Newton's laws: Grade 12 Past Paper Questions

An experiment in which a crate of mass 8,5 kg, lying stationary on a rough horizontal table, is connected to a mass hanger by means of a light inextensible string passing over a frictionless pulley. Mass pieces are added to the mass hanger and the acceleration of the crate is measured. The experiment is repeated several times by adding different masses to increase the hanging mass each time. Ignore the effects of air friction. The results obtained were used to draw the sketch graph below. 2.1 Define the term static friction. 2.2 Draw a labelled free-body diagram showing ALL the HORIZONTAL forces acting on the crate JUST BEFORE it starts moving. 2.3 Calculate the: 2.3.1 Coefficient of static friction (μs). 2.3.2 Magnitude of the acceleration represented by Y on the graph if the coefficient of kinetic friction between the crate and the table is 0,40. 2.4 A 5 kg block is now placed inside the crate and the experiment is repeated. How will this affect the maximum static frictional force now experienced by the crate? Choose from INCREASES, DECREASES or REMAINS THE SAME. Give a reason for the answer.

Block A of mass 4,1 kg is connected to block B of mass 2,3 kg by a light inextensible string passing over a frictionless pulley. Block A is at rest on a rough horizontal table and block B hangs vertically, as shown in the diagram below. A force F of magnitude 49 N is applied on block A at an angle of 50° to the horizontal, causing block A to accelerate TO THE LEFT from rest along the table. The coefficient of kinetic friction between the surface of the table and block A is 0,35. 2.1 State Newton's Second Law of Motion in words. 2.2 Draw a labelled free-body diagram showing all the forces acting on block A while it accelerates to the left. 2.3 Calculate the magnitude of the: 2.3.1 Kinetic frictional force exerted on block A. 2.3.2 Acceleration of block A, by applying Newton's Second Law to each block separately.

A boy on a skateboard is pulled by a horizontal force F to the left, as shown in the sketch below. The combined mass of the boy and skateboard is 60 kg. A total frictional force of 70 N opposes the motion. The boy and skateboard accelerate at 1,5 m·s⁻² to the left. Ignore the rotational effects of the wheels. 2.1 Draw a labelled free-body diagram showing all the forces acting on the boy and skateboard together. 2.2 Calculate the magnitude of the force F. 2.3 The force F is increased several times, and the acceleration is measured for each value of F, while all other forces remain constant. Draw a sketch graph for the system showing the relationship between acceleration and F, from the moment the force F acts on the system. 2.4 When force F is removed, the boy and skateboard continue to move to the left for a short distance. The skateboard then hits a stone and stops. Explain what happens to the boy. 2.5 Name and state the physics law which is applied in QUESTION 2.4.

Block A of mass m is connected to block B of mass 7,5 kg by a light inextensible rope passing over a frictionless pulley. Block B is initially held at a height of 1,5 m above the ground, while block A is initially stationary on the ground, as shown in the diagram below. When block B is released, it moves vertically downwards and strikes the ground with a velocity of 3,41 m·s⁻¹. Ignore the effects of friction. 2.1 Show, by means of a calculation, that the magnitude of the acceleration of block B was 3,88 m·s⁻² while the block was moving vertically downwards. 2.2 Draw a labelled free-body diagram showing ALL the forces acting on block B immediately after it was released. 2.3 State Newton's Second Law of Motion in words. 2.4 Calculate the value of m by applying Newton's Second Law to EACH BLOCK while they are in motion. 2.5 Calculate the maximum height above the ground reached by block A.

Two blocks, A and B, of mass 8 kg and 5 kg, respectively, are connected by a light, inextensible string. The string is passed over a light, frictionless pulley so that the blocks hang down as shown. Initially, the blocks are held stationary at the same position above the floor. Each block is 0,3 m high. The blocks start moving when they are released. Ignore air friction when answering the questions below. 2.1 Draw a free-body diagram of ALL the forces acting on block B. 2.2 State Newton's Second Law of Motion in words. 2.3 Calculate the blocks' acceleration after they are released. Block A touches the floor a second later after the release. The blocks come to rest as shown below. 2.4 Calculate the vertical distance d measured from the top of block A to the bottom of block B at the instant block A touches the floor.

In an experiment to determine the length of a window, a learner pushes a 4 kg block against the wall with a force of 44,13 N at an angle of 19,9° as shown in the diagram below. The block reaches point P at a speed of 1,45 m·s⁻¹ and travels the distance, d, in 0,5 s. The coefficient of kinetic friction between the wall and the block is 0,1. Ignore the effects of air friction. 3.1 Define kinetic frictional force. 3.2 Draw a labelled free-body diagram indicating all the forces acting on the block whilst moving between point P and Q. 3.3 Calculate the: 3.3.1 Magnitude of kinetic frictional force acting on the block. 3.3.2 Length of the window (distance, d). 3.4 The same magnitude of the force is now applied at a smaller angle. What effect will this change have on the value calculated in QUESTION 3.3.1? Write down INCREASES, DECREASES or REMAINS THE SAME. Give a reason for the answer.

A block of mass 15 kg is pushed up an incline by a horizontal force F. The incline makes an angle with the horizontal. The coefficient of kinetic friction between the block and the surface is 0,20. 2.1 Define the term kinetic frictional force. 2.2 Draw a labelled free-body diagram showing ALL the forces acting on the block. 2.3 The block moves up the plane at a CONSTANT VELOCITY. 2.3.1 State Newton's First Law of Motion in words. 2.3.2 Calculate the magnitude of the force F. 2.4 A satellite that is 1000 km above the surface of the Earth is accelerating towards the Earth. If the weight of the satellite at 1000 km above the surface of the Earth is 3800 N, calculate its weight on the surface of the Earth.

A 20 kg block is placed on a rough surface inclined at 30° to the horizontal. A constant force F, acting parallel to the surface, is applied on the block so that the block moves up the incline at a CONSTANT VELOCITY of 2 m·s⁻¹. A constant kinetic frictional force of 18 N acts on the block. 2.1 State Newton's First Law in words. 2.2 Draw a labelled free-body diagram for the block. 2.3 Calculate the magnitude of force F. Force F is removed when the block reaches point X on the surface. The block continues to move up the surface and comes to rest momentarily at point Y. Assume that the kinetic frictional force acting on the block remains at 18 N as it moves from point X to point Y. 2.4 Write down the net force acting on the block as it moves from X to Y. 2.5 Calculate the distance between points X and Y.

The planet Omega has a mass of 6,4 × 10²³ kg. The diameter of planet Omega is equal to the radius of the Earth. 3.1 Describe the term weight of an object. 3.2 A 90 kg object is dropped from a height of 2 m above the surface of Omega. 3.2.1 Calculate the magnitude of the gravitational acceleration on the surface of Omega. 3.2.2 How long will it take the object to reach the surface of Omega compared to the time it would take on Earth? Write only SAME TIME, LESS TIME or MORE TIME. Give a reason for the answer. 3.3 The 90 kg object was projected upwards so that the distance between the surface of Omega and the centre of the object is 2 360 000 m. Calculate the gravitational force between Omega and the object at this distance.

A worker at a construction site pulls two blocks A and B of masses 16 kg and 24 kg respectively across a rough horizontal surface by means of a light inextensible rope, Y, at an angle of 64° to the horizontal. The 16 kg and 24 kg blocks experience frictional forces of 3,2 N and 4,3 N, respectively. The worker exerts a constant force of 120 N on block B. The blocks are joined by a light bar X; the masses of rope Y and bar X are negligible. 2.1 State Newton's Second Law of Motion in words. 2.2 Draw a labelled free-body diagram showing ALL the forces acting on the 24 kg block. 2.3 Calculate the magnitude of: 2.3.1 The normal force on the block. 2.3.2 Coefficient of kinetic friction on block B. 2.4 Determine the magnitude of the tension in bar X.

Two blocks A and B, of masses 2 kg and 6 kg respectively, are placed on a rough horizontal surface and are connected by a light, inextensible string. The string makes an angle θ with the horizontal. When a horizontal force of 32 N is applied to block B, the blocks accelerate to the right at 0,47 m·s⁻². Block A now experiences a constant frictional force of 3,74 N. 2.1 State Newton's Second Law of Motion in words. 2.2 Draw a labelled free-body diagram showing ALL the forces acting on block B. 2.3 Calculate: 2.3.1 The magnitude of the frictional force acting on block B by applying Newton's Second Law to each block separately. 2.3.2 θ, if the coefficient of kinetic friction for block A and the surface is 0,2. 2.4 As the blocks move, the string breaks. Will the kinetic frictional force experienced by block A now be GREATER THAN, LESS THAN or EQUAL TO 3,74 N? Explain the answer without the use of a calculation.

A crate of mass 25 kg slides down a rough inclined plane at a constant speed of 2 m·s⁻¹ towards point A while force F acts on it, parallel to the incline, as shown below. A constant kinetic frictional force of 40 N acts on the crate when the plane is inclined at an angle of 30° with the horizontal. 2.1 State Newton's First Law of Motion in words. 2.2 Draw a labelled free-body diagram showing ALL the forces acting on the crate, as it moves towards point A. 2.3 Calculate the magnitude of F. When the crate reaches point A, force F is removed, and the angle of inclination is decreased immediately to θ so that the crate continues moving at 2 m·s⁻¹ towards point B. 2.4 Use the relationship between the forces acting on the crate between points A and B to show that μk = sinθ/cosθ. 2.5 The coefficient of kinetic friction between the crate and the inclined plane is 0,19. Using the identity sinθ/cosθ = tanθ, calculate the frictional force as the crate slides from point A to point B.

Block A of mass 6 kg is connected to block B with a mass of 1 kg by means of a light, inextensible rope over a frictionless pulley. Initially, both blocks are stationary. Block B is pulled vertically up with a force of 43 N. Block A accelerates to the left with a constant acceleration of 2 m·s⁻² over a rough horizontal surface, as shown in the diagram below. Ignore the effects of air resistance. 2.1 State Newton's Second Law of Motion in words. 2.2 Draw a labelled free-body diagram, showing ALL the forces acting on block B. 2.3 Calculate the magnitude of the: 2.3.1 Tension in the rope. 2.3.2 Coefficient of kinetic friction between block A and the surface. 2.4 The rope connecting the two blocks breaks and the 6 kg block slows down and stops after a certain time. 2.4.1 In which direction will the acceleration of the 6 kg block be? Choose between TO THE LEFT or TO THE RIGHT. 2.4.2 Explain the answer to QUESTION 2.4.1.

A block X of mass 6 kg, at rest on a rough horizontal surface, is connected to another block Y of mass 3 kg by means of a light inextensible string which passes over a frictionless pulley. A force of 50 N is applied horizontally to block X, as shown in the diagram below. The coefficient of kinetic friction between the horizontal surface and block X is 0,3 and there is no friction between the surfaces of blocks X and Y. 2.1 Draw a labelled free-body diagram showing all the HORIZONTAL forces acting on block X. 2.2 State Newton's Second Law in words. 2.3 Calculate the magnitude of the: 2.3.1 Frictional force acting on block X. 2.3.2 Acceleration of each block. 2.4 A man on the surface of planet M weighs HALF his weight compared to his weight on the surface of the Earth. The mass of planet M is TWICE that of the Earth. 2.4.1 State Newton's Law of Universal Gravitation in words. 2.4.2 Calculate the radius of planet M in terms of the radius of the Earth.

QUESTION 2 Crate P of mass 1,25 kg is connected to another crate, Q, of mass 2 kg by a light inextensible string. The two crates are placed on a rough horizontal surface. A constant force F of magnitude 7,5 N, acting at angle θ to the horizontal, is applied on crate Q, as shown in the diagram below. The crates accelerate at a constant rate to the right. Crate P experiences a constant frictional force of 1,8 N and crate Q experiences a constant frictional force of 2,2 N. 2.1 State Newton's Second Law of Motion in words. 2.2 Draw a labelled free-body diagram for crate P. 2.3 Calculate the magnitude of: 2.3.1 The tension in the string. 2.3.2 Angle θ.

QUESTION 2: A 1 kg block and a 2 kg block are placed on a frictionless plane inclined at 30° to the horizontal. The two blocks are connected by a light, inextensible string that makes an angle θ with the surface of the incline. A constant force, F, is applied to the 2 kg block, pulling the system up the plane. 2.1 State Newton's Second Law of Motion in words. 2.2 Draw a free-body diagram for the 2 kg block whilst in motion. 2.3 Calculate the Normal force acting on the 2 kg block if the vertical component of tension (perpendicular to the plane) is 12,94 N. 2.4 How will an increase in the angle θ affect the magnitude of the Normal force exerted on the 1 kg block? Choose between INCREASE, DECREASE, or REMAIN THE SAME. Give a reason for your answer.

1.1 Several forces are acting on a moving object. Which ONE of the following statements is CORRECT when these forces are in equilibrium? A. The velocity of the object is increasing. B. The object is moving at a constant velocity. C. The kinetic energy of the object is decreasing. D. The object has a non-zero acceleration. 1.2 A stone thrown vertically downwards from the top of a building takes t seconds to strike the ground. Consider the acceleration-time graph below for the motion of the stone. The effects of air friction are ignored. What does the shaded area between 0 and t seconds, shown in the graph, represent? A. The final velocity of the stone. B. The change in position of the stone. C. The constant velocity of the stone. D. The change in velocity of the stone.

1.1 An astronaut with a mass of 70 kg is on a planet where his weight is 550 N. The gravitational acceleration on the planet is ... m·s⁻². A. 7,86. B. 0,13. C. 38 500. 1.2 A ball of mass m travelling to the right at velocity v strikes a wall and rebounds to the left at velocity 0,25v. The change in momentum of the ball is ... A. 0,75mv left. B. 1,25mv left. C. 0,75mv right. D. 1,25mv right. 1.3 A girl throws a ball upwards. Which ONE of the following combinations give the directions of the ball's velocity, acceleration, and the net force that the ball experiences as it travels upwards just after leaving the girl's hand?

1.1 Which ONE of the following quantities is the tendency of an object to resist a change to its state of motion? A. Inertia. B. Impulse. C. Momentum. D. Acceleration. 1.2 A ball is dropped from rest at a height above a concrete floor. The ball strikes the floor and bounces vertically up and down on the same spot on the floor. The velocity-time graph for the bouncing ball is shown below, with points P, Q, R and S representing different times during the motion. Ignore the effects of air resistance. At which time does the ball reach its maximum height after the first upward bounce? A. P. B. Q. C. R. D. S.

1.5 A hot-air balloon is moving vertically downwards at a CONSTANT SPEED. Assume that the mass of the hot-air balloon remains constant. Which ONE of the following physical quantities associated with the hot-air balloon changes during the motion? A. Weight. B. Momentum. C. Kinetic energy. D. Potential energy. 1.6 A learner standing at a roadside records the frequency of sound waves produced by the siren of an ambulance. The ambulance is moving at constant velocity along a straight horizontal road. The frequency-time graph for the detected sound is shown below. Which ONE of the following statements concerning the motion of the ambulance is CORRECT? The ambulance … A. approaches the learner and then passes the learner. B. moves away from the learner, then turns and approaches the learner. C. approaches the learner, then turns and moves away from the learner. D. moves away from the learner and then stops.

1.1 Which ONE of the following physical quantities is the rate of change of momentum? A. Impulse. B. Acceleration. C. Power. D. Force. 1.2 An object is dropped from the top of a tall building. After time t, the object's momentum is p. What will the momentum of the object be after time 2t? Ignore the effect of air friction. B. p. C. 2p. D. 3p. 1.3 A boy pushes a heavy box across a rough floor with a constant force of 250 N. The box experiences a constant frictional force of 50 N while it is moving. The magnitude of the force exerted by the box on the boy is ... A. 50 N. B. 200 N. C. 250 N. D. 300 N.

1.1 The physical quantity which is a quantitative measure of the resistance of an object to any change in its state of rest or motion is called ... A. Weight. B. Acceleration. C. Mass. D. Friction. 1.2 The magnitude of the gravitational acceleration on Earth is g. What will the value of the gravitational acceleration be on planet X, which has the same mass as Earth, but half the radius? A. ¼g. B. ½g. C. 2g. D. 4g. 1.3 Which one of the following best describes an inelastic collision? A. Both momentum and kinetic energy are conserved. B. Total kinetic energy is not conserved but total linear momentum is conserved. C. Neither kinetic energy nor momentum are conserved. D. Kinetic energy is conserved but total linear momentum is not conserved.

1.1 Which ONE of the following is NOT TRUE about the frictional force? A. Is proportional to the applied force. B. Is proportional to the normal force. C. Is independent of the area of contact. D. Is independent of the velocity of motion. 1.2 A ball is thrown vertically upwards. Which ONE of the following combinations of physical quantities of the ball have non-zero values at its highest point? Ignore the effects of air friction. A. Kinetic energy and time. B. Acceleration and weight. C. Displacement and momentum. D. Potential energy and velocity. 1.3 Which ONE of the following is equal to the rate of change of momentum? A. FΔt. B. Δp. C. ma. D. p.

3.4 Two isolated bodies, A and B, with masses M and 3M respectively, are placed a distance 2r from each other's centres. The gravitational force between them is F. The diagram is not drawn to scale. Determine the gravitational force between A and B in terms of F if the distance is increased to 6r. QUESTION 4 Ball A is dropped vertically downwards from the top of a high building with an unknown height h. ONE second later, another ball, B, is thrown vertically downwards from the same height with a speed of 20 m·s⁻¹. Ball B passes ball A when the balls reach the top of the window. The top of the window is 3 m above the ground. The diagram is not drawn to scale. Ignore the effects of friction. 4.1 Define the term free fall. 4.2 Use only equations of motion and calculate: 4.2.1 The velocity of ball A after falling for 2 seconds. 4.2.2 How long after ball A was dropped will ball B pass it. 4.2.3 The height of the building.

1.1 A horizontal force F is applied to a crate, causing it to move over a rough, horizontal surface. The kinetic frictional force between the crate and the surface on which it is moving depends on... A. the applied force. B. how fast the crate moves on the surface. C. the surface area of the crate in contact with the floor. D. the upward force exerted by the surface on the crate. 1.2 Two forces, F1 and F2, can be represented by a single resultant force of 8 N. If the magnitude of F1 is 3 N, which one of the following can be the magnitude of force F2? A. 3 N B. 4 N C. 10 N D. 13 N. 1.3 Two hypothetical planets, X and Y, have the same mass. The diameter of planet Y is twice that of planet X. If the acceleration due to gravity on the surface of planet X is g, then the acceleration due to gravity on the surface of planet Y will be .... A. ¼g B. ½g C. 2g D. 4g.

1.4 Which ONE of the following organic compounds will RAPIDLY decolourise bromine water? A. CH₂=CH₂. B. CH₃CH₃. C. CH₃CHO. D. CH₃COOH. 1.5 Which ONE of the following organic compounds has STRUCTURAL ISOMERS? A. Ethanal. B. 1,1-dibromoethane. C. Propane. D. Methanoic acid. QUESTION 2: A satellite of mass 2×10⁴ kg orbits around the surface of planet X at a distance of 4 000 km. Planet X has a mass FOUR TIMES the mass of planet EARTH and a radius which is a THIRD of the radius of the EARTH. 2.1 State Newton's law of Universal gravitation in words. 2.2 Calculate the gravitational force that planet X exerts on the satellite when the satellite is at a distance of 4 000 km from the surface of the planet. 2.3 How does the mass of the satellite on the surface of planet X compare to the mass of the satellite on the surface of planet EARTH? Write down GREATER THAN, LESS THAN OR EQUAL TO.

1.1 The gravitational force experienced by an object on the surface of a planet is inversely proportional to the … A. mass of the planet. B. mass of the object. C. square of the radius of the planet. D. radius of the planet. 1.2 A horizontal force F acts on a block placed on a rough horizontal surface. The block, starting from rest, moves to the right at constant acceleration. Which ONE of the following statements is CORRECT? A. F is equal to the kinetic frictional force. B. The momentum of the block increases. C. The net work done on the block is zero. D. The normal force is less than the weight of the block. 1.3 Objects A and B are thrown vertically upwards with velocities v and 2v respectively. Object A reaches a maximum height h. What is the maximum height reached by object B? Ignore the effects of friction. A. h. B. 2h. C. 3h. D. 4h.

1.1 Consider the statement below. The perpendicular force exerted by a surface on an object in contact with the surface. Which ONE of the following forces is defined by the statement above? A. Normal force. B. Resultant force. C. Frictional force. D. Gravitational force. 1.2 Two balls of masses m and 2m are dropped simultaneously from the same height above the ground. Ignore air resistance. When the balls strike the ground, which ONE of the following physical quantities will be the same for both balls? A. Weight. B. Velocity. C. Momentum. D. Kinetic energy.

1.1 Three forces act on an object so that the resultant force is zero. Which ONE of the following vector diagrams is the CORRECT representation of the three forces? 1.2 Two large objects P and R, each of mass m, are placed with their centres r metres apart, as shown in the diagram below. They exert a gravitational force of magnitude F on each other. The mass of R is increased to 2m and the objects are now placed so that the distance between their centres is 2r metres. Which ONE of the following is the magnitude of the gravitational force that R now exerts on P? A. ½F B. F C. 2F D. 4F.

1.1 Two objects of equal mass move towards each other at the same speed. Object A moves to the right and collides with object B which is moving to the left. Both objects stop immediately after the collision. Ignore the effects of friction. Which of the following statements is INCORRECT during the collision? A. The force exerted by object A is equal to the force exerted by object B. B. The total linear momentum is conserved. C. The collision is inelastic. D. The magnitude of the impulse of object A is equal to the magnitude of the impulse of object B. 1.2 Two objects, object X and object Y, of equal mass move towards each other due to their gravitational force of attraction. Which of the combinations below is CORRECT for the acceleration of the objects towards each other and the gravitational force between them? A. Acceleration decreases, gravitational force remains the same. B. Acceleration increases, gravitational force remains the same. C. Acceleration remains the same, gravitational force increases. D. Acceleration increases, gravitational force increases.

1.1 A physics learner stands on a scale in a lift that is moving upwards at CONSTANT VELOCITY. The reading on the scale, compared to the reading when the lift was stationary, would be: A. zero. B. greater. C. smaller. D. the same. 1.2 Two blocks of masses m₁ and m₂ are connected to each other by a light inextensible string. The blocks are accelerated upwards by a force F. The tension in the string between the blocks will be: A. equal to F. B. equal to m₂g. C. less than m₂g. D. greater than m₂g. 1.3 A ball is dropped from a height h and hits the ground with a speed v. The speed of the ball at the moment when it reaches half its initial height is: A. v. B. v/√2. C. v/2. D. v/4.

QUESTION 1: MULTIPLE-CHOICE QUESTIONS. Various options are provided as possible answers to the following questions. Each question has only ONE correct answer. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in the ANSWER BOOK, e.g. 1.11 E. 1.1 A book rests on a table. Which ONE of the following forces will form an action-reaction pair with the weight of the book? A. Force of the Earth on the book. B. Force of the book on the Earth. C. Force of the book on the table. D. Force of the table on the book. 1.2 A person is standing on a bathroom scale in a moving lift. Which ONE of the following motions of the lift will result in the SMALLEST reading on the scale? A. The lift accelerates upwards. B. The lift accelerates downwards. C. The lift moves upwards at a constant velocity. D. The lift moves downwards at a constant velocity. 1.3 The velocity versus time sketch graph below represents the motion of a ball which was in free fall. The ball struck the ground after 3t seconds. Which ONE of the following statements is CORRECT? The ball was … A. dropped from a height above the ground. B. thrown vertically upwards from the ground. C. thrown vertically upwards from a height above the ground. D. thrown vertically downwards from a height above the ground.

QUESTION 1: MULTIPLE-CHOICE QUESTIONS. Four options are provided as possible answers to the following questions. Each question has only ONE correct answer. Choose the answer and write only the letter (A–D) next to the question number (1.1–1.6) in the ANSWER BOOK. E.g. 1.7 A. 1.1 If the net force acting on an object doubles while its mass remains constant, the acceleration will – A. Remain the same. B. Double. C. Be halved. D. Become zero. 1.2 The velocity-time graph for the motion of the ball from the instant it is projected from a cliff until it reaches point T is shown below. The quantity t₂ − t₁ represents: A. The time taken for the ball to reach maximum height. B. The duration of motion after the bounce until the ball reaches point T. C. The total time of flight. D. The time taken for the velocity to become zero for the first time.