State Newton's second law of motion in the form of an equation relating force, mass and acceleration.
(Total for Question 1 is 1 mark)
2
A resultant force of 12 N acts on a particle of mass 3 kg. Find the acceleration of the particle.
(Total for Question 2 is 1 mark)
3
A particle of mass 2 kg rests in equilibrium on a horizontal table. Take g = 9.8 m/s2. Find the normal reaction between the particle and the table.
(Total for Question 3 is 1 mark)
4
Two forces, of magnitude 8 N and 5 N, act on a particle in the same direction along a straight line. Find the magnitude of the resultant force.
(Total for Question 4 is 1 mark)
5
A box of mass 6 kg is pushed along smooth horizontal ground by a horizontal force of 18 N. Find the acceleration of the box.
(Total for Question 5 is 2 marks)
6
Two forces of magnitude 20 N and 8 N act on a particle of mass 3 kg in opposite directions along the same straight line. Find the acceleration of the particle.
(Total for Question 6 is 2 marks)
7
A block of mass 5 kg rests on rough horizontal ground. The coefficient of friction between the block and the ground is 0.2. Take g = 9.8 m/s2. Find the maximum possible friction force before the block slips.
(Total for Question 7 is 2 marks)
8
A block of mass 10 kg rests in equilibrium on a smooth plane inclined at 25 degrees to the horizontal, held by a light inextensible string parallel to the line of greatest slope. Take g = 9.8 m/s2. Find the tension in the string, giving your answer to 3 significant figures.
(Total for Question 8 is 2 marks)
9
A block of mass 6 kg rests in equilibrium on a smooth plane inclined at 40 degrees to the horizontal, held by a light inextensible string parallel to the line of greatest slope. Take g = 9.8 m/s2. Find the normal reaction between the block and the plane, giving your answer to 3 significant figures.
(Total for Question 9 is 2 marks)
10
A particle of mass 3 kg hangs in equilibrium, suspended from a fixed point by a light inextensible string. Take g = 9.8 m/s2. Find the tension in the string.
(Total for Question 10 is 1 mark)
11
A car of mass 1000 kg experiences a driving force of 2400 N and a constant resistance force of 400 N as it moves along a straight horizontal road. Find the acceleration of the car.
(Total for Question 11 is 2 marks)
12
Two blocks A (mass 4 kg) and B (mass 2 kg) are connected by a light inextensible string and lie on smooth horizontal ground. A horizontal force of 18 N pulls block A, with B connected behind it, so both move with the same acceleration. Find the acceleration of the system.
(Total for Question 12 is 2 marks)
13
Two blocks connected by a light inextensible string move with acceleration 3 m/s2. Block B, of mass 2 kg, has no horizontal force acting on it other than the tension in the string. Find the tension in the string.
(Total for Question 13 is 2 marks)
14
State what is meant by modelling a string in mechanics as "light".
(Total for Question 14 is 1 mark)
15
A particle of mass 4 kg is pulled along rough horizontal ground by a horizontal force of 30 N. The resistance to motion is modelled as a constant frictional force of magnitude 0.25 times the normal reaction between the particle and the ground. Take g = 9.8 m/s2. Find the acceleration of the particle.
(Total for Question 15 is 3 marks)
16
A lift, of total mass 850 kg including passengers, accelerates upwards at 0.6 m/s2. Take g = 9.8 m/s2. Find the tension in the lift cable.
(Total for Question 16 is 3 marks)
17
Particles A and B, of mass 6 kg and 2 kg respectively, are connected by a light inextensible string which passes over a smooth fixed pulley. The particles hang at rest on either side of the pulley and are released from rest. Take g = 9.8 m/s2. Find the acceleration of the system and the tension in the string.
(Total for Question 17 is 4 marks)
18
A block of mass 8 kg rests on a rough plane inclined at 30 degrees to the horizontal. The coefficient of friction between the block and the plane is 0.3. A force P, acting parallel to the plane and directed up the line of greatest slope, is applied to the block so that it is on the point of sliding up the plane. Take g = 9.8 m/s2. Find the value of P, giving your answer to 3 significant figures.
(Total for Question 18 is 4 marks)
19
A particle P of mass 4 kg moves on a smooth horizontal plane under the action of two constant forces, F1 = (5i - 2j) N and F2 = (1i + 6j) N, where i and j are perpendicular unit vectors in the plane. Given that P starts at rest, find the speed of P after 3 seconds, giving your answer to 3 significant figures.
(Total for Question 19 is 4 marks)
Mark scheme · M2D Mechanics: Forces and Newton's Laws: Fluency and Exam Drill
Question 1
B1 F = ma
Answer: F = ma
Question 2
B1 4 cao
Answer: 4 m/s2
Question 3
B1 19.6 cao
Answer: 19.6 N
Question 4
B1 13 cao
Answer: 13 N
Question 5
M1 use F = ma with F=18, m=6
A1 3 m/s2 cao
Answer: 3 m/s2
Question 6
M1 resultant force = 20 - 8 = 12 N
A1 4 m/s2 cao
Answer: 4 m/s2
Question 7
M1 friction = μ R with R = mg = 5(9.8) = 49
A1 9.8 N cao
Answer: 9.8 N
Question 8
M1 resolve parallel to the plane: T = mg sin25
A1 awrt 41.4 N
Answer: 41.4 N (3 s.f.)
Question 9
M1 resolve perpendicular to the plane: R = mg cos40
A1 awrt 45.0 N
Answer: 45.0 N (3 s.f.)
Question 10
B1 29.4 cao
Answer: 29.4 N
Question 11
M1 resultant force = 2400 - 400 = 2000, then a = 2000/1000