Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
A small block of mass $1.25\,\text{kg}$ rests on a horizontal surface. Three horizontal forces, with the magnitudes and directions shown in the diagram, act on the block. The angle $\theta$ is such that $\cos\theta = 0.28$ and $\sin\theta = 0.96$. A horizontal frictional force also acts on the block, and the block is in equilibrium.
(a)[4]
Show that the magnitude of the frictional force is $7.5\,\text{N}$ and state the direction of this force.
(b)[2]
Given that the block is in limiting equilibrium, find the coefficient of friction between the block and the surface.
(c)[3]
The force of magnitude $6.1\,\text{N}$ is now replaced by a force of magnitude $8.6\,\text{N}$ acting in the same direction, and the block begins to move. Find the magnitude and direction of the acceleration of the block.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolving forces in the $x$ or $y$ direction” …