A-level · Forces & Newton's laws

Resolving forcesExam-style questions

Splitting a force at an angle into two perpendicular components, F cosθ and F sinθ — to add forces in any directions and to solve equilibrium by resolving in two perpendicular directions.

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16 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
[In this question $\mathbf{i}$ and $\mathbf{j}$ are horizontal unit vectors.]

A particle $P$ of mass $5$ kg is free to move on a smooth horizontal surface. The only horizontal forces acting on $P$ are

$\mathbf{F}_1 = (7\mathbf{i} - 4\mathbf{j})\text{ N} \qquad \mathbf{F}_2 = (-11\mathbf{i} + 9\mathbf{j})\text{ N} \qquad \mathbf{F}_3 = (-4\mathbf{i} + 10\mathbf{j})\text{ N}$
(a) Find the magnitude of the acceleration of $P$ .

(4 marks)

The force $\mathbf{F}_3$ is now removed, and the force $\mathbf{F}_4 = (2p\mathbf{i} - p\mathbf{j})$ N, where $p$ is a constant, is applied to $P$ in its place.

The resultant of $\mathbf{F}_1$ , $\mathbf{F}_2$ and $\mathbf{F}_4$ is parallel to the vector $(5\mathbf{i} - \mathbf{j})$ .
(b) Find the value of $p$ .

(4 marks)
Level 3 · 8 marksTry it
2
Figure 1 (not accurately drawn)

A tree trunk is dragged along horizontal ground by two tractors. Each tractor is attached to the trunk by a horizontal chain, and both chains are fixed to the trunk at the same point.

The trunk moves in a straight line. Figure 1 shows the tension in each chain and the angle, $30°$ or $\alpha°$ , that each chain makes with the direction of motion of the trunk. The two chains are on opposite sides of the line along which the trunk moves.

The trunk is modelled as a particle.
(a) Find the value of $\alpha$

(3 marks)

The trunk has mass $1.2$ tonnes. As it moves, the trunk is subject to a constant resistance of magnitude $3600$ N from the ground.
(b) Find the acceleration of the trunk.

(4 marks)
Level 3 · 7 marksTry it
3
A particle of weight $50$ N hangs in equilibrium, held by a horizontal force $P$ and a light string at $60^\circ$ to the horizontal with tension $T$ . Find $T$ and $P$ , to 3 s.f.
Level 3 · 4 marksTry it
4
Forces of $8$ N due east and $6$ N due north act on a particle. Find the magnitude and bearing (from east) of the resultant.
Level 3 · 3 marksTry it
5
A force of $30$ N acts on a box at $20^\circ$ above the horizontal. Find the component of the force in the horizontal direction, to 3 s.f.
Level 3 · 2 marksTry it

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