Hooke's Law Work Done - What is the equation W = F(average) * extension? Watch

vector12
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I used E = 1/2fx and multiplied that by 5 to get it for all 5 springs.

And for their method of W = F(average) * X, why do they divide 60N of force by 2?
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username3460126
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im only in yr10 and we've learnt that to calculate work its force x distance
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Joinedup
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(Original post by vector12)
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I used E = 1/2fx and multiplied that by 5 to get it for all 5 springs.

And for their method of W = F(average) * X, why do they divide 60N of force by 2?
Did you get the right answer by a reasonable method? (E=1/2 kx2) would also be a reasonable method.

The markscheme isn't a model answer - I think in this instance the markscheme is showing an unusual method of calculation that should also receive full marks... but IMO it would always be better to use the appropriate well known formula like
1/2 kx2 because that's what the examiner will be expecting to see.
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uberteknik
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(Original post by vector12)


And for their method of W = F(average) * X, why do they divide 60N of force by 2?
The extension of the spring is proportional to the applied force.

Work done = force x distance (provided the force remains constant throughout the distance travelled). i.e. work done is the area under a graph of force vs distance.

With the spring (and Hookes law), the force does not remain constant as the spring extends. i.e. both extension and force start at zero and as force increases, so does the extension.

Hence we must use the "average force" applied throughout the extension.

To visualise this, plotting a graph of force vs extension (within the linear portion of extension), produces a straight line of constant gradient.

We still need the area which is a the same as \frac{1}{2} base \text { x } height

Using axes labels Work = \frac{1}{2} extension \text{ x }force

which is exactly the same as writing:

W = \frac{force}{2} \text{ x }extension


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