Work done by a spring on a block when released from 14cm?

AI Thread Summary
A block attached to a spring is pulled to different positions and released, prompting a calculation of the work done by the spring as the block moves. The spring constant, k, is derived from the force required to hold the block at a certain position. The work done by the spring is calculated using the formula W=1/2k(xi^2 - xf^2). It’s crucial to ensure all measurements are in consistent SI units to avoid errors in calculations. The user discovered they had made a mistake with unit conversions, resulting in an incorrect answer by factors of ten.
rockchalk1312
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A block is attached to a spring which is attached to a stationary wall. When the block is pulled out to x = +5.0 cm, we must apply a force of magnitude 370 N to hold it there. We pull the block to x = 14.0 cm and then release it. How much work does the spring do on the block when the block moves from xi=+6.0 cm to (a)x= +3.0 cm, (b)x=-3.0 cm, (c)x=-6.0 cm, and (d)x=-10.0 cm?

Fs=-kd
Ws=1/2kxi2-1/2kxf2

Tried to find k by doing 370=-k(5)=-74
but then plugging this into:
W=1/2kxi^2-1/2kxf^2
W=1/2k(6^2)-1/2k(3^2)
W=18k-4.5k
W=13.5k
W=(13.5)(74)=999

This was definitely not the right answer. How do you go about finding k, or do you have to do something differently since the block was originally released from 14cm? Thank you!
 
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Make sure all your numbers are in the same system of units.
 
rockchalk1312 said:
A block is attached to a spring which is attached to a stationary wall. When the block is pulled out to x = +5.0 cm, we must apply a force of magnitude 370 N to hold it there. We pull the block to x = 14.0 cm and then release it. How much work does the spring do on the block when the block moves from xi=+6.0 cm to (a)x= +3.0 cm, (b)x=-3.0 cm, (c)x=-6.0 cm, and (d)x=-10.0 cm?

Fs=-kd
Ws=1/2kxi2-1/2kxf2

Tried to find k by doing 370=-k(5)=-74
but then plugging this into:
W=1/2kxi^2-1/2kxf^2
W=1/2k(6^2)-1/2k(3^2)
W=18k-4.5k
W=13.5k
W=(13.5)(74)=999

This was definitely not the right answer. How do you go about finding k, or do you have to do something differently since the block was originally released from 14cm? Thank you!

Be careful with units. The distance is 5 cm. If the problem is expecting an answer in Nm, then you must make sure everything is in SI units, which means converting distances to m. Of course, if you did the rest of it right, then your answer should be in N*cm, which means it should only have been off by some factors of ten. :wink:
 
cepheid said:
Of course, if you did the rest of it right, then your answer should be in N*cm, which means it should only have been off by some factors of ten. :wink:

I was off by two factors of ten. Thank you very much!
 

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