A-Level CAIE Mathematics A2 4.1 Forces and equilibrium Question Bank

A block B of mass 2.7 kg is pulled at constant speed along a straight line on a rough horizontal floor. The pulling force has magnitude 25 N and acts at an angle of $\theta$ above the horizontal. The normal component of the contact force acting on B has magnitude 20 N .

Coplanar forces of magnitudes $7 \mathrm{~N}, 6 \mathrm{~N}$ and 8 N act at a point in the directions shown in the diagram. Given that $\sin \alpha=\frac{3}{5}$, find the magnitude and direction of the resultant of the three forces.

Three coplanar forces of magnitudes $F \mathrm{~N}, 20 \mathrm{~N}$ and 30 N act at a point P, as shown in the diagram. The resultant of the three forces acts in a direction perpendicular to the force of magnitude $F \mathrm{~N}$. Find the value of F.

A block is at rest on a rough horizontal plane. The coefficient of friction between the block and the plane is 1.25 .

A particle of mass 2 kg is initially at rest on a rough horizontal plane. A force of magnitude 10 N is applied to the particle at $15^{\circ}$ above the horizontal. It is given that 10 s after the force is applied, the particle has a speed of $3.5 \mathrm{~m} \mathrm{~s}^{-1}$.

A particle P of mass 0.3 kg is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point X. A horizontal force of magnitude $F \mathrm{~N}$ is applied to the particle, which is in equilibrium when the string is at an angle $\alpha$ to the vertical, where $\tan \alpha=\frac{8}{15}$ (see diagram). Find the tension in the string and the value of F.

A small block of weight 5.1 N rests on a smooth plane inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha=\frac{8}{17}$. The block is held in equilibrium by means of a light inextensible string. The string makes an angle $\beta$ above the line of greatest slope on which the block rests, where $\sin \beta=\frac{7}{25}$ (see diagram). Find the tension in the string.

A block B of mass 7 kg is at rest on rough horizontal ground. A force of magnitude $X \mathrm{~N}$ acts on B at an angle of $15^{\circ}$ to the upward vertical (see diagram).

Four horizontal forces act at a point O and are in equilibrium. The magnitudes of the forces are $F \mathrm{~N}$, $G \mathrm{~N}, 15 \mathrm{~N}$ and $F \mathrm{~N}$, and the forces act in directions as shown in the diagram.

A small ball B of mass 4 kg is attached to one end of a light inextensible string. A particle P of mass 3 kg is attached to the other end of the string. The string passes over a fixed smooth pulley. The system is in equilibrium with the string taut and its straight parts vertical. B is at rest on a rough plane inclined to the horizontal at an angle of $\alpha$, where $\cos \alpha=0.8$ (see diagram). State the tension in the string and find the normal component of the contact force exerted on B by the plane.