# A Level Maths: Forces In Two Dimensions

**Introduction**

What we are going to look at in this article is a few examples that involve forces along a rough horizontal plane as well as look at how we can solve problems where the plane is an inclined slope.Â

In order to understand the questions it is going to be taken that you understand how to resolve forces parallel and perpendicular to the plane whether an object is travelling horizontally or whether an object is moving on an inclined plane.Â

As part of **A Level Maths Mechanics **you must understand how forces work and how to apply them when writing down the equations of motion.Â

We will look at three examples that show you the various different stages and the working that you need to be able to show clearly. As always, you need to make sure that you produce a clear force diagram.Â

## Example

To answer this question the first thing that you need to do is to draw a force diagram. It does not need to be a work of art, but it needs to be clear and it needs to show all the appropriate forces that are acting on the object.Â

There are two parts to the question. The first part requires you to determine the acceleration of the object. To do this you need to apply F = ma and the standard convention is to take the right as the positive direction.Â

\begin{aligned} F=m a & \\ 45 \cos 50-8 & =8 a \\ a & =\frac{45 \cos 50-8}{8} \\ & =2.62 \mathrm{~ms}^{-2} \end{aligned}Now that we have the acceleration we can now determine the distance that has been travelled. This can be done using an appropriate SUVAT equation.Â

\begin{aligned} & u=0 \quad t=5 \quad a=2.62 \quad s=s \\ & s=u t+\frac{1}{2} a t^2 \\ & =\frac{1}{2}(2.62)(5)^2=32.75 \mathrm{~m} \end{aligned}## Example

In this question we now have an object that is on an inclined slope. Again a force diagram is needed.Â