Newton's laws: Grade 11 Past Paper Questions

QUESTION 5 Two blocks, of mass 4 kg and 10 kg, connected by a light, inextensible string, are on a rough horizontal surface, with a force of 60 N applied to the system at an angle to the horizontal, as shown in the diagram below. The kinetic frictional forces acting on the 4 kg and 10 kg blocks are 2 N and 3,5 N respectively. 5.1 State Newton's second law of motion in words. 5.2 Draw a labelled free-body diagram showing all the forces acting on the 4 kg block. 5.3 Calculate the magnitude of the: 5.3.1 Acceleration of the system. 5.3.2 Tension in the string connecting the two blocks. 5.4 The angle at which the force is applied is decreased to 20°. How will the frictional force experienced by the 4 kg block change? Write down only INCREASES, DECREASES or REMAINS THE SAME.

QUESTION 4 A block of mass 4 kg is sliding down a rough plane (AB) inclined at 30° to the horizontal, as shown in the diagram below. The coefficient of kinetic friction between the surface and the block is 0,2. 4.1 Define the term frictional force. 4.2 Calculate the magnitude of the: 4.2.1 Kinetic frictional force between the 4 kg block and the surface. 4.2.2 Acceleration of the block while it is moving on section AB. The block is now moving on section BC, which is frictionless. 4.3 Will the block in section BC have a LOWER, a HIGHER or a ZERO ACCELERATION? Give the reason for the answer.

QUESTION 2. Three forces Fa, Fb and Fc act on a point O in the directions shown in the diagram below. The magnitudes of Fa and Fc are 44 N and 31 N respectively. The magnitude of Fb is unknown. The forces are NOT drawn to scale. 2.1 Define the term resultant vector. The resultant of the three forces is 26,69 N at an angle of 25,82° to the horizontal, and lies in the first quadrant. 2.2 Calculate the magnitude of Fb. 2.3 Determine θ.

1.5 A car, moving to the right along a rough horizontal surface, is brought to rest by a constant net force. If the direction of motion is taken as positive, which ONE of the following acceleration versus time graphs is correct for the motion of the car? (Four acceleration-time graphs are given as options.)

QUESTION 4. 4.1 The sketch below shows a tow-truck of mass 2500 kg pulling a car of mass 800 kg up a rough inclined surface which makes an angle with the horizontal, as shown in the diagram below. The co-efficient of kinetic friction between the car and the surface is 0,25. The net force acting on the truck is 1520 N, and the tension in the cable is T. Ignore the rotational effects of the wheels. 4.1.1 State Newton's Second Law of motion in words. 4.1.2 Draw a labelled free body diagram showing all the forces acting on the car. 4.1.3 Calculate the kinetic frictional force that the car experiences as it moves up the surface. 4.1.4 Calculate the tension T in the cable. 4.2 A spaceship, with its engines switched off, is moving towards Earth. The mass of the spaceship is 1250 kg. 4.2.1 State Newton's Law of universal gravitation in words. 4.2.2 Calculate the distance between the spaceship and the centre of Earth when Earth exerts a force of 2458 N on the spaceship.

3.5 The trolley is now accelerated by first using one rubber band, then two rubber bands and finally three rubber bands. The rubber bands are stretched to the same extent each time. The three sets of results are plotted on the velocity-time graph shown below. 3.5.1 Which graph represents the results when THREE rubber bands were used? Choose from A or B. Give a reason for the answer. 3.5.2 Sketch a graph to show the relationship between the acceleration of the trolley and the force (in rubber bands units) acting on the trolley.

QUESTION 4. Learners set up an experiment to determine the coefficient of static friction (μs) for a block placed on an inclined plane. They set up the experiment as shown below. They used the following apparatus: a wooden board (for an inclined surface), a wooden block, a protractor to measure the angle of inclination. The following procedure was followed: a block was placed on the inclined surface and the incline was adjusted until the block just begins to move on its own (run 1). The angle at which the block starts to move (θs) was recorded and the procedure was repeated for an additional 3 runs. The data obtained from the four runs, and the average coefficient of static friction (μs), is shown in the table below.

5.2 The diagram below shows two blocks A and B of mass 20 kg and 10 kg respectively, connected by a light, inextensible string over a frictionless pulley. Block A is held at rest on a rough surface. 5.2.1 Define the term normal force. When block A is released, it accelerates to the right. The tension in the string is T and the coefficient of kinetic friction (μk) between block A and the surface is 0,25. 5.2.2 Draw a labelled free body diagram showing all the forces acting on block A while it accelerates. 5.2.3 Calculate the magnitude of the acceleration of the blocks, by applying Newton's second law separately to each block. A 4 kg block is now placed on top of block A while it is accelerating to the right. The 4 kg block does not slide on block A. 5.2.4 How will the tension in the string, T, be affected? Choose from INCREASES, DECREASES or REMAINS THE SAME. Explain the answer.

QUESTION 2. An object with a mass of 2,5 kg hangs from a string that is attached to the ceiling at point P. A force F of magnitude 50 N, acting horizontally from point Q on the string, pulls the string to the left, as shown in the diagram below. The forces acting at point Q are in equilibrium. 2.1 Write down a conclusion that can be made from the underlined statement above. 2.2 Calculate the magnitude of the tension T in the string.

A force of 177 N is applied to the left of the 10 kg block, to control the LOWERING of the 20 kg block to the ground. The kinetic frictional force between the 10 kg block and the surface is 11,5 N. 5.1 State Newton's second law of motion in words. 5.2 Draw a labelled free-body diagram showing all forces acting on the 20 kg block. 5.3 Calculate the magnitude of the: 5.3.1 Acceleration of the 20 kg block. 5.3.2 Tension in the string connecting the blocks. 5.4 The 177 N force is now applied at an angle to the horizontal, as shown in the diagram below. Will the kinetic frictional force on the 10 kg block INCREASE, DECREASE or REMAIN THE SAME? Explain the answer.

QUESTION 4 An investigation is conducted to determine the relationship between the net force acting on an object and its acceleration. The apparatus used in the experiment is shown below, comprising a ticker-timer, ticker-tape, trolley, and a hanger with mass pieces. The trolley moves down a friction-compensated ramp, pulled by mass pieces on a mass hanger. The hanger is attached to the trolley by a light, inextensible string that passes over a frictionless pulley. The net force is increased by moving mass pieces from the trolley to the hanger. 4.1 Explain how a ticker-timer and ticker-tape are used to adjust the ramp in order to compensate for friction. 4.2 Identify: 4.2.1 The dependent variable. 4.2.2 A controlled variable. 4.3 Write down an investigative question for this experiment. The ticker-timer has a frequency of 50 Hz, and the ticker-tape shown below (not drawn to scale) is divided into intervals of five dots, measuring 7 mm, 21 mm and 35 mm.

QUESTION 3 Three forces, F1, F2 and F3, act on an object at point O as shown in the diagram below, where F2 = 12 N. The object moves from rest in a straight line at a bearing of 25°. The forces are not drawn to scale. 3.1 Define the term resultant vector. 3.2 Calculate the magnitude of the RESULTANT of: 3.2.1 The horizontal components of F1 and F2 ONLY. 3.2.2 The vertical components of F1 and F2 ONLY. 3.3 Determine the magnitude of F3. 3.4 A fourth force F4 now also acts at point O along the vertical axis, so that the object moves due EAST, along the positive x-axis. Determine the magnitude and bearing of F4.

QUESTION 2 A box is lifted vertically upwards at CONSTANT VELOCITY using two light, inextensible strings, P and Q. The strings pass over frictionless pulleys attached to a horizontal ceiling and are attached to the box at point X, as shown in the diagram below. The tension in string P, which makes an angle of 50° with the ceiling, is 200 N. String Q makes an angle of 40° with the ceiling. Ignore the effects of air resistance and assume that the box does not rotate while being lifted. 2.1 What is meant by a closed vector diagram? 2.2 Draw a fully labelled closed vector diagram representing all forces acting on the box. Indicate any TWO angles. 2.3 Calculate: 2.3.1 The magnitude of the tension in string Q. 2.3.2 The mass of the box.

QUESTION 6 A satellite of mass 1 200 kg is orbiting the Earth at a distance d from the surface of the Earth, as shown on the diagram below. The radius of the Earth is 20 times the distance d. 6.1 State Newton's Law of Universal Gravitation in words. 6.2 Calculate the: 6.2.1 Distance between the surface of the Earth and the centre of the satellite (distance d). 6.2.2 Magnitude of the force that the Earth exerts on the satellite to keep it in orbit. 6.3 Calculate the weight of the satellite on the Earth's surface.

QUESTION 3. A student conducts an experiment to investigate the relationship between the resultant force on an object, and acceleration. The experiment is set up using a trolley on an inclined runway, and a ticker-timer that makes 50 dots every second. 3.1 Calculate the period of the ticker-timer. When the trolley is released from the top of the runway, it moves down the slope and the following ticker-tape is produced, showing the direction of motion down the incline. 3.2 Briefly explain why the dots on the tape are initially close together. The slope of the runway is adjusted so that the dots become evenly spaced. 3.3 Was the ramp angle INCREASED or DECREASED? 3.4 What is the magnitude of the resultant force now acting on the trolley?

QUESTION 2 Two forces act simultaneously on a small boat in a flat part of a river: the motor exerts a force of 1200 N at an angle of 40° north of east; the river current exerts a force of 800 N in a northerly direction. The forces, not drawn to scale, are shown in the diagram below. The boat is at point O. 2.1 Define the term resultant vector. 2.2 Using an accurate scale drawing, determine the magnitude and direction of the resultant force acting on the boat. Use the scale 1 cm : 200 N.

After moving 0,70 m up the incline, the string connecting blocks A and B breaks. 4.1.4 Will the maximum distance covered by block A along the incline be GREATER THAN, LESS THAN or EQUAL TO 0,7 m? Explain the answer. 4.2 A space agency is designing landing equipment for a mission to the Moon. Engineers need accurate information on the Moon's gravitational acceleration. Earth exerts a gravitational force of 2,34 × 10²⁰ N on the Moon. The shortest distance between the surfaces of Earth and the Moon is 3,46 × 10⁸ m, as indicated in the diagram below. The Moon has a mass of 7,35 × 10²² kg. 4.2.1 State Newton's law of universal gravitation in words. 4.2.2 Determine the gravitational acceleration on the surface of the Moon.

QUESTION 3 A trolley of UNKNOWN MASS rests on a rough horizontal surface. A horizontal force is applied to the trolley towards the right, as shown in the diagram below. The trolley initially remains at rest. The magnitude of F is gradually increased, until the trolley begins to move. The maximum static frictional force (fs max) between the trolley and the surface is 7 N. The acceleration of the trolley is measured for different values of F. The graph below shows the relationship between the acceleration of the trolley (a) and the applied force (F). 3.1 Define the term static friction in words. 3.2 Write down the magnitude of the static frictional force when the applied force acting on the trolley is 6 N to the right. 3.3 Draw a labelled free-body diagram showing all HORIZONTAL forces acting on the trolley when the trolley is in motion.

QUESTION 3. A student conducts an experiment to investigate the relationship between the resultant force on an object, and acceleration. The experiment is set up using a trolley on an inclined runway, and a ticker timer that makes 50 dots every second. 3.1 Calculate the period of the ticker timer. When the trolley is released from the top of the runway, it moves down the slope and the following ticker tape is produced. 3.2 Briefly explain why the dots on the tape are initially close together. The slope of the runway is adjusted so that the dots become evenly spaced. 3.3 Was the ramp angle INCREASED or DECREASED? 3.4 What is the magnitude of the resultant force now acting on the trolley? 3.5 The trolley is now accelerated by first using one rubber band, then two rubber bands and finally three rubber bands. The rubber bands are stretched to the same extent each time. The three sets of results are plotted on a velocity-time graph shown below. 3.5.1 Which graph represents the results when THREE rubber bands were used? Choose from A or B. Give a reason for the answer. 3.5.2 Sketch a graph to show the relationship between the acceleration of the trolley and the force (in rubber band units) acting on the trolley.

4.4 Determine the time elapsed for every 5-dot section of the tape. 4.5 Using the data on the ticker-tape above, calculate the magnitude of the trolley's acceleration. The results obtained are shown on the graph below: Acceleration vs Net Force (with net force values 0,49 N, 0,98 N and 1,47 N marked on the horizontal axis). 4.6 Write down the mathematical relationship between the net force exerted on the trolley and the acceleration produced. 4.7 Give a reason why the mass pieces added to the hanger were initially placed on the trolley. QUESTION 5 A 10 kg block resting on a rough horizontal surface is connected to a 20 kg block by a light, inextensible string passing over a frictionless pulley. The 20 kg block hangs vertically, as shown in the diagram below, with a force Fa = 177 N applied to the 10 kg block.

1.6 The graphs P, Q, R and S drawn below show a relationship between the force of attraction that two masses exert on each other and the inverse of the square of the distance between their centres. In which graph will the product of their masses be the largest? A. P. B. Q. C. R. D. S. 1.7 The force of attraction between two charges q₁ and q₂ is F. If the distance between the charges is made four times smaller, then the new force of attraction will be ... A. 0,5F. B. 1,78F. C. 2,5F. D. 16F.

2.4 Calculate the maximum weight that force Fa and force Fb will be able to lift from the ground. Show ALL calculations. 2.5 Explain why the rope and pulley system will be less effective if the distance x between the pulleys is increased. QUESTION 3 A horizontal force, F, is applied to a 200 kg block by means of a massless, inextensible rope, as shown in the sketch below. The block remains stationary when the rope makes an angle of 15° with the vertical. 3.1 Explain why the block is stationary. 3.2 Determine the magnitude of the tension in the rope. 3.3 Determine the magnitude of the force, F.

4.1 Define static friction in words. 4.2 Using relevant formulae, show that μs = tanθ. 4.3 Determine the values of X and Y in the table. 4.4 Angle θ is now set so that the block is allowed to slide down the inclined surface at constant velocity. How does the coefficient of kinetic friction compare to the coefficient of static friction? Choose from GREATER THAN, LESS THAN or EQUAL TO. QUESTION 5. 5.1 A man of mass 80 kg stands on a scale placed on the floor of a stationary lift. When the lift accelerates upwards the tension in the cable, T, is 17 000 N. 5.1.1 State Newton's Second law of motion in words. 5.1.2 Calculate the magnitude of the acceleration of the lift as it moves upwards. 5.1.3 Will the reading on the scale be GREATER THAN, LESS THAN or EQUAL TO the weight of the man? Briefly explain the answer by referring to the forces involved. The lift now accelerates downwards at 1 m·s⁻². 5.1.4 Calculate the reading on the scale.

QUESTION 1. Four options are provided as possible answers to the following questions. Each question has only ONE correct answer. Write only the letter (A–D) next to the question number (1.1–1.10) in the ANSWER BOOK, e.g. 1.11 E. 1.1 Two forces P and Q act at a point O. As the angle θ between P and Q varies, the MAXIMUM and MINIMUM resultant forces are 13 N and 3 N respectively. The magnitudes of the two forces are: A. 3 N and 10 N. B. 16 N and 10 N. C. 8 N and 5 N. D. 10 N and 7 N. 1.2 A passenger standing in a moving bus moves forward when the bus suddenly stops. This can best be explained by A. Newton's First law of motion. B. Newton's Second law of motion. C. Newton's Third law of motion. D. Newton's law of Universal gravitation. 1.3 A learner sits on a chair. What is the reaction force to her sitting on the chair? A. Force that the learner exerts on the chair. B. Weight of the learner. C. Force that the chair exerts on the learner. D. Force that the learner exerts on Earth.

QUESTION 6. The mass of planet Jupiter is 300 times the mass of Earth and its radius is 11 times larger than that of Earth. An astronaut has a mass of 120 kg. 6.1 State Newton's law of universal gravitation in words. 6.2 What will the weight of the astronaut be on the surface of Jupiter? QUESTION 7. 7.1 Two spheres P and Q, placed on insulated stands, carry charges of +5 μC and −8 μC respectively. 7.1.1 Explain why the charges are placed on insulated stands. The charges are brought into contact and are then separated. 7.1.2 Are electrons transferred from P to Q or from Q to P during contact? Give a reason for the answer. 7.1.3 Calculate the number of electrons transferred. 7.1.4 Name and state the law used in the calculation in QUESTION 7.1.3.

QUESTION 1: MULTIPLE CHOICE. Four options are provided as possible answers to the following questions. Each question has only ONE correct answer. Write only the letter (A–D) next to the question number (1.1–1.5) in the ANSWER BOOK, for example 1.6 E. 1.1 Two forces P and Q can be represented by a single resultant force of magnitude 12 N. If the magnitude of force P is 5 N, which ONE of the following is a possible magnitude of force Q? A. 20 N. B. 14 N. C. 6 N. D. 5 N. 1.2 Which of the following best demonstrates the concept of inertia? A. A ball moving through a vacuum in space. B. An object comes to rest after the force acting on it is removed. C. The driver of a car moves in a forward direction when the car suddenly stops. D. A ball striking the ground and bouncing back up. 1.3 An object of mass m is pulled up a rough incline at a CONSTANT VELOCITY, as shown in the diagram below. Which ONE of the following is correct for the relationship between the forces acting on the object? A. F cosθ + fk = mg sinθ. B. mg sinθ + fk − F cosθ = 0. C. F cosθ − fk + mg sinθ = 0. D. F cosθ = mg sinθ.

QUESTION 6 A rocket, with its fuel, has a mass of 20 000 kg on the surface of Earth. The rocket is launched vertically upwards and its mass decreases uniformly as the fuel burns. At a height of 6,4 × 10⁸ m above the surface of Earth, the rocket's mass DECREASES by 5000 kg. 6.1 State Newton's law of universal gravitation in words. 6.2 Calculate the weight of the rocket on the surface of Earth. 6.3 Determine the percentage reduction in the rocket's weight when it is 6,4 × 10⁸ m above the surface of Earth. The rocket's mass decreased by 25% as it ascends from the ground to 6,4 × 10⁸ m above the surface of Earth. 6.4 Explain why the percentage reduction in the rocket's weight is considerably larger than the percentage reduction in the rocket's mass. QUESTION 7 A metal sphere P, which was initially neutral, is given a charge of −8 μC. 7.1 Determine the number of electrons added to P to obtain a charge of −8 μC. Sphere R, carrying a charge of 5 μC, is placed 20 cm to the right of sphere P along a straight line. Point X is located 5 cm to the right of sphere R, as shown in the diagram below. 7.2 Define the term electric field at a point in words. 7.3 Calculate the net electric field at point X.

1.5 The acceleration due to gravity on the surface of Earth is g. Which ONE of the following is the gravitational acceleration on another planet which has HALF the mass of Earth and ONE-QUARTER of Earth's radius? A. 2g. B. 4g. C. 8g. D. 16g. 1.6 A small sphere, carrying a constant charge, is placed r metres from a fixed point, P. The electric field E at P is measured for different values of r. Which of the following graphs correctly shows the relationship between the electric field E at P and r²? (Four E-versus-r² graphs are given as options.)

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 (1.1-1.7) in the ANSWER BOOK, for example 1.8 E. 1.1 Consider the vector diagram below, showing vectors W, X, Y and Z. Which ONE of the vectors is the resultant of the other three? A. W. B. X. C. Y. D. Z. 1.2 The forces acting on an object are in equilibrium. Consider the following statements: (i) The object could be stationary. (ii) The object could be moving at a constant velocity. (iii) The acceleration of the object is zero. Which of the above statements is/are true? A. (i) only. B. (ii) only. C. (i) and (iii) only. D. (i), (ii) and (iii).

1.5 A force of magnitude F acts on a block at an angle θ to the horizontal, as shown in the diagram below. The block, at rest on a flat, frictionless surface, accelerates. Angle θ is now changed. How will the NORMAL FORCE and the NET HORIZONTAL FORCE acting on the block change? 1.6 Three objects of mass 1,6 kg, 2 kg and 0,7 kg respectively, are suspended by a light string, as shown in the diagram below. Calculate the tension in the string at point P. A. 15 N. B. 42 N. C. 27 N.

QUESTION 1: MULTIPLE-CHOICE QUESTIONS. Four options are provided as possible answers to the following questions. Each question has only ONE correct answer. Write only the letter (A – D) next to the question number (1.1-1.10) in the ANSWER BOOK, for example 1.11 D. 1.1 The statement below refers to vector and scalar quantities. (i) A vector has magnitude and direction, while a scalar has magnitude only. (ii) A scalar quantity can always be added to a vector quantity. (iii) Force is an example of a vector quantity, while distance is an example of a scalar quantity. Which of the above statements is/are TRUE? A. (i) only. B. (i) and (ii) only. C. (i) and (iii) only. D. (i), (ii) and (iii). 1.2 Four forces act on a body in the diagram below. Determine the magnitude and direction of the resultant force. (Two of the four answer options are legible: C. 8 N east; D. 8 N south.)

3.4 Show that the relationship between the applied force and acceleration can be written as: a = F/m − fk/m. 3.5 Use the graph to calculate the mass of the trolley. 3.6 Hence calculate the coefficient of static friction between the surface and the trolley. 3.7 Determine the magnitude of the kinetic frictional force acting on the trolley. QUESTION 4 4.1 Block A of unknown mass and block B of mass 7 kg are placed on a rough incline that makes an angle of 35° with the horizontal. The blocks, initially at rest, are connected by a light, inextensible string. A constant force of 112 N, acting parallel to the incline, is applied to block B so that both blocks move up the incline. Each block travels 0,7 m up the incline in 0,536 seconds. The kinetic frictional force acting on blocks A and B are 3 N and 5 N respectively. 4.1.1 Show by means of a calculation that the magnitude of the acceleration of the blocks was 4,87 m·s⁻² while moving up the incline. 4.1.2 Draw a labelled free-body diagram for block B while it was moving up the slope. 4.1.3 Determine the mass of block A.

1.3 A net force F is applied on an object of mass m and causes an acceleration of a m·s⁻². When the net force F on the same object is doubled, the resulting acceleration will be ... 1.4 A 4 kg mass is pulled along a frictionless slope, inclined at an angle θ, by a force F, as shown in the sketch below. Which ONE of the following equations can be used to calculate the magnitude of the normal force (N)? A. N = (4)(9,8) sinθ. B. N = F − (4)(9,8) cosθ. C. N = F + (4)(9,8) cosθ.

1.10 A negative charge Q is placed at a distance of 5d from another charge R, as shown in the diagram below. (The answer options give different combinations of the ratio of the charges and the sign of the charge on R.) QUESTION 2 A heavy object is lifted using two ropes and two pulleys, as shown in the diagram below. The two pulleys are a distance X apart. The force FA, in rope A, is 530 N and the force FB, in rope B, is 1240 N. Rope A makes an angle of 60° with the horizontal and rope B makes an angle of 20° with the vertical. 2.1 Define the term resultant vector. 2.2 Explain why the vector diagram of force FA, force FB and the weight will NOT be a closed vector diagram. 2.3 Calculate the: 2.3.1 Vertical component of FA. 2.3.2 Horizontal component of FA.

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 (1.1–1.7) in the ANSWER BOOK, for example 1.8 E. 1.1 Two forces, F1 and F2, act simultaneously at a point. The resultant force is 17 N when they act in the same direction, and 5 N when they act in opposite directions. The magnitudes of the two forces are… A. 14 N and 3 N. B. 11 N and 6 N. C. 5 N and 12 N. D. 10 N and 7 N. 1.2 A person stands on a bathroom scale that is calibrated in newtons, in a stationary elevator. The reading on the bathroom scale is W. The elevator now moves downward with a constant acceleration of ¼g, where g is the gravitational acceleration on Earth. What will the reading on the bathroom scale now be? A. ¼W. B. ¾W. C. W. D. 5/4 W.

1.3 Two objects of masses 2m and m are arranged as shown in the diagram below. Which of the following changes will result in the largest increase in the gravitational force the two objects exert on each other? A. Double the mass of each object. B. Double the larger mass and double the distance between their centres. C. Double the larger mass and half the distance between their centres. D. Triple the smaller mass and half the distance between their centres. 1.4 Two charges, +Q and −Q, are each placed a distance d from a negative charge −q. The charges, +Q and −Q, are located along lines that are perpendicular to each other, as shown in the diagram below. Which ONE of the following arrows CORRECTLY shows the direction of the net force acting on charge −q due to the presence of charges +Q and −Q? (Four directional-arrow diagrams are given as options.)

QUESTION 1. 1.1 Consider the vector diagram below: W, X, Y, Z. Which ONE of the following vectors is the resultant of the other three? A. W B. X C. Y D. Z. 1.2 The forces acting on an object are in equilibrium. Consider the following statements: (i) The object could be stationary (ii) The object could be moving at a constant velocity (iii) The acceleration of the object is zero. Which of the above statements is/are true? A. (i) only B. (ii) only C. (i) and (iii) only D. (i), (ii) and (iii). 1.5 The acceleration due to gravity on the surface of Earth is g. Which ONE of the following is the gravitational acceleration on another planet which has HALF the mass of Earth and ONE-QUARTER of Earth's radius? A. 2g B. 4g C. 8g D. 16g. 1.6 A small sphere, carrying a constant charge, is placed r metres from a fixed point, P. The electric field E at P is measured for different values of r. Which of the following graphs correctly shows the relationship between the electric field E at P and r²? 1.7 Two identical conducting spheres carrying charges Q and −2Q are placed r metres apart. The electrostatic force acting on each sphere is F. The spheres are brought into contact and are then separated so that the distance between them remains r metres. Which ONE of the following is the magnitude of the electrostatic force that the spheres exert on each other after they are separated? A. F B. F/2 C. F/8 D. F/4. QUESTION 2. A box is lifted vertically upwards at CONSTANT VELOCITY using two light, inextensible strings, P and Q. The strings pass over frictionless pulleys attached to a horizontal ceiling and are attached to the box at point X, as shown in the diagram below. The tension in string P, which makes an angle of 50° with the ceiling, is 200 N. String Q makes an angle of 40° with the ceiling. Ignore the effects of air resistance and assume that the box does not rotate while being lifted. 2.1 What is meant by a closed vector diagram? 2.2 Draw a fully labelled closed vector diagram representing all forces acting on the box. Indicate any TWO angles. 2.3 Calculate: 2.3.1 The magnitude of the tension in string Q 2.3.2 The mass of the box.

QUESTION 1: MULTIPLE-CHOICE QUESTIONS. 1.1 The statement below refers to vector and scalar quantities: (i) A vector has magnitude and direction, while a scalar has magnitude only. (ii) A scalar quantity can always be added to a vector quantity. (iii) Force is an example of a vector quantity, while distance is an example of a scalar quantity. Which of the above statements is/are TRUE? A. (i) only B. (i) and (ii) only C. (i) and (iii) only D. (i), (ii) and (iii). 1.3 A net force F is applied on an object of mass m kg and causes an acceleration of a m·s⁻². When the net force F on the same object is doubled, the resulting acceleration, in m·s⁻², will be... 1.4 A 1 kg mass is pulled along a frictionless slope, inclined at an angle, by a force shown in the sketch below. Which ONE of the following equations can be used to calculate the magnitude of the normal force (N)? A. N = (1)(9,8) sin θ B. N = F − (1)(9,8) cos θ C. N = F + (1)(9,8) cos θ D. N = (1)(9,8) cos θ. 1.7 The distance between two charges, Q₁ and Q₂, is r. The force exerted by the spheres on each other is F. Both charges are now doubled without changing the distance between them. The magnitude of the electrostatic force on Q₁ will be: A. 4F B. ½F C. 2F D. ¼F. 1.8 Two bodies, X and Y, of mass M and m respectively, exert a force F on each other when they are a certain distance apart. The mass of one of the bodies is doubled and the distance between their centres is halved. What is the new force that the bodies exert on each other, in terms of F? A. 8F B. 16F C. 4F D. 2F. QUESTION 2. A heavy object is lifted using two ropes and two pulleys, as shown in the diagram below. The two pulleys are a distance X apart. The force Fₐ, in rope A, is 530 N and the force F_B, in rope B, is 1 240 N. Rope A makes an angle of 60° with the horizontal and rope B makes an angle of 20° with the vertical. 2.1 Define the term resultant vector. 2.2 Explain why the vector diagram of force Fₐ, force F_B and the weight will NOT be a closed vector diagram. 2.3 Calculate the: 2.3.1 Vertical component of Fₐ 2.3.2 Horizontal component of Fₐ. 2.4 Calculate the maximum weight that force Fₐ and force F_B will be able to lift from the ground. Show ALL calculations. 2.5 Explain why the rope and pulley system will be less effective if the distance X between the pulleys is increased.

QUESTION 1. 1.1 Two forces P and Q act at a point O. As the angle θ between P and Q varies, the MAXIMUM and MINIMUM resultant forces are 13 N and 3 N respectively. The magnitudes of the two forces are: A. 3 N and 10 N B. 16 N and 10 N C. 8 N and 5 N D. 10 N and 7 N. 1.2 A passenger standing in a moving bus moves forward when the bus suddenly stops. This can best be explained by A. Newton's First law of motion B. Newton's Second law of motion C. Newton's Third law of motion D. Newton's law of Universal gravitation. 1.3 A learner sits on a chair. What is the reaction force to her sitting on the chair? A. Force that the learner exerts on the chair. B. Weight of the learner. C. Force that the chair exerts on the learner. D. Force that the learner exerts on Earth. 1.5 A car, moving to the right along a rough horizontal surface, is brought to rest by a constant net force. If the motion to the right is taken as positive, which ONE of the following acceleration versus time graphs is correct for the motion of the car? 1.6 The graphs P, Q, R and S drawn below show a relationship between the force of attraction that two masses exert on each other and the inverse of the square of the distance between their centres. In which graph will the product of their masses be the largest? A. P B. Q C. R D. S. 1.7 The force of attraction between two charges q₁ and q₂ is F. If the distance between the charges is made four times smaller, then the new force of attraction will be... A. 0,5F B. 1,78F C. 2,5F D. 16F. 1.8 The north pole of a bar magnet is pushed into a solenoid, as shown in the sketch below. The polarity of X on the solenoid and the direction of flow of the induced current through the solenoid will be... 1.9 The ampere second (A·s) is the unit for A. Current strength B. Quantity of charge C. Resistance D. Potential difference. 1.10 Which ONE of the following graphs represents the relationship between the total electrical energy transferred (W) and the electric current (I) in the element of a kettle? The resistance of the element and the time for which the current flows are constant. QUESTION 2. Three forces Fₐ, F_B and F_C act on a point O in the directions shown in the diagram below. The magnitudes of Fₐ and F_C are 44 N and 31 N respectively. The magnitude of F_B is unknown. The forces are NOT drawn to scale. 2.1 Define the term resultant vector. The resultant of the three forces is 26,69 N at an angle of 25,82° to the horizontal, and lies in the first quadrant. 2.2 Calculate the magnitude of F_B. 2.3 Determine θ.

4.2 A spaceship, with its engines switched off, is moving towards Earth. The mass of the spaceship is 1250 kg. 4.2.1 State Newton's Law of universal gravitation in words. 4.2.2 Calculate the distance between the spaceship and the centre of Earth when Earth exerts a force of 2458 N on the spaceship. QUESTION 5. Two small, identical positively charged spheres, A and B, are suspended from the ceiling at point C by non-conducting threads as shown below. 5.1.1 Draw a labelled closed vector triangle showing all the forces acting on sphere A. Include TWO angles in the triangle. 5.1.2 If the mass of each sphere is 1,5 g, calculate the magnitude of the electrostatic force acting on sphere A. 5.1.3 Calculate the magnitude of the electric field at sphere A due to sphere B if the charge on each sphere is 4,80 nC.

QUESTION 1. 1.1 Two forces, F₁ and F₂, act simultaneously at a point. The resultant force is 17 N when they act in the same direction, and 5 N when they act in opposite directions. The magnitude of the two forces are: A. 14 N and 3 N B. 11 N and 6 N C. 5 N and 12 N D. 10 N and 7 N. 1.2 A person stands on a bathroom scale that is calibrated in newton, in a stationary elevator. The reading on the bathroom scale is W. The elevator now moves downward with a constant acceleration of ¼g, where g is the gravitational acceleration on Earth. What will the reading on the bathroom scale now be? A. ¼W B. ¾W C. W D. 5/4 W. 1.3 Two objects of masses 2m and m are arranged as shown in the diagram below. Which of the following changes will result in the largest increase in the gravitational force the two objects exert on each other? A. Double the mass of each object. B. Double the larger mass and double the distance between their centres. C. Double the larger mass and halve the distance between their centres. D. Triple the smaller mass and halve the distance between their centres. 1.4 Two charges, +Q and −Q, are each placed a distance d from a negative charge −q. The charges, +Q and −Q, are located along lines that are perpendicular to each other, as shown in the diagram below. Which ONE of the following arrows CORRECTLY shows the direction of the net force acting on charge −q due to the presence of charges +Q and −Q? 1.5 The diagram below shows a magnet that is moved towards a solenoid. Which ONE of the following combinations are CORRECT? A. North, X to Y B. North, Y to X C. South, X to Y D. South, Y to X. 1.6 Which ONE of the following graphs best represents the relationship between the electrical power (P) dissipated by a resistor and the potential difference (V) across the resistor if the resistance of the resistor remains constant? 1.7 Which ONE of the following is the unit of measurement for the rate of flow of charge? A. Coulomb B. Ampere C. Volts D. Watts. QUESTION 2. Two forces act simultaneously on a small boat in a flat part of a river: the motor exerts a force of 1 200 N at an angle of 40° north of east; the river current exerts a force of 800 N in a northerly direction. The boat is at point O. 2.1 Define the term resultant vector. 2.2 Using an accurate scale drawing, determine the magnitude and direction of the resultant force acting on the boat. Use the scale 1 cm : 200 N.