Mechanics: Forces and Newton's Laws Depth: Fluency and Exam Drill - Worksheets, Questions and Revision

19 original exam-style questions - 3 pages of questions with a full mark scheme - free printable PDF.

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A-Level · Mechanics

M6D Mechanics: Forces and Newton's Laws Depth: Fluency and Exam Drill

EDEXCEL 9MA0 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Two forces, (3i + 4j) N and (1i - 2j) N, act on a particle. Find the resultant force, giving your answer in the form (π + qj) N.

(Total for Question 1 is 1 mark)

A block of mass 4 kg rests on rough horizontal ground. Take g = 9.8 m/s². Find the normal reaction between the block and the ground.

(Total for Question 2 is 1 mark)

A particle is in limiting equilibrium on a rough plane inclined at angle θ to the horizontal, under gravity alone (no other forces act). State the relationship between the coefficient of friction μ and θ at this angle.

(Total for Question 3 is 1 mark)

Using μ = tan(θ), find the coefficient of friction for a plane inclined at 30 degrees, giving your answer to 3 significant figures.

(Total for Question 4 is 1 mark)

A block of mass 5 kg experiences a normal reaction of 39.2 N and a maximum friction force of 15.68 N. Find the coefficient of friction between the block and the surface.

(Total for Question 5 is 1 mark)

State the direction in which friction acts on a block that is on the point of sliding up a rough inclined plane.

(Total for Question 6 is 1 mark)

A block of mass 6 kg rests on rough horizontal ground and is on the point of sliding when a horizontal force of 18 N is applied. Take g = 9.8 m/s². Find the coefficient of friction between the block and the ground, giving your answer to 3 significant figures.

(Total for Question 7 is 2 marks)

Two forces, (5i - j) N and (-2i + 4j) N, act on a particle of mass 0.5 kg which is initially at rest. Find the magnitude of the acceleration of the particle, giving your answer to 3 significant figures.

(Total for Question 8 is 2 marks)

A particle A of mass 3 kg lies on a smooth horizontal table and is connected by a light inextensible string, passing over a smooth pulley fixed at the edge of the table, to a particle B of mass 2 kg hanging freely. The system is released from rest with the string taut and B descends. Take g = 9.8 m/s². Find the acceleration of the system.

(Total for Question 9 is 2 marks)

A particle A of mass 3 kg lies on a smooth horizontal table and is connected by a light inextensible string, passing over a smooth pulley, to a particle B hanging freely. Given that the acceleration of the system is 3.92 m/s², find the tension in the string by considering particle A alone.

(Total for Question 10 is 2 marks)

A person of mass 70 kg stands on the floor of a lift that is moving downward and decelerating at 1.2 m/s². Take g = 9.8 m/s². Find the normal reaction force exerted on the person by the lift floor.

(Total for Question 11 is 2 marks)

A car of mass 1000 kg tows a trailer of mass 500 kg along a straight horizontal road using a light, rigid tow-bar. The driving force is 3500 N and the total resistance to motion is 500 N. Find the acceleration of the car and trailer.

(Total for Question 12 is 2 marks)

A trailer of mass 500 kg is towed by a car via a light rigid tow-bar, with the system accelerating at 2 m/s². The only horizontal forces on the trailer are the tow-bar force and a resistance of 200 N. Find the force in the tow-bar.

(Total for Question 13 is 2 marks)

A particle P of mass 4 kg is in limiting equilibrium on a rough plane inclined at 22 degrees to the horizontal, under gravity alone. Find the friction force acting on P, giving your answer to 3 significant figures.

(Total for Question 14 is 2 marks)

A block of mass 6 kg rests on rough horizontal ground. The coefficient of friction between the block and the ground is 0.35. A horizontal force of P newtons is applied to the block. Take g = 9.8 m/s². Find the minimum value of P required to make the block start to move, giving your answer to 3 significant figures.

(Total for Question 15 is 3 marks)

A block of mass 8 kg rests on rough horizontal ground. The coefficient of friction between the block and the ground is 0.3. A force of magnitude P acts on the block at an angle of 25 degrees above the horizontal, pulling it so that it is on the point of sliding. Take g = 9.8 m/s². Find the value of P, giving your answer to 3 significant figures.

(Total for Question 16 is 3 marks)

A particle A of mass 4 kg lies on a rough horizontal table, where the coefficient of friction between A and the table is 0.25. A light inextensible string connects A to a particle B of mass 3 kg which hangs freely over a smooth pulley fixed at the edge of the table, with the string between A and the pulley horizontal. The system is released from rest with the string taut and B descends. 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)

A person of mass 75 kg stands on the floor of a lift. The lift is moving downward and decelerating at 2 m/s² as it comes to rest at a floor. Take g = 9.8 m/s². Find the magnitude of the normal reaction force exerted on the person by the lift floor while it is decelerating, and hence find the magnitude of the force that the person exerts on the floor, stating the law used.

(Total for Question 18 is 4 marks)

A block A of mass 4 kg lies on a rough plane inclined at 25 degrees to the horizontal. The coefficient of friction between A and the plane is 0.2. A light inextensible string is attached to A, passes over a smooth pulley fixed at the top of the plane, and hangs vertically down to a block B of mass 6 kg, which hangs freely. The system is released from rest with the string taut, and B moves downward, pulling A up the plane. Take g = 9.8 m/s². Find the acceleration of the system and the tension in the string, giving each answer to 3 significant figures.

(Total for Question 19 is 4 marks)

Mark scheme · M6D Mechanics: Forces and Newton's Laws Depth: Fluency and Exam Drill

Question 1

B1 (4i + 2j) N cao
Answer: (4i + 2j) N

Question 2

B1 39.2 cao
Answer: 39.2 N

Question 3

B1 μ = tan(θ)
Answer: μ = tan(θ)

Question 4

B1 awrt 0.577
Answer: 0.577 (3 s.f.)

Question 5

B1 0.4 cao
Answer: 0.4

Question 6

B1 friction acts down the plane, opposing the impending motion
Answer: Down the plane (opposing the impending motion).

Question 7

M1 R = mg = 58.8, μ = 18/58.8
A1 awrt 0.306
Answer: 0.306 (3 s.f.)

Question 8

M1 resultant force = (3i + 3j) N, then a = resultant/mass = (6i + 6j) m/s²
A1 awrt 8.49 m/s²
Answer: 8.49 m/s² (3 s.f.)

Question 9

M1 whole-system equation: 2g = (3+2)a
A1 3.92 m/s² cao
Answer: 3.92 m/s²

Question 10

M1 equation of motion for A: T = 3a (the table is smooth, so tension is the only horizontal force)
A1 11.76 N cao
Answer: 11.76 N

Question 11

M1 decelerating while moving down means the acceleration is upward: R - mg = ma with a=+1.2
A1 770 N cao
Answer: 770 N

Question 12

M1 whole-system equation: 3500 - 500 = 1500a
A1 2 m/s² cao
Answer: 2 m/s²

Question 13

M1 equation of motion for the trailer: T - 200 = 500(2)
A1 1200 N cao
Answer: 1200 N

Question 14

M1 resolve parallel to the plane: friction = mg sin22
A1 awrt 14.7 N
Answer: 14.7 N (3 s.f.)

Question 15

M1 R = mg = 58.8
M1 maximum friction = μ R = 0.35(58.8)
A1 awrt 20.6 N
Answer: 20.6 N (3 s.f.)

Question 16

M1 resolve vertically: R = mg - P sin25
M1 resolve horizontally at limiting equilibrium: P cos25 = μ R, substitute and solve for P
A1 awrt 22.8 N
Answer: 22.8 N (3 s.f.)

Question 17

M1 whole-system equation: 3g - μ(4)g = 7a, with friction = 0.25(4)(9.8)
A1 2.8 m/s² cao
M1 equation of motion for B: T = 3(g - a)
A1 21 N cao
Answer: a = 2.8 m/s², T = 21 N

Question 18

M1 decelerating downward motion means acceleration is upward: R - mg = ma with a=+2
A1 R = 885 N cao
B1 invoke Newton's third law
A1 force on floor = 885 N (equal magnitude, opposite direction to the force on the person)
Answer: R = 885 N; by Newton's third law, the person pushes on the floor with a force of 885 N

Question 19

M1 whole-system equation: 6g - 4g sin25 - μ(4)g cos25 = 10a (weight component and friction both oppose A moving up the plane)
A1 awrt 3.51 m/s²
M1 equation of motion for B: T = 6(g - a)
A1 awrt 37.7 N
Answer: a = 3.51 m/s², T = 37.7 N (both 3 s.f.)

Question 19

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Mechanics: Forces and Newton's Laws Depth: Fluency and Exam Drill - Worksheets, Questions and Revision

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M6D Mechanics: Forces and Newton's Laws Depth: Fluency and Exam Drill

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