Newton's third law, pulleys and connected particlesAQA A-Level Maths: Subtopic test

1. 1
   A car of mass $1200$ kg tows a trailer of mass $400$ kg along a straight, level road, using a light horizontal tow bar. The driving force on the car is $2400$ N. Resistances to motion are negligible.

   (a)

   Find the acceleration of the car and trailer.

   [1 mark]

   • A$2$ m s⁻²
   • B$6$ m s⁻²
   • C$0.67$ m s⁻²
   • D$1.5$ m s⁻²

   (b)

   Find the tension in the tow bar.

   [1 mark]

   • A$2400$ N
   • B$1800$ N
   • C$600$ N
   • D$800$ N

   (c)

   Use Newton's third law to describe the force the trailer exerts on the tow bar.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two particles $A$ and $B$, of masses $3$ kg and $5$ kg, are connected by a light inextensible string that passes over a smooth fixed pulley. The particles hang vertically with the string taut and are released from rest. Take $g=9.8$ m s⁻².

   (a)

   Find the acceleration of the particles.

   [1 mark]

   • A$0.25$ m s⁻²
   • B$2.45$ m s⁻²
   • C$3.92$ m s⁻²
   • D$9.8$ m s⁻²

   (b)

   Find the tension in the string.

   [1 mark]

   • A$36.75$ N
   • B$49$ N
   • C$29.4$ N
   • D$39.2$ N

   (c)

   Find the magnitude and direction of the force exerted by the string on the pulley.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle $P$ of mass $4$ kg lies on a smooth horizontal table. It is connected by a light inextensible string, passing over a smooth pulley at the edge of the table, to a particle $Q$ of mass $6$ kg that hangs freely. The string is taut and $P$ is released from rest. Take $g=9.8$ m s⁻².

   (a)

   Find the acceleration of the particles.

   [3 marks]

   (b)

   Find the tension in the string, and the magnitude of the force the string exerts on the pulley.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle $A$ of mass $2$ kg lies on a smooth plane inclined at $30^\circ$ to the horizontal. It is connected by a light inextensible string, passing over a smooth pulley at the top of the plane, to a particle $B$ of mass $3$ kg that hangs freely. The string is taut and parallel to a line of greatest slope, and the system is released from rest with $B$ moving downwards. Take $g=9.8$ m s⁻².

   (a)

   Find the acceleration of the particles and the tension in the string.

   [6 marks]

   (b)

   $B$ is initially $1.2$ m above the ground and stops when it hits the ground, so the string goes slack. Find how much further up the plane $A$ moves before it first comes to rest. You may assume $A$ does not reach the pulley.

   [6 marks]

   Total for question 4: 12 marks

End of questions