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

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

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A-Level · Mechanics

M6 Mechanics: Forces and Newton's Laws Depth

EDEXCEL 9MA0 · Calculator allowed · about 130 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Two forces, (5i - 2j) N and (-3i + 6j) N, act on a particle P of mass 0.8 kg which is initially at rest. Take i and j as horizontal and vertical unit vectors.
(a)Find the acceleration of P, giving your answer as a vector in terms of i and j.(3)
(b)Find the magnitude of the acceleration of P, giving your answer to 3 significant figures.(2)
(Total for Question 1 is 5 marks)
2
A particle A of mass 3 kg lies on a smooth horizontal table. A light inextensible string connects A to a particle B of mass 2 kg which hangs freely over a smooth pulley fixed at the edge of the table, with the part of the string between A and the pulley horizontal and the part between the pulley and B vertical. The system is released from rest with the string taut and B descends. Take g = 9.8 m/s2.
(a)Show that the acceleration of the system is 3.92 m s-2.(4)
(b)Find the tension in the string.(2)
(c)Find the magnitude of the force exerted on the pulley by the string.(3)
(Total for Question 2 is 9 marks)
3
A block of mass 5 kg lies on rough horizontal ground. A horizontal force of magnitude 14 N is applied to the block, and the block is on the point of sliding. Take g = 9.8 m/s2.
(a)Find the normal reaction between the block and the ground.(1)
(b)Hence find the coefficient of friction between the block and the ground, giving your answer to 3 significant figures.(3)
(Total for Question 3 is 4 marks)
4
A particle P rests in limiting equilibrium on a rough plane inclined at 25 degrees to the horizontal, under gravity alone (no other forces act on P).
(a)Find the coefficient of friction between P and the plane, giving your answer to 3 significant figures.(4)
(b)The plane is now tilted further so that it is inclined at 32 degrees to the horizontal, with P resting on the same rough surface (same coefficient of friction as in part (a)). Determine, with justification, whether P remains in equilibrium at this new angle, or whether it slides.(3)
(Total for Question 4 is 7 marks)
5
A particle of mass 2 kg is projected up a line of greatest slope of a rough plane inclined at 20 degrees to the horizontal, with initial speed 8 m s-1. The coefficient of friction between the particle and the plane is 0.3. Take g = 9.8 m/s2.
(a)Show that the deceleration of the particle while it moves up the plane is 6.11 m s-2, correct to 3 significant figures.(5)
(b)Find the distance travelled by the particle up the plane before it comes to instantaneous rest.(3)
(c)Determine, with justification, whether the particle remains at rest at this point or slides back down the plane.(2)
(Total for Question 5 is 10 marks)
6
Two particles A and B, of masses m and km respectively, where k > 1, are connected by a light inextensible string which passes over a smooth pulley fixed at the top of a smooth plane inclined at angle α to the horizontal. Particle A lies on the inclined plane and particle B hangs freely, vertically below the pulley. The system is released from rest with the string taut, and B moves downward, pulling A up the plane.
(a)Show that the acceleration of the system is a = g(k - sin(α)) / (k + 1).(5)
(b)State one physical assumption made about the string in this model.(1)
(Total for Question 6 is 6 marks)
7
A person of mass 68 kg stands on the floor of a lift. The lift is moving downward and decelerating at a rate of 1.5 m s-2 as it comes to rest at a floor. Take g = 9.8 m/s2.
(a)Find the magnitude of the normal reaction force exerted on the person by the lift floor while it is decelerating.(4)
(b)Hence find the magnitude of the force that the person exerts on the floor of the lift, stating the law used.(2)
(Total for Question 7 is 6 marks)
8
A car of mass 900 kg is towing a trailer of mass 300 kg along a straight horizontal road using a light, rigid tow-bar which is parallel to the road. The car's engine produces a constant driving force of 3000 N. As the car and trailer move, the resistance to motion of the car is 400 N and the resistance to motion of the trailer is 200 N. The car and trailer are modelled as particles.
(a)Find the acceleration of the car and trailer.(3)
(b)Find the tension in the tow-bar, stating whether the tow-bar is in tension or in thrust (compression).(4)
(c)The tow-bar suddenly breaks. Given that the driving force on the car and the resistance to the car remain unchanged, and the resistance to the trailer remains unchanged, find the acceleration of the car and the deceleration of the trailer immediately after the tow-bar breaks.(4)
(Total for Question 8 is 11 marks)
9
A block A of mass 5 kg lies on a rough plane inclined at 30 degrees to the horizontal. The coefficient of friction between A and the plane is 0.3. A light inextensible string is attached to A, passes over a small smooth pulley fixed at the top of the plane, and hangs vertically down to a block B of mass 7 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.
(a)Show that the acceleration of the system is 2.61 m s-2, correct to 3 significant figures.(6)
(b)Find the tension in the string.(2)
(c)Given that B hits the ground after descending 0.8 m, and the string then becomes slack, find the further distance A travels up the plane before it comes to instantaneous rest, assuming A does not reach the pulley.(5)
(Total for Question 9 is 13 marks)
10
A block of mass 10 kg rests on rough horizontal ground. The coefficient of friction between the block and the ground is 0.4. A force of magnitude P newtons acts on the block at an angle of 20 degrees above the horizontal, pulling the block so that it is on the point of sliding along the ground. Take g = 9.8 m/s2.
(a)Show that P = 10g μ / (cos20 + μ sin20).(5)
(b)Hence find the value of P, giving your answer to 3 significant figures.(2)
(Total for Question 10 is 7 marks)
11
Two particles, P of mass 7 kg and Q of mass 4 kg, are connected by a light inextensible string which passes over a smooth fixed pulley. The particles hang freely on either side of the pulley and the system is released from rest with the string taut. Take g = 9.8 m/s2.
(a)Find the acceleration of the system.(4)
(b)Find the tension in the string.(2)
(c)Find the magnitude of the force exerted on the pulley by the string.(1)
(Total for Question 11 is 7 marks)
12
A particle P of mass 3 kg is held at rest on a rough plane inclined at 15 degrees to the horizontal. The coefficient of friction between P and the plane is 0.35. A force of magnitude 20 N acts on P at an angle of 10 degrees to the line of greatest slope, measured so that the force has a component up the plane and a component directed away from the plane (tending to lift P off the surface). P is released from rest and moves up the plane. Take g = 9.8 m/s2.
(a)Show that the normal reaction between P and the plane is R = 3g cos15 - 20 sin10, and find its value to 3 significant figures.(4)
(b)Show that the acceleration of P up the plane is 1.12 m s-2, correct to 3 significant figures.(6)
(c)Find the distance travelled by P up the plane, and its speed, after 2 seconds, assuming P remains on the plane throughout.(3)
(Total for Question 12 is 13 marks)
Mark scheme · M6 Mechanics: Forces and Newton's Laws Depth

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12