Resultant forces and dynamics in a planeEdexcel A-Level Maths: Subtopic test

1. 1
   Two horizontal forces act on a particle: a force of 8 N acting due east and a force of 6 N acting due north.

   (a)

   Find the magnitude of the resultant of the two forces.

   [1 mark]

   • A$10$ N
   • B$14$ N
   • C$2$ N
   • D$48$ N

   (b)

   Find the bearing of the resultant.

   [1 mark]

   • A$037^\circ$
   • B$127^\circ$
   • C$307^\circ$
   • D$053^\circ$

   (c)

   These are the only forces on a particle of mass 4 kg, initially at rest. Find the speed of the particle after 3 s.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two horizontal forces act on a particle: a force of 12 N on a bearing of $060^\circ$ and a force of 5 N on a bearing of $150^\circ$.

   (a)

   Find the magnitude of the resultant of the two forces.

   [1 mark]

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

   (b)

   Find the bearing of the resultant, to the nearest degree.

   [1 mark]

   • A$023^\circ$
   • B$037^\circ$
   • C$083^\circ$
   • D$127^\circ$

   (c)

   A third horizontal force $\mathbf{F}$ is applied so that the particle is in equilibrium. State the magnitude of $\mathbf{F}$ and the bearing on which it acts.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two horizontal forces of magnitudes 20 N and 15 N act on a particle of mass 3 kg, which moves on a smooth horizontal plane. The angle between the lines of action of the two forces is $60^\circ$.

   (a)

   Find the magnitude of the resultant of the two forces.

   [3 marks]

   (b)

   Find the acceleration of the particle and the angle between the resultant force and the 20 N force.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle of mass 5 kg is at rest on a smooth horizontal plane. Three horizontal forces then act on it: 10 N on a bearing of $000^\circ$, 14 N on a bearing of $090^\circ$ and 6 N on a bearing of $210^\circ$.

   (a)

   Find the magnitude of the resultant force and the bearing on which it acts.

   [6 marks]

   (b)

   After 4 s the 6 N force is removed and the other two forces remain unchanged. Find the speed of the particle a further 2 s later.

   [6 marks]

   Total for question 4: 12 marks

End of questions