Force diagrams, resultant forces, F = ma on a single particle, weight, normal reaction, tension, motion on a rough or smooth surface with a given friction force.
12 original questions, 84 marks. 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 4 kg lies on a smooth horizontal floor. The box is pulled along the floor by a constant horizontal force of magnitude 18 N, as shown in the diagram. The box is modelled as a particle.
Find the acceleration of the box.
Find the magnitude of the normal reaction, R N, between the box and the floor.
The box starts from rest. Find the time it takes to reach a speed of 9 m s−1.
5 marks
Show answer
a) 4.5 m s-2b) 39.2 Nc) 2 s
2
Two forces F1 = (3i − 2j) N and F2 = (−5i + 6j) N act on a particle P of mass 0.5 kg. No other forces act on P.
Find the resultant force acting on P.
Find the acceleration of P, giving your answer in the form (ai + bj) m s−2.
Find the magnitude of the acceleration of P.
5 marks
Show answer
a) (-2i + 4j) Nb) (-4i + 8j) m s-2c) 4√5 = 8.94 m s-2
3
A crate of mass 25 kg rests on a horizontal floor. A light rope is attached to the top of the crate and the rope is held vertical, as shown in the diagram. The tension in the rope is T N.
When T = 80 the crate stays at rest on the floor. Find the normal reaction between the crate and the floor.
The tension is increased to 300 N and the crate rises vertically. Find the acceleration of the crate.
The crate starts from rest. Find the speed of the crate when it has risen 1.5 m.
6 marks
Show answer
a) 165 Nb) 2.2 m s-2c) 2.57 m s-1
4
A car of mass 1200 kg starts from rest on a straight horizontal road. The engine of the car produces a constant driving force of 3000 N and the total resistance to the motion of the car is modelled as a constant force of magnitude 840 N.
Find the acceleration of the car.
Find the speed of the car after 8 seconds.
After 8 seconds the engine is switched off. The resistance to motion is unchanged.
Find the distance the car travels from the moment the engine is switched off until it comes to rest.
7 marks
Show answer
a) 1.8 m s-2b) 14.4 m s-1c) 148 m
5
Two forces F1 = (2i + 3j) N and F2 = (ci − 5j) N, where c is a constant, act on a particle P of mass 1.5 kg. No other forces act on P.
The acceleration of P is in the direction of the vector (2i − j).
Find the value of c.
Find the magnitude of the acceleration of P.
Find the angle between the direction of the acceleration of P and the vector i.
7 marks
Show answer
a) c = 2b) 2.98 m s-2c) 26.6°
6
A particle P of mass 2 kg is at rest in equilibrium under the action of three forces F1 = (6i − 2j) N, F2 = (−3i + 5j) N and F3.
Find F3 in the form (ai + bj) N.
The force F3 is now removed. Forces F1 and F2 continue to act on P.
Find the magnitude of the acceleration of P.
Find the distance travelled by P in the first 4 seconds after F3 is removed.
7 marks
Show answer
a) (-3i - 3j) Nb) 2.12 m s-2c) 17.0 m
7
Nadia pulls a sledge of mass 15 kg along horizontal snow using a horizontal rope. The tension in the rope is 60 N and the resistance to motion is a constant force of magnitude F N, as shown in the diagram.
The sledge starts from rest and reaches a speed of 3 m s−1 after moving 5 m.
Find the acceleration of the sledge.
Find the value of F.
When the speed of the sledge is 3 m s−1, Nadia lets go of the rope.
Find how much further the sledge travels before it comes to rest.
State one modelling assumption you have made about the rope.
8 marks
Show answer
a) 0.9 m s-2b) F = 46.5c) 1.45 md) The rope is light (or inextensible), so the tension is the same throughout
8
A small stone of mass 0.4 kg is released from rest at a height of 1.6 m above the surface of a pond. The stone falls vertically. Air resistance may be ignored.
Show that the stone hits the surface of the water with speed 5.6 m s−1.
In the water the stone continues to move vertically downwards and the water exerts a constant resistance of magnitude 2.6 N on the stone. The pond is 3 m deep.
Find the speed of the stone when it reaches the bottom of the pond.
Suggest one way in which the model for the resistance of the water could be refined.
7 marks
Show answer
a) v = 5.6 m s-1 (shown)b) 7.15 m s-1c) Let the resistance depend on the speed of the stone
9
A van of mass m kg moves along a straight horizontal road. The engine produces a constant driving force of 2400 N and the resistance to motion is a constant 600 N. The speed of the van increases from 8 m s−1 to 20 m s−1 in 15 seconds.
Show that m = 2250
When the van is moving at 20 m s−1 the engine is switched off and the brakes are applied. The van comes to rest in a distance of 50 m. The total force resisting the motion while the van brakes is modelled as a constant force of magnitude R N.
Find the value of R.
Find the time it takes the van to stop.
7 marks
Show answer
a) m = 2250 (shown)b) R = 9000c) 5 s
10
A hot-air balloon, together with its basket and passengers, has a total mass of 450 kg. The balloon is moving vertically downwards with a constant acceleration of 0.4 m s−2. The air exerts a constant vertical upward force of magnitude L N on the balloon. Air resistance is ignored.
Find the value of L.
To slow the descent, the crew throw out a bag of sand of mass m kg. The balloon then moves with a constant upward acceleration of 0.3 m s−2. The upward force on the balloon is still L N.
Find the value of m.
State how you have used the modelling assumption that the balloon is a particle.
7 marks
Show answer
a) L = 4230b) m = 31.2c) All the forces act at a single point (no turning, size ignored)
11
Two forces (3i + 2j) N and (λi − 8j) N, where λ is a constant, act on a particle Q of mass 2 kg. No other forces act on Q. The resultant of the two forces has magnitude 10 N.
Find the two possible values of λ.
Given that λ > 0,
find the magnitude of the acceleration of Q,
find the angle between the acceleration of Q and the vector i.
Q starts from rest.
Find the speed of Q after 3 seconds and the distance it has travelled in that time.
9 marks
Show answer
a) λ = 5 or λ = -11b) 5 m s-2c) 36.9° (below i)d) 15 m s-1, 22.5 m
12
A crane lifts a crate of mass 300 kg vertically using a light inextensible cable. The crate starts from rest on the ground. It accelerates uniformly at 0.5 m s−2 for 4 seconds, then moves at constant speed for 10 seconds, then decelerates uniformly, coming to rest after a further 3 seconds.
Find the tension in the cable during each of the three stages of the motion.
Find the height of the crate above the ground when it comes to rest.
The cable will break if the tension in it exceeds 3200 N. Find the greatest upward acceleration the crane can give the crate.
9 marks
Show answer
a) 3090 N, 2940 N, 2740 Nb) 27 mc) 0.867 m s-2
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.