Work Done by Spring Homework: Solve Equations for W

[McAfee]

Homework Statement

A spring with a spring constant of 10 N/cm has a cage attached to one end (Fig. 7-53). Taking rightward as the positive direction, (a) how much work does the spring force do on the cage when the spring is stretched from its relaxed length by 7.6 mm? (b) How much additional work is done by the spring force when the spring is stretched by an additional 7.6 mm?

Homework Equations

W= -(½)*k*(d)^2

The Attempt at a Solution

First, I changed the units.
d=.0076m
k=1000 N/m

For

a) W = ½*1000*x0.0076² = 0.02888 J


b) W = ½*1000*(0.0152² - 0.0076²) = 0.08664 J

I know that I did the right work but I am still wrong. Does the answer have to be negative? But the problem states that the right is positive. I can't find my mistake.

 

[McAfee]

any help?

 

[PeterO]

Homework Statement

A spring with a spring constant of 10 N/cm has a cage attached to one end (Fig. 7-53). Taking rightward as the positive direction, (a) how much work does the spring force do on the cage when the spring is stretched from its relaxed length by 7.6 mm? (b) How much additional work is done by the spring force when the spring is stretched by an additional 7.6 mm?

Homework Equations

W= -(½)*k*(d)^2

The Attempt at a Solution

First, I changed the units.
d=.0076m
k=1000 N/m

For

a) W = ½*1000*x0.0076² = 0.02888 J


b) W = ½*1000*(0.0152² - 0.0076²) = 0.08664 J

I know that I did the right work but I am still wrong. Does the answer have to be negative? But the problem states that the right is positive. I can't find my mistake.

While stretching the spring to the right, you have done a positive amount of work. All that time the spring has been pulling to the left, so the spring force has been doing negative work.

 

[McAfee]

While stretching the spring to the right, you have done a positive amount of work. All that time the spring has been pulling to the left, so the spring force has been doing negative work.

Thanks a lot for helping making this clear for me.

 

[asteriatic]

Your calculations for work done by the spring force are correct. However, the answer for part (a) should be negative because the displacement is in the opposite direction of the force. In this case, the force is being applied in the positive direction (rightward) but the displacement is in the negative direction (leftward). Therefore, the work done by the spring force is negative, indicating that energy is being transferred from the system to the surroundings.

For part (b), the additional work done by the spring force should be positive because both the force and displacement are in the same direction (rightward). This means that energy is being transferred from the surroundings to the system.

Overall, it is important to pay attention to the direction of the force and displacement when calculating work done. The negative sign indicates the direction of energy transfer.