Newton's laws of motionEdexcel International A Level Maths: Subtopic test

1. 1
   A lift of mass $400$ kg carries a passenger of mass $70$ kg. The lift moves vertically upwards with constant acceleration $0.6$ m s⁻² and is supported by a vertical cable. Take $g=9.8$ m s⁻².

   (a)

   Find the magnitude of the resultant force acting on the passenger.

   [1 mark]

   • A$686$ N
   • B$728$ N
   • C$42$ N
   • D$644$ N

   (b)

   Find the normal reaction of the floor of the lift on the passenger.

   [1 mark]

   • A$728$ N
   • B$686$ N
   • C$644$ N
   • D$42$ N

   (c)

   Find the tension in the cable.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A particle $P$ of mass $3$ kg moves on a smooth horizontal plane under the action of two forces, $(5\mathbf{i}-2\mathbf{j})$ N and $(-\mathbf{i}+8\mathbf{j})$ N, only. The vectors $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in the plane.

   (a)

   Find the resultant force on $P$.

   [1 mark]

   • A$(6\mathbf{i}-10\mathbf{j})$ N
   • B$(4\mathbf{i}-6\mathbf{j})$ N
   • C$\left(\frac43\mathbf{i}+2\mathbf{j}\right)$ N
   • D$(4\mathbf{i}+6\mathbf{j})$ N

   (b)

   Find the acceleration of $P$.

   [1 mark]

   • A$(12\mathbf{i}+18\mathbf{j})$ m s⁻²
   • B$\left(\frac43\mathbf{i}+2\mathbf{j}\right)$ m s⁻²
   • C$(4\mathbf{i}+6\mathbf{j})$ m s⁻²
   • D$(4\mathbf{i}+2\mathbf{j})$ m s⁻²

   (c)

   The particle is at rest at time $t=0$. Find the speed of $P$ when $t=3$ s.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A crate of mass $15$ kg is pulled along a horizontal floor by a rope inclined at $30^\circ$ above the horizontal. The tension in the rope is $60$ N and the resistance to the motion of the crate is constant at $20$ N. Model the crate as a particle and take $g=9.8$ m s⁻².

   (a)

   Find the acceleration of the crate.

   [3 marks]

   (b)

   The crate starts from rest. After $5$ s the rope breaks and the resistance remains $20$ N. Find the further distance the crate travels before it comes to rest.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle $P$ of mass $0.5$ kg moves on a smooth horizontal plane under the action of two constant horizontal forces, $(2\mathbf{i}+5\mathbf{j})$ N and $(p\mathbf{i}+q\mathbf{j})$ N, where $p$ and $q$ are constants. The acceleration of $P$ is $(6\mathbf{i}-4\mathbf{j})$ m s⁻². The vectors $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in the plane.

   (a)

   Find the values of $p$ and $q$, and the magnitude of the second force.

   [6 marks]

   (b)

   At time $t=0$ the particle passes through the origin $O$ with velocity $(2\mathbf{i}+3\mathbf{j})$ m s⁻¹. Find the speed of $P$ and its distance from $O$ when $t=4$ s.

   [6 marks]

   Total for question 4: 12 marks

End of questions