A Level Maths: Mechanics Pulley Question
Introduction
We are going to take a look at a question involving mechanics and in particular how to solve a question involving a pulley and to use the equations of motion to help find values such as tension in the string and also the acceleration.
When it comes to questions involving mechanics it is important to make sure that you have a very clear diagram especially if one is not provided to you. If there is a diagram make sure that you are using and you are drawing on any forces as required to help you determine directions and so on.
The Question - Part a)
You can see that the question is worth a total of 11 marks. It is a big question so give yourself plenty of room to work and present your working in a clear manner. Remember you need to be on the side of the examiner.
Part a) of the question is a “show that” question which means that you are not able to use the answer that is given you, you have to derive the answer.
First you should complete all forces on the diagram and any other relevant information.
For the first part of the question in order to determine the value of the acceleration it is important to recognise that you need to use SUVAT.
Look for clues within the question as to what information you can use. For instance the question states that the system is released from rest which means that the initial velocity is zero.
u=0, s=3, t=2.5, a=aThis is the information that we have so the SUVAT equation that can be used is s=u t+\frac{1}{2} a t^2
Substituting the values into the equation we have:
\begin{aligned} & 3=\frac{1}{2} a(2.5)^2 \\ & a=0.96 \mathrm{~ms}^{-2} \end{aligned}
You would have learnt about SUVAT as a part of your year one A Level Maths course. There are several formulas and even though you are more than likely to get them in a formula booklet you should learn them. The reason is because most students tend to use the wrong formula which indicates a lack of understanding. If you know them you have a greater chance of applying the correct formula for the question concerned.
If you are having difficulty with the mechanics component of your A Level maths course then you can consider an A Level Maths Tutor Online who will guide you through the various stages of working through mechanics questions as they can be quite big in terms of the work involved.
The Question - Part b)
In the second part of the question you are asked to determine the mass of block B. The only information that we have is that the mass of block B is less than the mass of block A. This information is important because when the system is released from rest, it is Block B that will fall towards the ground and it is block A that will rise as shown in the diagram.
Knowing this direction is important when writing down the equations of motion i.e F=m a . Applying F=m a to both blocks will give:
\begin{aligned} &2 k g: 2 g-T=2 a\\ &m k g: T-m g=m a \end{aligned}Note that the question is not asking for T (tension), we are only asked to find the unknown mass. Adding the above two equations will cancel out T so we will obtain:
2 g-m g=2 a+m aThe value of a is known, so substituting this in and moving all m terms over to the right we get:
\begin{aligned} &2 g-m g=2(0.96)+0.96 m\\ &2 g-2(0.96)=m g+0.96 m\\ &2 g-2(0.96)=m(g+0.96)\\ &m=\frac{2 g-2(0.96)}{g+0.96}=1.64 \mathrm{~kg} \end{aligned}And this is the required answer.
The Question – Part c)
Here you can say something along the lines of because there is no slack in the string means the acceleration is the same and the tension is also the same throughout.
It is important to have added the necessary information to the question in order to have determined the correct direction for each of the masses. Getting the direction wrong means that the equations of motion will be wrong which means everything else will be wrong.
If you are in year 13 then you will, at the time of writing, be in October half term. We have just completed our first revision courses of the year. Our next courses take place in the Christmas half term holiday where you will have covered much more of the content. You will also be revising for any January 2024 mock exams and our A Level Maths Revision Course over Christmas is the perfect way for you to get ready.
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