Hooke's Law Work Done - What is the equation W = F(average) * extension? Watch
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.
- Study Helper
And for their method of W = F(average) * X, why do they divide 60N of force by 2?
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
Using axes labels
which is exactly the same as writing: