How Is Work Done by a Spring Calculated?

[brunettegurl]

work done by the spring URGENT! pls. help

Homework Statement

An ideal spring is hung vertically from the ceiling. When a 2.0 kg mass hangs at rest from it, the spring us extended 6.0 cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10 cm. while the spring is being extended by the forxe, the work done by the spring is?

Homework Equations

Ws=o.5kx^2
Fs=kx
Weight=mg

The Attempt at a Solution

so first i found k of the string by equating mg=kx with x=0.06 m where i got a value of 326.67 N/m. then i used Ws=o.5kx^2 with delta x=0.1m and tried to solve for work and my answer is coming out wrong. The answer is supposed to be -3.6 J ..i'm not getting that or close to it..pls help

 

[LowlyPion]

You need to account for the potential energy in the spring already as a result of the initial weight hanging on it don't you?

 

[brunettegurl]

aare you saying that i should use this equation W=o.5kx^2 +mg where x=0.1 and k=326.67N/m

 

[LowlyPion]

aare you saying that i should use this equation W=o.5kx^2 +mg where x=0.1 and k=326.67N/m

No. I'm saying that the work that goes into increasing the potential energy in the spring is from .06 to .16, not from .00 to .10.

 

[brunettegurl]

i'm sorry but I'm really confused by what you mean wouldn't delta x= 0.1[0.16-0.06] ? or do you mean that when I'm solving for k value in the equation mg=kx my x should actually be the difference between 0.06-0.16 and not 0.06?

 

[LowlyPion]

Remember that

W = F*d

but in this case it's

W = ∫ F_x dx = ∫ -k*x dx

and your limits are from .06 to .16

This comes out to W = -1/2*k*x² from .06 to .16 or

W = -1/2*k*(.16² - .1²)

 

[LowlyPion]

i'm sorry but I'm really confused by what you mean wouldn't delta x= 0.1[0.16-0.06] ? or do you mean that when I'm solving for k value in the equation mg=kx my x should actually be the difference between 0.06-0.16 and not 0.06?

You have the correct value of k by the way, so that's not the issue.

 

[brunettegurl]

ok but then would the k value still be right as i used x=0.06 m?? because i used this equation W = -1/2*k*(.16^2 - .1^2) with the k value of 326.67 N and still am not getting the right answer

 

[LowlyPion]

Sorry. I typed it wrong.

1/2*k*(.16² - .06²)

Is what it should be.

 

[brunettegurl]

i'm getting -2.54J

W=-0.5*(326.67N)(0.16^2-0.1^2)
W=-0.5*(326.67)(0.0156)
W=-2.548026 J

 

[brunettegurl]

ok yea now I'm getting the answer thank you so much :)