Newton's second law on inclined planes, connected particles with one on a slope, pulleys over the edge of a rough or smooth slope, equilibrium of a particle under several forces.
12 original questions, 91 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
A box of mass 5 kg is pulled up a line of greatest slope of a smooth ramp inclined at 15° to the horizontal. The pulling force has magnitude 40 N and acts parallel to the ramp.
The box is modelled as a particle.
A particle C of weight 20 N hangs in equilibrium from two light inextensible strings AC and BC. The points A and B are on a horizontal ceiling. The string AC makes an angle of 30° with the ceiling and the string BC makes an angle of 60° with the ceiling, as shown in the diagram.
Find the tension in each string.
A particle A of mass 3 kg rests on a smooth plane inclined at 30° to the horizontal. It is attached to one end of a light inextensible string which passes over a small smooth pulley fixed at the top of the plane. The other end of the string is attached to a particle B of mass 2 kg, which hangs freely below the pulley. The part of the string from A to the pulley is parallel to a line of greatest slope, as shown in the diagram.
The system is released from rest with the string taut.
Three horizontal forces act on a particle O, which is in equilibrium. One force has magnitude 10 N and acts due east. A second force has magnitude 7 N and acts in a direction making an angle of 120° with the first force, measured anticlockwise (so it points north of west). The third force has magnitude P newtons.
A rough plane is inclined to the horizontal at an angle α, where tan α = 34. A particle A of mass 4 kg is on the plane and is attached to a light inextensible string. The string passes over a small smooth pulley at the top of the plane, and a particle B of mass 5 kg hangs freely on the other end. The coefficient of friction between A and the plane is 0.25
The system is released from rest with the string taut and A moves up the plane.
A particle A of mass 2 kg is on a rough plane inclined at 20° to the horizontal. The coefficient of friction between A and the plane is 0.2. A is attached to a light inextensible string which passes over a small smooth pulley at the top of the plane. A particle B of mass 3 kg hangs on the other end of the string, 1.5 m above the ground.
The system is released from rest with the string taut. B hits the ground and does not rebound. In the subsequent motion A does not reach the pulley.
A particle A of mass 4 kg rests on a smooth plane inclined at an angle θ to the horizontal. A is attached to a light inextensible string which passes over a small smooth pulley at the top of the plane. A particle B of mass 2.5 kg hangs freely on the other end of the string. The system is in equilibrium.
B is replaced by a particle of mass 3.5 kg and the system is released from rest.
A car of mass 1200 kg tows a trailer of mass 400 kg up a straight road inclined at an angle α to the horizontal, where sin α = 120. The tow bar is light and parallel to the road. The engine produces a driving force of 2400 N. The resistances to motion are 300 N on the car and 100 N on the trailer.
When the speed is 12 m s−1 the tow bar breaks. The resistance on the trailer is unchanged.
A particle A of mass 5 kg is on a rough plane inclined at 30° to the horizontal. The coefficient of friction between A and the plane is 0.4. A is attached to a light inextensible string which passes over a small smooth pulley at the top of the plane. A particle B of mass m kg hangs freely on the other end of the string.
Given that the system is in equilibrium, find the range of possible values of m.
A rough plane is inclined to the horizontal at an angle α, where sin α = 35. A particle A of mass 2m is on the plane and is attached to a light inextensible string which passes over a small smooth pulley P at the top of the plane. A particle B of mass 3m hangs freely on the other end of the string. The part of the string from A to P is parallel to a line of greatest slope. The coefficient of friction between A and the plane is 12
The system is released from rest with the string taut.
Two boxes, A of mass 10 kg and B of mass 6 kg, are joined by a light inextensible rope and are pulled up a line of greatest slope of a rough ramp inclined at 15° to the horizontal. A is higher up the ramp than B, and the rope is parallel to the ramp. A force of magnitude 150 N, parallel to the ramp, acts on A, as shown in the diagram. The coefficient of friction between each box and the ramp is 0.3
The boxes are modelled as particles.
When the boxes are moving at 3 m s−1 the rope breaks.
A fixed wedge has two faces, one inclined at 30° to the horizontal and one inclined at 60° to the horizontal, meeting at a ridge. A small smooth pulley is fixed at the ridge. A particle A of mass 4 kg is on the 30° face and a particle B of mass 6 kg is on the 60° face. They are joined by a light inextensible string which passes over the pulley, with each part of the string parallel to a line of greatest slope of its face, as shown in the diagram.
The 30° face is rough, with coefficient of friction 0.2 between A and the face. The 60° face is smooth.
The system is released from rest with the string taut, and B moves down its face.
After B has moved 1.2 m the string breaks. A does not reach the pulley.
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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.