Two particles A and B, of mass 3 kg and 5 kg respectively, are attached to the ends of a light inextensible string. The string passes over a small smooth pulley which is fixed to a ceiling. The particles hang with the string taut and the hanging parts of the string vertical, as shown in the diagram. The system is released from rest.
Find the acceleration of A.
Find the tension in the string.
Find the magnitude of the force exerted on the pulley by the string.
6 marks
Show answer
a) 2.45 m s-2b) 36.8 Nc) 73.5 N
2
A car of mass 1000 kg tows a trailer of mass 400 kg along a straight horizontal road using a light horizontal tow bar. The engine of the car produces a driving force of 2500 N. The resistances to motion are constant forces of 300 N on the car and 200 N on the trailer, as shown in the diagram.
Find the acceleration of the car and trailer.
Find the tension in the tow bar.
State how you have used the modelling assumption that the tow bar is light.
6 marks
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a) 1.43 m s-2b) 771 Nc) The tension is the same at both ends of the tow bar (its mass is ignored)
3
Two boxes A and B, of mass 6 kg and 4 kg respectively, rest side by side in contact on a smooth horizontal floor. A horizontal force of magnitude 30 N is applied to A, pushing it into B, as shown in the diagram. The boxes move together.
Find the acceleration of the boxes.
Find the magnitude of the force exerted on B by A.
4 marks
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a) 3 m s-2b) 12 N
4
A particle A of mass 2 kg rests on a smooth horizontal table. It is attached to one end of a light inextensible string. The string passes over a small smooth pulley fixed at the edge of the table, and its other end is attached to a particle B of mass 1.5 kg which hangs freely. A is 1.5 m from the pulley and B is 0.9 m above the floor, as shown in the diagram.
The system is released from rest with the string taut.
Find the acceleration of A and the tension in the string.
Find the speed of B as it hits the floor.
B does not rebound.
Find the time from the moment B hits the floor until A reaches the pulley.
9 marks
Show answer
a) 4.2 m s-2, 8.4 Nb) 2.75 m s-1c) 0.218 s
5
A particle P of mass 4 kg lies on a rough horizontal table. P is attached to one end of a light inextensible string which passes over a small smooth pulley fixed at the edge of the table. The other end of the string is attached to a particle Q of mass 3 kg which hangs freely below the pulley. The part of the string between P and the pulley is horizontal.
The system is released from rest with the string taut. As P moves, the table exerts a constant resistance of magnitude 12 N on P, as shown in the diagram.
Find the acceleration of P.
Find the tension in the string.
Find the magnitude and direction of the resultant force exerted on the pulley by the string.
8 marks
Show answer
a) 2.49 m s-2b) 21.9 Nc) 31.0 N at 45° below the horizontal, towards P
6
Two particles P and Q have masses 1.2 kg and m kg respectively. They are attached to the ends of a light inextensible string which passes over a small smooth peg. The particles hang freely with the string taut and the hanging parts of the string vertical.
The system is released from rest and Q moves downwards with acceleration 2.8 m s−2.
Find the tension in the string.
Show that m = 2.16
Find the magnitude of the force exerted on the peg by the string.
State where in your working you have used the fact that the peg is smooth.
7 marks
Show answer
a) 15.1 Nb) m = 2.16 (shown)c) 30.2 Nd) The tension is the same on both sides of the peg
7
A car of mass 1200 kg is towing a trailer of mass 600 kg along a straight horizontal road. The car and trailer are joined by a light rigid horizontal tow bar. The resistances to motion are constant forces of 400 N on the car and 200 N on the trailer.
The car and trailer are moving at 20 m s−1 when the driver applies the brakes. The brakes produce a constant braking force of F N on the car only. The car and trailer come to rest in a distance of 80 m.
Find the deceleration of the car and trailer.
Find the value of F.
Find the magnitude of the force in the tow bar and state whether it is a tension or a thrust.
Explain why the trailer could not have been towed with a rope during the braking.
8 marks
Show answer
a) 2.5 m s-2b) F = 3900c) 1300 N, a thrustd) A rope cannot push (exert a thrust), so it would go slack
8
A particle A of mass 3 kg is attached to one end of a light inextensible string. The string passes over a small smooth fixed pulley and its other end is attached to a scale pan of mass 1 kg. A block B of mass 2.5 kg rests in the scale pan, as shown in the diagram. The hanging parts of the string are vertical.
The system is released from rest.
Find the acceleration of A.
Find the tension in the string.
Find the magnitude of the force exerted on the scale pan by B.
8 marks
Show answer
a) 0.754 m s-2b) 31.7 Nc) 22.6 N
9
A lift of mass 400 kg is raised and lowered by a vertical cable. A parcel of mass 8 kg rests on the floor of the lift. At one moment the normal reaction of the floor on the parcel has magnitude 70 N.
Find the magnitude and direction of the acceleration of the lift at this moment.
Find the tension in the cable at this moment.
Ella says the lift must be moving downwards. Explain why she may be wrong.
7 marks
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a) 1.05 m s-2 downwardsb) 3570 Nc) It could be moving upwards and slowing down
10
A car of mass 900 kg tows a boat trailer of mass 600 kg along a straight horizontal road using a light inextensible horizontal tow rope. The resistances to motion are constant forces of 250 N on the car and 350 N on the trailer. The car and trailer start from rest and accelerate at 0.8 m s−2.
Find the driving force produced by the engine of the car.
Find the tension in the tow rope.
After 10 seconds the tow rope breaks. The driving force and the resistances do not change.
Find the distance travelled by the trailer from the moment the rope breaks until it comes to rest.
Find the distance travelled by the car in the same time.
9 marks
Show answer
a) 1800 Nb) 830 Nc) 54.9 md) 272 m
11
Particles A and B, of mass 2 kg and 3 kg respectively, are attached to the ends of a light inextensible string which passes over a small smooth fixed pulley. The particles hang with the string taut and the hanging parts vertical. B is 1.5 m above the ground, as shown in the diagram. The system is released from rest.
Find the tension in the string while both particles are moving.
Find the speed of B as it reaches the ground.
B does not rebound. A does not reach the pulley.
Find the greatest height of A above its starting position.
Find the time from release until A reaches its greatest height.
9 marks
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a) 23.5 Nb) 2.42 m s-1c) 1.8 md) 1.48 s
12
Amara, of mass 60 kg, stands on a set of bathroom scales on the floor of a lift. The scales measure the normal reaction on Amara, in newtons. The lift has mass 640 kg, including the scales, and is moved by a vertical cable.
The lift starts from rest and moves upwards. It accelerates uniformly to a speed of 3 m s−1 in 2 seconds, travels at 3 m s−1 for 5 seconds, then decelerates uniformly to rest in 3 seconds.
Find the reading on the scales during each of the three stages.
Find the greatest tension in the cable during the journey.
Find the total distance travelled by the lift.
9 marks
Show answer
a) 678 N, 588 N, 528 Nb) 7910 Nc) 22.5 m
Every question here is original and written by Robinson Tuition. It follows the Edexcel AS specification and suits AQA and OCR AS maths too; this is not an exam-board paper.