Forces and Newton's first lawAQA A-Level Maths: Subtopic test

1. 1
   A particle is acted on by two horizontal forces: one of magnitude $12$ N, and one of magnitude $5$ N at right angles to it.

   (a)

   Find the magnitude of the resultant of the two forces.

   [1 mark]

   • A$17$ N
   • B$7$ N
   • C$13$ N
   • D$60$ N

   (b)

   Find the angle between the resultant and the $12$ N force.

   [1 mark]

   • A$22.6^\circ$
   • B$67.4^\circ$
   • C$24.6^\circ$
   • D$45^\circ$

   (c)

   A third force $\mathbf{F}$ is now applied so that the particle moves with constant velocity. Find the magnitude and direction of $\mathbf{F}$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A crate of mass $40$ kg is pulled along level ground by a horizontal rope. The tension in the rope is $150$ N and the crate moves at constant velocity. Take $g=9.8$ m s⁻².

   (a)

   Find the magnitude of the resistance to the motion of the crate.

   [1 mark]

   • A$0$ N
   • B$392$ N
   • C$3.75$ N
   • D$150$ N

   (b)

   Find the magnitude of the normal reaction of the ground on the crate.

   [1 mark]

   • A$150$ N
   • B$392$ N
   • C$542$ N
   • D$9.8$ N

   (c)

   The tension is suddenly increased to $300$ N, with the resistance unchanged. Explain, using Newton's first law, why the crate no longer moves at constant velocity.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle is in equilibrium under the action of three forces $\mathbf{F}_1=(4\mathbf{i}+7\mathbf{j})$ N, $\mathbf{F}_2=(-9\mathbf{i}+2\mathbf{j})$ N and $\mathbf{F}_3$, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.

   (a)

   Find $\mathbf{F}_3$.

   [3 marks]

   (b)

   Find the magnitude of $\mathbf{F}_3$ and the angle that $\mathbf{F}_3$ makes with the $\mathbf{i}$ direction.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle $P$ of weight $60$ N rests in equilibrium on a smooth plane inclined at $30^\circ$ to the horizontal.

   (a)

   (i) Name the three forces acting on $P$ and give the direction of each, given that $P$ is held by a light string parallel to the plane.
   (ii) Find the tension $T$ in the string.

   [6 marks]

   (b)

   The string is now replaced by a light horizontal string, and $P$ remains in equilibrium on the plane. Find the tension $S$ in this string and the normal reaction $R$.

   [6 marks]

   Total for question 4: 12 marks

End of questions