Newton's second law, weight and gravityAQA A-Level Maths: Subtopic test

1. 1
   A box of mass $8$ kg is pulled across smooth horizontal ground by a constant horizontal force of $20$ N. The box starts from rest.

   (a)

   Find the acceleration of the box.

   [1 mark]

   • A$2.5$ m s⁻²
   • B$160$ m s⁻²
   • C$0.4$ m s⁻²
   • D$12$ m s⁻²

   (b)

   Find the speed of the box after $4$ s.

   [1 mark]

   • A$80$ m s⁻¹
   • B$6.5$ m s⁻¹
   • C$20$ m s⁻¹
   • D$10$ m s⁻¹

   (c)

   Find the distance travelled by the box in the first $4$ s.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A lift of mass $500$ kg is raised and lowered by a vertical cable. Take $g=9.8$ m s⁻² and ignore air resistance.

   (a)

   Find the tension in the cable when the lift accelerates upwards at $1.2$ m s⁻².

   [1 mark]

   • A$4900$ N
   • B$4300$ N
   • C$5500$ N
   • D$600$ N

   (b)

   Find the tension in the cable when the lift moves upwards at a constant speed of $2$ m s⁻¹.

   [1 mark]

   • A$0$ N
   • B$4900$ N
   • C$1000$ N
   • D$5900$ N

   (c)

   While the lift is moving upwards at $2$ m s⁻¹ the cable snaps. Find the further height the lift rises before it is instantaneously at rest.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle of mass $2$ kg is acted on by two forces $\mathbf{F}_1=(6\mathbf{i}-2\mathbf{j})$ N and $\mathbf{F}_2=(\mathbf{i}+8\mathbf{j})$ N, and no other forces. The vectors $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.

   (a)

   Find the acceleration of the particle.

   [3 marks]

   (b)

   The particle is initially at rest. Find its speed after $5$ s.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A probe of mass $12$ kg is released from rest close to the surface of a planet and falls $20$ m in $5$ s. Air resistance is negligible and the acceleration due to gravity, $g_p$, is constant.

   (a)

   (i) Find $g_p$.
   (ii) Find the weight of the probe on this planet, and state its mass.

   [6 marks]

   (b)

   The probe is raised by a light vertical cable with acceleration $0.5$ m s⁻² on this planet.
   (i) Find the tension in the cable.
   (ii) The cable can safely carry a tension of at most $120$ N. Determine whether it could safely raise the probe with the same acceleration on Earth, where $g=9.8$ m s⁻².

   [6 marks]

   Total for question 4: 12 marks

End of questions