Work energy and power: Grade 12 Past Paper Questions

A 12 kg block is initially at rest at point A at the bottom of a ROUGH inclined plane. The block is pulled up the incline by a constant force F acting parallel to the incline. The block reaches point B, which is at a vertical height of 4,5 m above the horizontal, with a speed of 2,25 m·s⁻¹. 5.1 Define the term non-conservative force. 5.2 Draw a labelled free-body diagram for the block when it is pulled up the inclined plane. 5.3 Calculate the total work done on the block by the NON-CONSERVATIVE forces when the block moved from point A to point B. The same constant force F now moves the block at a CONSTANT VELOCITY across a rough horizontal surface from point B to point C. Force F acts parallel to the horizontal surface. The magnitude of the constant frictional force acting on the block while moving from point B to point C is 42 N larger than the magnitude of the constant frictional force acting on the block when it moves from point A to point B. 5.4 Calculate the distance from point A to point B.

A constant force F is applied at an angle of 30° to the horizontal on a crate of mass 6 kg that is initially at rest, as shown in the diagram below. A constant frictional force of 10 N acts on the crate as it moves from rest at point A along a horizontal surface to point B. The distance between point A and point B is 1,5 m. The speed of the crate at point B is 2 m·s⁻¹. 5.1 Define the term work done by a force. 5.2 Draw a labelled free-body diagram showing ALL the forces acting on the crate as it moves. 5.3 Using ENERGY PRINCIPLES ONLY, calculate the magnitude of force F. 5.4 A 2 kg object is placed in the crate. What effect will this have on the work done by the same force F when the crate is again moved from point A to point B? Write only INCREASES, DECREASES or REMAINS THE SAME.

An electric motor pulls a 20 kg crate from rest at point A up an inclined plane by means of a light inextensible rope. The inclined plane makes an angle of 18° with the horizontal. B, C and D are points on the inclined plane and the distance between points A and C is 15,6 m, as shown in the diagram below. The motor exerts a constant force of 96,8 N parallel to the inclined plane on the rope. A constant frictional force of 13,5 N acts on the crate as it moves on the inclined plane. 5.1 Define a non-conservative force. 5.2 Use ENERGY PRINCIPLES to calculate the speed of the crate when it reaches point C. 5.3 Calculate the minimum average power dissipated by the electric motor to pull the crate from point A to point C. When the crate reaches point C, the rope breaks. The crate continues moving up the inclined plane, comes to a stop at point D, and then slides down the plane past point B. 5.4 Draw a labelled free-body diagram for the crate as it slides down the plane past point B. 5.5 Draw a velocity-time graph for the entire motion of the crate starting from point A until it passes point B again on its motion down the inclined plane.

A bullet of mass 6 g is shot horizontally into a 194 g wooden block, which is at rest on a horizontal surface. The bullet hits the block with a velocity of 200 m·s⁻¹ and remains stuck in the block. Ignore the effects of friction. 4.1 State the principle of conservation of momentum in words. 4.2 Calculate the speed of the block-bullet system immediately after the bullet struck the block. Immediately after the impact, the block-bullet system enters a rough section PQ, which is 5 m long, before coming to rest. 4.3 Calculate the acceleration of the block-bullet system. 4.4 A box, of mass 60 kg, slides down a rough incline which makes an angle of 25° with the horizontal. The box experiences a constant frictional force of 180 N. 4.4.1 Draw a free-body diagram showing all the forces acting on the box. 4.4.2 Write down the name of the force which does zero work on the box.

A 2 kg box is released from rest at point P, 5 m above the ground. It slides down a smooth frictionless curved track PQ. 5.1 State the principle of conservation of mechanical energy in words. 5.2 Use the PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY to calculate the speed of the box when it reaches point Q. The box passes point Q and moves 10 m on a rough horizontal surface before striking a barrier at point R at a speed of 4 m·s⁻¹. 5.3 Use ENERGY PRINCIPLES to calculate the magnitude of the average frictional force acting on the box as it moves from Q to R. The barrier exerts an impulse of 14 N·s to the left on the box when the box strikes the barrier. 5.4 Calculate the change in kinetic energy of the box after striking the barrier.

Water is drawn from a water source 12,5 m below the ground by an electric pump. The water is lifted vertically upwards at a constant speed, as shown in the simplified diagram below. The pump lifts the water upwards at a rate of 2,5 kg·s⁻¹. Ignore ALL frictional and capillarity effects. 5.1 Define the term non-conservative force. 5.2 Draw a labelled free-body diagram showing ALL the forces acting on a fixed mass of water as it moves from the source to the ground. 5.3 The pump lifts 200 kg of water from the source to the ground at a constant speed. Calculate the: 5.3.1 Work done by the pump. 5.3.2 Constant speed at which the water is lifted. 5.3.3 Average power dissipated by the pump. Ignore energy losses in the form of heat and sound.

A block of mass M kg moves along a rough horizontal surface while experiencing a constant frictional force of 3 N. It passes point X with a speed of 8 m·s⁻¹ and reaches point Y with a speed v. Point Y is 4 m to the right of point X. 5.1 Using ENERGY PRINCIPLES ONLY, show that v is given by v = √(64 − 24/M). The block then moves up an incline that is at an angle of 30° with the horizontal. The block experiences a constant frictional force of 2 N as it moves a distance of 5,03 m up the incline and comes to rest at point P. 5.2 Using ENERGY PRINCIPLES ONLY, calculate the mass of the block.

A person on a sandboard, with a combined mass of 62 kg, goes sandboarding down a sand dune in Boksburg, Mount Mayhem, South Africa. The person’s velocity increases from 8,5 m·s⁻¹ to 23,3 m·s⁻¹ from point A to point B. The work done by friction from point A to point B is 8 700 J. 6.1 Define the term non-conservative force. 6.2 Calculate the height at which the person starts, at point A, using ENERGY PRINCIPLES ONLY. 6.3 Define the term power. 6.4 Draw a free-body diagram of all the horizontal forces acting on the person while moving from point B to point C. 6.5 The average power dissipated by the person until he stops, is 4 593,83 W. Calculate the average force experienced by the person during this motion.

A box of mass 7 kg, which is initially at rest, is acted upon by a constant force of 80 N that is applied at an angle θ to the horizontal. The box experiences a constant frictional force of 8 N as it moves from rest at point X along a horizontal surface to point Y and passes point Y with a speed of 1,5 m·s⁻¹. 5.1 Draw a labelled free-body diagram showing ALL the forces acting on the box as it moves. 5.2 Define the term work done by a force. 5.3 Calculate the size of angle θ, by using ENERGY PRINCIPLES only. 5.4 The angle between the applied force of 80 N and the horizontal is now decreased. What effect will this have on the work done by the same applied force when the box is moved from point X to point Y? Write only INCREASES, DECREASES or REMAINS THE SAME.

1.4 A car travels at CONSTANT VELOCITY along a horizontal road. A constant frictional force acts on the car during its motion. Which ONE of the following statements about the power dissipated by the engine of the car during the motion is CORRECT? The power… A. is zero. B. increases. C. decreases. D. remains constant. 1.5 Block X is placed on a horizontal table and is connected to block Y by a light inextensible string passing over a frictionless pulley, as shown below. A constant frictional force acts on block X while it moves to the right. P, Q and R are points on the table such that the distance from P to Q is equal to that from Q to R. When block X reaches point Q, the string is cut and block X continues to move towards point R. Ignore the effect of air friction. Consider the following statements: (i) The work done by the frictional force acting on block X is greater when the block moves from point P to point Q than when the block moves from point Q to point R. (ii) Both the momentum and kinetic energy of block X decrease when the block moves from point Q to point R. (iii) The total mechanical energy of block X remains constant when the block moves from point Q to point R. Which of the statements above is/are CORRECT as block X moves from point Q to point R? A. (i) only. B. (ii) only. C. (i) and (ii) only. D. (ii) and (iii) only.

1.3 A ball moving horizontally has constant momentum p and kinetic energy K. The ball collides with a wall and bounces back horizontally. Immediately after the collision, the ball has momentum ½p. The mass of the ball remains constant. Which ONE of the following is the kinetic energy of the ball immediately after the collision? A. ¼K. B. ½K. C. 2K. D. 4K. 1.4 A force F acts on a box as the box moves from rest down a rough incline at a constant acceleration. The force is parallel to the incline, as shown in the diagram below. Choose the option that correctly completes the following statement. The work done by the gravitational force is … the work done by the frictional force and the work done by F. A. Equal to the sum of. B. Less than the sum of. C. Greater than the sum of. D. Equal to the difference between.

1.4 A ball is thrown vertically upwards into the air. Ignore the effects of air friction. The net force acting on the ball when the ball is at its highest point is ... A. Zero. B. Equal to the weight of the ball. C. Less than the weight of the ball. D. Greater than the weight of the ball. 1.5 Which ONE of the following statements is always true for inelastic collisions in an isolated system? A. Both momentum and kinetic energy are conserved. B. Both momentum and kinetic energy are not conserved. C. Momentum is conserved, but kinetic energy is not conserved. D. Kinetic energy is conserved, but momentum is not conserved. 1.6 An object moving horizontally at a constant velocity suddenly encounters a rough horizontal surface. The object continues to move over this rough surface. Which ONE of the following statements is correct? The net work done on the object during the motion over the rough surface is ... A. Zero. B. Positive. C. Negative. D. Constant. 1.7 The hooter of a car emits sound of constant frequency as the car moves away from a stationary listener. Which ONE of the following properties of the sound heard by the listener will NOT change? A. Speed. B. Frequency.

1.4 A person of mass M is moving to the left on a skateboard of mass m. The initial velocity of the person and the skateboard is v. The person then jumps off the skateboard and is stationary while the skateboard continues to move to the left. Which of the following expressions can be used to correctly calculate the speed of the skateboard after the person jumps off? A. (M+m)v/m. B. (Mv+mv)/m. C. mv/(M+m). D. (M−m)v/m. 1.5 An apple falls from a tree. Which of the following statements about the falling apple is TRUE? Ignore all effects of air friction. A. Total momentum is conserved. B. Total kinetic energy is conserved. C. The total mechanical energy is conserved. D. The gravitational potential energy is conserved. 1.6 An ambulance moves towards a stationary listener at a constant speed while emitting soundwaves with a wavelength of 0,72 m. The wavelength of a soundwave observed by the listener becomes ... A. Larger than 0,72 m. B. Smaller than 0,72 m. C. Equal to 0,72 m. D. Larger and then zero.

The box now passes point A on the incline at a speed of 4 m·s⁻¹ before passing point B, which is 15 m lower down the incline. 4.4.3 Calculate the kinetic energy of the box as it passes point A. 4.4.4 Calculate the magnitude of the resultant force acting on the box between point A and B. 4.4.5 State the work-energy theorem in words. 4.4.6 Use the work-energy theorem to calculate the speed of the box as it passes point B. A 200 W motor, operating at a certain efficiency, pulls a crate of mass 90 kg up a slope at a constant speed, taking 30 s to raise the crate from point X to Y of the slope. 5.1 Define the term power. 5.2 Calculate the: 5.2.1 Energy supplied by the motor to the crate in 30 s. 5.2.2 Gain in gravitational potential energy of the crate between X and Y. 5.2.3 Magnitude of the frictional force acting on the crate between X and Y.

1.4 A trolley with a mass m has momentum p. The kinetic energy of the trolley will be: A. pm. B. p/m. C. pm/2. D. p²/(2m). 1.5 An object is moved from rest in a straight line across a flat surface by a changing horizontal force. The changing force is plotted against the position of the object to produce the graph below. The work done on the object by the applied force from x = 0 m to x = 8 m is: A. 40 J. B. 80 J. C. 108 J. D. 125 J. 1.6 The reason why the observed pitch of the sound wave of an ambulance decreases as the ambulance moves away from a stationary observer is because the: A. amplitude of the sound wave increases. B. amplitude of the sound wave decreases. C. wavelength of the sound wave increases. D. wavelength of the sound wave decreases.