Mechanics: Forces and Newton's Laws: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

19 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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A-Level · Mechanics

M2DB Mechanics: Forces and Newton's Laws: Fluency and Exam Drill (Part 2)

EDEXCEL 9MA0 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

State Newton's third law of motion.

(Total for Question 1 is 1 mark)

State what is meant by modelling a surface in mechanics as "smooth".

(Total for Question 2 is 1 mark)

A resultant force of 15 N acting on a particle produces an acceleration of 2.5 m/s². Find the mass of the particle.

(Total for Question 3 is 1 mark)

A parcel has mass 12 kg. Take g = 9.8 m/s². Find the weight of the parcel.

(Total for Question 4 is 1 mark)

Two forces, of magnitude 17 N and 6 N, act on a particle in opposite directions along the same straight line. Find the magnitude of the resultant force.

(Total for Question 5 is 1 mark)

Two forces, F1 = (3i - 2j) N and F2 = (-1i + 5j) N, act on a particle, where i and j are perpendicular unit vectors. Find the resultant force acting on the particle, giving your answer in the form (ai + bj) N.

(Total for Question 6 is 1 mark)

Two forces act on a particle at right angles to each other, of magnitude 9 N and 12 N. Find the magnitude of the resultant force.

(Total for Question 7 is 2 marks)

A block of mass 5 kg rests on rough horizontal ground. The maximum frictional force before the block slips is found to be 14.7 N. Take g = 9.8 m/s². Find the coefficient of friction between the block and the ground.

(Total for Question 8 is 2 marks)

A block of mass 10 kg rests on rough horizontal ground. The coefficient of friction between the block and the ground is 0.5. A horizontal force of magnitude 35 N is applied to the block, which remains in equilibrium. Take g = 9.8 m/s². Find the frictional force acting on the block.

(Total for Question 9 is 2 marks)

Three forces act on a particle. Their components are given in the table below.

Force	i-component (N)	j-component (N)
F1	4	5
F2	3	1
F3	-1	2

Find the magnitude of the resultant force acting on the particle.

(Total for Question 10 is 2 marks)

A crate of mass 8 kg is pulled along smooth horizontal ground by a force of magnitude 25 N acting at 40 degrees above the horizontal. Find the acceleration of the crate, giving your answer to 3 significant figures.

(Total for Question 11 is 3 marks)

A block of mass 6 kg rests in limiting equilibrium on a rough plane inclined at 32 degrees to the horizontal. The block is on the point of sliding down the plane. Take g = 9.8 m/s². Find the coefficient of friction between the block and the plane, giving your answer to 3 significant figures.

(Total for Question 12 is 3 marks)

A student attempts to find the tension in the cable of a lift of mass 900 kg accelerating upwards at 0.5 m/s². Take g = 9.8 m/s². The student's working is shown below, but the final answer is incorrect.

T - mg = ma
T = m(g - a)
T = 900 x (9.8 - 0.5)
T = 8370

(a)Identify the error in the student's working.(1)

(b)Find the correct value of the tension.(1)

(Total for Question 13 is 2 marks)

A block of mass 5 kg is pulled up a rough plane inclined at 20 degrees to the horizontal by a force of magnitude 35 N acting parallel to the line of greatest slope. The coefficient of friction between the block and the plane is 0.2. Take g = 9.8 m/s². Show that the acceleration of the block is 1.81 m/s², correct to 3 significant figures.

(Total for Question 14 is 3 marks)

A box of mass 6 kg is pulled along rough horizontal ground by a force of magnitude 40 N acting at 25 degrees above the horizontal. The coefficient of friction between the box and the ground is 0.3. Take g = 9.8 m/s². Find the acceleration of the box, giving your answer to 3 significant figures.

(Total for Question 15 is 4 marks)

A particle P, of weight 20 N, hangs in equilibrium, held by two light inextensible strings attached to a fixed horizontal ceiling, as shown in the diagram. String PA makes an angle of 40 degrees with the horizontal ceiling and string PB makes an angle of 60 degrees with the horizontal ceiling, on the opposite side of P.

Figure (to be drawn): A particle P hangs below a horizontal ceiling, held in equilibrium by two light strings. String PA rises up and to the left from P to a fixed point A on the ceiling, making an angle of 40 degrees with the horizontal ceiling. String PB rises up and to the right from P to a fixed point B on the ceiling, making an angle of 60 degrees with the horizontal ceiling. The weight of the particle, 20 N, acts vertically downward from P.

(a)Find the tension in string PA, giving your answer to 3 significant figures.(2)

(b)Find the tension in string PB, giving your answer to 3 significant figures.(2)

(Total for Question 16 is 4 marks)

Particle A, of mass 4 kg, lies on a rough horizontal table. The coefficient of friction between A and the table is 0.2. A light inextensible string attached to A passes over a smooth pulley fixed at the edge of the table and hangs vertically, carrying particle B, of mass 3 kg, freely at its other end, as shown in the diagram. The system is released from rest. Take g = 9.8 m/s². Find the acceleration of the system and the tension in the string.

Figure (to be drawn): Particle A of mass 4 kg rests on a rough horizontal table. A light inextensible string is attached to A, runs horizontally to a smooth pulley fixed at the edge of the table, then turns through the pulley and hangs vertically down the side of the table to particle B of mass 3 kg, which hangs freely in the air. The system starts at rest and is then released.

(Total for Question 17 is 3 marks)

A car of mass 1200 kg tows a trailer of mass 400 kg along a straight horizontal road using a light rigid tow-bar. The car's engine provides a driving force of 2800 N. The resistance to the motion of the car is 300 N and the resistance to the motion of the trailer is 100 N.

(a)Find the acceleration of the car and trailer.(3)

(b)Find the tension in the tow-bar.(2)

(Total for Question 18 is 5 marks)

A particle Q, of mass 2 kg, moves on a smooth horizontal plane under the action of three constant forces, F1 = (3i - 5j) N, F2 = (-1i + 2j) N and F3 = (4i + 1j) N, where i and j are perpendicular unit vectors in the plane. Given that Q starts at rest, find the speed of Q after 5 seconds, giving your answer to 3 significant figures.

(Total for Question 19 is 4 marks)

Mark scheme · M2DB Mechanics: Forces and Newton's Laws: Fluency and Exam Drill (Part 2)

Question 1

B1 if body A exerts a force on body B, then body B exerts a force of the same magnitude but in the opposite direction on body A (oe)
Answer: If A exerts a force on B, then B exerts an equal and opposite force on A.

Question 2

B1 it exerts no friction (the frictional force is negligible / zero) (oe)
Answer: It exerts no frictional force (friction is negligible).

Question 3

B1 6 cao
Answer: 6 kg

Question 4

B1 117.6 cao
Answer: 117.6 N

Question 5

B1 11 cao
Answer: 11 N

Question 6

B1 (2i + 3j) cao
Answer: (2i + 3j) N

Question 7

M1 use of Pythagoras: R² = 9² + 12² (oe)
A1 15 cao
Answer: 15 N

Question 8

M1 R = mg = 5(9.8) = 49, then μ = F/R (oe)
A1 0.3 cao
Answer: 0.3

Question 9

M1 recognise the block remains in equilibrium, so friction balances the applied force (not μ R) (oe)
A1 35 cao
Answer: 35 N

Question 10

M1 resultant = (4+3-1)i + (5+1+2)j = 6i + 8j (oe)
A1 10 cao
Answer: 10 N

Question 11

M1 horizontal component of the force = 25cos40 (oe)
M1 use F=ma with the horizontal component: a = 25cos40/8
A1 awrt 2.39 m/s²
Answer: 2.39 m/s² (3 s.f.)

Question 12

M1 resolve perpendicular to the plane: R = mg cos32 (oe)
M1 resolve parallel to the plane, with friction acting up the slope since the block is about to slide down: mg sin32 = μ R (oe)
A1 awrt 0.625
Answer: 0.625 (3 s.f.)

Question 13

(a) B1 the student wrote T = m(g - a); since the lift accelerates upwards, T - mg = ma gives T = m(g + a), so a should be added to g, not subtracted (oe)
(a) Answer: The student subtracted a from g instead of adding it: T should equal m(g+a), not m(g-a).
(b) B1 9270 cao
(b) Answer: 9270 N

Question 14

M1 resolve perpendicular to the plane: R = mg cos20 (oe)
M1 resolve parallel to the plane: 30 - mg sin20 - μ R = ma (oe)
A1 cso: correct working leading to 1.85 (3 s.f.)
Answer: a = 1.85 m/s² (3 s.f.), as given.

Question 15

M1 resolve vertically: R + 40sin25 = mg, so R = mg - 40sin25 (oe)
M1 friction = μ R
M1 resolve horizontally: 40cos25 - friction = ma
A1 awrt 3.95 m/s²
Answer: 3.95 m/s² (3 s.f.)

Question 16

(a) M1 resolve horizontally and vertically to form simultaneous equations: T_A cos40 = T_B cos60 and T_A sin40 + T_B sin60 = 20 (oe)
(a) A1 awrt 10.2 N
(a) Answer: 10.2 N (3 s.f.)
(b) M1 substitute back into the simultaneous equations (ft from part (a))
(b) A1 awrt 15.6 N
(b) Answer: 15.6 N (3 s.f.)

Question 17

M1 equations of motion for A and B, e.g. T - μ(4)(9.8) = 4a and 3(9.8) - T = 3a, combined to eliminate T and find a
A1 a = 3.08 m/s² cao
B1 T = 20.16 N cao (ft from a)
Answer: a = 3.08 m/s², T = 20.16 N

Question 18

(a) M1 resultant force on the whole system = driving force - (resistance on car + resistance on trailer) (oe)
(a) M1 = (mass of car + mass of trailer) x a (oe)
(a) A1 1.5 m/s² cao
(a) Answer: 1.5 m/s²
(b) M1 consider the trailer alone: T - 100 = 400(1.5) (oe), using a from part (a), ft
(b) A1 700 N cao
(b) Answer: 700 N

Question 19

M1 resultant force = (3-1+4)i + (-5+2+1)j = 6i - 2j N
M1 a = resultant force / mass = 3i - j m/s²
M1 v = u + at with u=0: v = 5(3i - j) = 15i - 5j m/s
A1 awrt 15.8 m/s
Answer: 15.8 m/s (3 s.f.)

Question 19

4 marks

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Mechanics: Forces and Newton's Laws: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

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