Is anybody able to help out with the attached questions please?
OK, for a (i) can you see how the lengths are related, right?
From the diagram you should be able to see that
by equating the distances that get you from the wall to the mass .
ii. &iii. What are the salient features here:
1. The string over the pulley transmits the same tension force, to each mass.
2. The fact that and are connected in this way means they must have the same acceleration.
3. The table is smooth so there's no friction forces on .
So for the mass you must have:
[1]
where is the acceleration due to gravity and is the inertial acceleration. This is from Newton II.
Using Newton II for mass we must have:
[2]
where is the force due to the extension of the spring.
I hope the diagrams should be obvious from the above. As for the pulley the forces you have are the tension acting away from the pulley at each corner and reaction force diagonally outwards from the pulley (at a 45 degree angle to the horizontal).
The only force equation left is that of the spring where:
[3].
Sub [3] into [2] and you get:
[4]
and now add [1] to [4] to give you
,
rearranging this and substituting for y gives us:
.
Hope that was of some help!