

An unstretched spring has a force constant of 1300 N/m .

Part A

How large a force is required to stretch the spring by 1.8 m from its unstretched length.

Express your answer using two significant figures.

Part B

How much work is required to stretch the spring by 1.8 m from its unstretched length.

Express your answer using two significant figures.

Part C

How large a force is required to stretch the spring by 1.8 m beyond the length reached in part A?

Express your answer using two significant figures.

Part D

How much additional work is required to stretch the spring by 1.8 m beyond the length reached in part A?

Express your answer using two significant figures.

Solution:-

Part A

We know the force F = -kx

k = 1300 N/m and x = 1.8 m

hence F = 1300 * 1.8 =2340 N...........Ans.

Part B.

work done on a spring = 1/2 kx^2

to stretch the spring 1.8 m requires

W=1/2 x 1300N/m x (1.8m)^2 = 2106 J .............Ans.

Part C:-

The force required to stretch to stretch the spring by 1.8 m beyond the length of 1.8 m

F = -k(x2-x1)

F = -1300 * (3.6- 1.8) =2340 N...........Ans.

Part D:-

the spring 3.6 meters requres

W=1/2(1300N/m)(3.6m)^2 = 8424J

the work done in stretching the spring from x=1.8m to x=3.6m is

8424J - 2106J = 6318 J ...........Ans.