Work Energy Power
for secondary 3 and 4 students
Math Arena
Subject Content
Energy (Kinetic and Potential) and its relationship with work
Discuss the different forms of kinetic energy Q1
Discuss the different types of potential energy Q2
A box is being pushed horizontally on a smooth surface by a 10 N force for 6m [WEP1] Q3
A box of mass 2 kg is being pushed horizontally on a smooth surface by a 10 N force for 6m [WEP1] Q4
A box of mass 2 kg is being pushed horizontally on a rough surface by a 10 N force for 6m [WEP1] Q5
A box of mass 2 kg is being pushed horizontally on a smooth surface by a 10 N force for 6m (by the weight of the box) [WEP1] Q6
A box of 2kg is being pushed horizontally on a smooth surface by a 10 N force for 60 cm [WEP1] Q7
A box of mass 2 kg is moving at a constant speed [WEP1] Q8
A box of mass 500g is moving at a constant speed of 72 km/h [WEP1] Q9
A box of mass 2 kg increases its speed from 3 m/s to 7 m/s [WEP1] Q10
A box of mass 2 kg is lifted vertically upwards by 3m. [WEP1] Q11
A box of mass 2 kg is lifted vertically upwards by 3m. [WEP1] Q11 Go Deeper
A box of mass 2 kg is lifted vertically upwards by 3m. (What is the GPE?) [WEP1] Q12
There are 3 paths leading up to a hill [WEP1] Q13
A box of mass 2 kg moves up a ramp from point A to point B. [WEP1] Q14
A box of mass 2 kg moves up a ramp from point A to point B. [WEP1] Q14 Go deeper
A pendulum bob pivots at a point P. [WEP1] Q15
Three different stones are lifted from ground level (Different Planets) [WEP1] Q16
A box is being pushed horizontally on a smooth surface by a 10 N force for 6 m. [WEP1] Q17
A 1.2 kg box is being pushed horizontally on a smooth surface by a 10 N force for 6 m. [WEP1] Q18
A 6 kg box is being pushed horizontally on a smooth surface by a 10 N force for 6 m. [WEP1] Q19
A 6 kg box is being pushed horizontally on a rough surface by a 10N force [WEP1] Q20
A 6 kg box is being pushed horizontally on a rough surface by a 10N force [WEP1] Q20 Go deeper
A 6 kg box is being pushed horizontally on a surface by a 10N force for 6m [WEP1] Q21
A 6 kg box is being pulled up a ramp by a force F at a constant speed (involves GPE)[WEP1] Q22
A 6 kg box is being pulled up a ramp by a force F at a constant speed [WEP1] Q22 Vector triangles method
A 6 kg box is being pulled up a ramp by a force F from rest [WEP1] Q23
A box of 6 kg mass is being pulled by a 50N force from an initial speed of 4 m/s [WEP1] Q24
A box on unknown mass is being pulled by a 8 N force (requires trigonometry) [WEP] Q25
A box of 2 kg mass has initial speed of 10 m/s at the foot of the ramp (max ht, requires trigonometry) [WEP1] Q26
A box of mass 2kg has an initial speed of 10 m/s at the foot of the ramp (height h, requires trigonometry) [WEP1] Q27
A box of mass 2 kg slides down from the top of the ramp with an initial speed of 0 m/s [WEP1] Q 28
A box is being pushed horizontally on a smooth surface by a 10N force [WEP1] Q29
A man lifts a box of mass 2 kg vertically upwards by 3m [WEP1] Q30
A 1000 kg motorcar travels at a constant speed of 30 m/s [WEP1] Q31
A 1000 kg motorcar travels at a constant speed of 30 m/s [WEP1] Q31 Go deeper
A motor car of mass 500 kg generate a power of 1000W [WEP1] Q32
A motor car of mass 500 kg generates a power of 10000W (resistance on the motor car is 200 N) [WEP1] Q33
A 100 W spotlight has an efficiency of 40% [WEP1] Q34
The speed time graph shows the motion of a motorcar on a level road within a 10s duration [WEP1] Q35
A 100 g mass drops from a 10m building (finding kinetic energy) [WEP1] Q36
A 100 g mass drops from a 10m building (finding speed) [WEP1] Q37
A worm of mass 2g crawls up a flight of steps from point A to point B [WEP1] Q38
A worm of mass 2g crawls up a flight of steps from point A to point B (with friction) [WEP1] Q39
A bullet hits a target board at a speed of 300 m/s. [WEP1] Q40
A mass of 2kg is suspended by a 1.0m string and is set free at point A [WEP1] Q41
A 3kg mass is being pulled along a horizontal bench at a constant speed of 5 m/s by a 10 N horizontal force [WEP1] Q42
A bullet leaves the vertical barrel of a rifle and reaches a height of 720m [WEP1] Q43
A car of mass M has an engine which can deliver power P [WEP1] Q44
A block of mass 1kg has a speed of 20 m/s at a point A [WEP1] Q45
A bullet leaves the vertical barrel of a rifle and reaches a height of 720 m [WEP1] Q46
A cable car of mass 200 kg travels up a hill from an altitude 1030 m to an altitude of 1150 m [WEP1] Q47
A block resting on a smooth horizontal floor is being pushed by a constant horizontal force. [WEP1] Q48
A 1 kg mass and a 5 kg mass are held at a position along the ramps as shown [WEP1] Q50
A mass hangs on a string fixed at point P. It starts from position 1 and swings to the furthest position on the opposite side, position 2. [WEP 2] Set A Q1
A man standing at the top of a cliff throws a stone. Which forms of energy does the stone have at X and at Y? [WEP 2] Set A Q2
A rubber ball is dropped from a height of 2 m on to a table. Whilst in contact with the table, some of its energy is converted into internal energy. What is the highest possible point the ball could reach after bouncing? [WEP 2] Set A Q3
A ball is released from rest and rolls down a track from the position shown. What is the furthest position the ball could reach? [WEP 2] Set A Q4
The graph shows how the height above the ground of a bouncing ball changes with time. Which statement explains why the height of each peak decreases with time? [WEP 2] Set A Q5
A workman rolls a barrel of weight 2000 N up a plank of length 2.00 m and on to a lorry. The back of the lorry is 0.80 m above the horizontal surface of the road. What is the work done on the barrel against gravity? [WEP 2] Set A Q6
A 2 kg mass is moving at constant speed. The kinetic energy of the mass is 400 J. What is the speed of the mass? [WEP 2] Set A Q7
An object is lifted vertically 2.0 m and held there. If the object weighs 90 N, how much work was done in lifting it? [WEP 2] Set A Q8
A 500-kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0 m. What is the work done by the weight of the elevator? [WEP 2] Set A Q9
A 15.0-kg object is moved from a height of 7.00 m above a floor to a height of 13.0 m above the floor. What is the change in gravitational potential energy? [WEP 2] Set A Q10
A boy holds a 40-N weight at arm's length for 10 s. His arm is 1.5 m above the ground. The work done by the force of the boy on the weight while he is holding it is: [WEP 2] Set A Q11
A 2-kg object is moving at 3 m/s. A 4-N force is applied in the direction of motion and then removed after the object has traveled an additional 5 m. The work done by this force is: [WEP 2] Set A Q12
A wooden block of mass 30 kg is pulled up a rough inclined plane at a constant speed by a force of 70 N. [WEP 2] Set A Q13
Hydroelectric, tidal and fossil fuels are three sources of energy. Which of these are renewable energy sources? [WEP 2] Set A Q14
Which represents the main energy changes that take place in a coal-fired power station? [WEP 2] Set A Q15
In a hydroelectric power station, water from a reservoir falls down a long pipe before entering the turbines. The turbines then turn the generator. What is the overall energy conversion? [WEP 2] Set A Q16
Which type of power station does not use steam from boiling water to generate electricity? [WEP 2] Set A Q17
Which type of power station does not use steam from boiling water to generate electricity? [WEP 2] Set A Q18
The diagram shows water stored behind a dam. The water flows to a turbine and turns a generator. Which sequence for the conversion of energy is correct? [WEP 2] Set A Q19
Which process in the Sun produces energy? [WEP 2] Set A Q20
A large electric motor is used to lift a container off a ship. Which of the following values are enough to allow the power of the motor to be calculated? [WEP 2] Set A Q21
A girl of weight 500 N runs up a flight of stairs in 10 seconds. The vertical height of the stairs is 5 m. What is the average power developed by the girl? [WEP 2] Set A Q22
Four students exercise in a gym. Which student does the most work? [WEP 2] Set A Q23
When a 300 N force is applied to a box weighing 600 N, the box moves 3.0 m horizontally in 20 s. What is the average power? [WEP 2] Set A Q24
A boy and a girl run up a hill in the same time. The boy weighs more than the girl. Which statement is true about the power produced? [WEP 2] Set A Q25
A worker is lifting boxes of identical weight from the ground onto a moving belt. At first, it takes him 2 s to lift each box. Later in the day, it takes him 3 s. Which statement is correct? [WEP 2] Set A Q26
Four people of equal weight on a beach use different routes to get to the top of a sea wall. Which person produces the greatest average power? [WEP 2] Set A Q27
A man of mass 80 kg is raised by a lift of 500 kg at a constant speed of 2.0 ms-1. What is the power of the lift’s motor? (Acceleration due to gravity = 10 ms-2) [WEP 2] Set A Q28
A small electric motor is used to raise a weight of 2.0 N at constant speed through a vertical height of 80 cm in 4.0 s. Assuming that the motor is 100% efficient, what is the electrical power supplied to the motor? [WEP 2] Set A Q29
Initially, four identical uniform blocks, each of mass m and thickness h, are spread on a table. How much work is done on the blocks in stacking them on top of one another? [WEP 2] Set A Q30
Which formula gives the efficiency of an energy conversion? [WEP 2] Set A Q31
The input power to a motor is 300 W. In 20 s it lifts a load of 400 N through a height of 6.0 m. What is the efficiency of the motor? [WEP 2] Set A Q32
A car is driven along a level road. The total energy input from the petrol is 60 kJ, and the car wastes 45 kJ of energy. What is the efficiency of the car? [WEP 2] Set A Q33
Energy from petrol is used to operate an engine. The engine drives a generator, which produces electrical energy. What is the overall efficiency of the process? [WEP 2] Set A Q34
A crane lifts a weight of 1000 N through a vertical height of 30 m. It uses 60 000 J of energy. What is the efficiency of the crane? [WEP 2] Set A Q35
A crane lifts a load of 1000 N through a vertical height of 3.0 m in 10 s. The input power to the crane is 500 J/s. What is the efficiency of the crane? [WEP 2] Set A Q36
The diagram below represents a 3.0-kilogram mass being moved at a constant speed by a force of 6.0 Newtons. [WEP 2] Set B Q1
The diagram below shows a 20N force pulling an object up a hill at a constant rate of 2 meters per second. [WEP 2] Set B Q2
A student rides a bicycle up a 30.º hill at a constant speed of 6.00 meters per second. The combined mass of the student and bicycle is 70.0 kilograms. What is the kinetic energy of the student-bicycle system during this ride? [WEP 2] Set B Q3
A cart of mass m traveling at speed v has kinetic energy KE. If the mass of the cart is doubled and its speed is halved, the kinetic energy of the cart will be [WEP 2] Set B Q4
Which cart shown below has the greatest kinetic energy? [WEP 2] Set B Q5
An object moving at a constant speed of 25 meters per second possesses 450 joules of kinetic energy. What is the object’s mass? [WEP 2] Set B Q6
Which graph best represents the relationship between the kinetic energy, KE, and the velocity of an object accelerating in a straight line? [WEP 2] Set B Q7
The diagram below shows an object at A that moves over a frictionless surface from A to E. The object has a mass of M. [WEP 2] Set B Q8
The diagram below shows block A, having mass 2m and speed v, and block B having mass m and speed 2v. Compared to the kinetic energy of block A, the kinetic energy of block B is [WEP 2] Set B Q9
If the direction of a moving car changes and its speed remains constant, which quantity must remain the same? [WEP 2] Set B Q10
The graph below represents the velocity-time relationship for a 2.0-kilogram mass moving along a horizontal frictionless surface. The kinetic energy of the mass is greatest during interval [WEP 2] Set B Q11
An inclined plane is 10 m long and is elevated 5 m on one end as shown. Starting from rest at the top of the incline, a box weighing 100 N accelerates down the incline at a rate of 2.5 m s-2 [WEP 2] Set B Q12
The diagram below shows a cart held motionless by an external force F on a frictionless incline. [WEP 2] Set B Q13
A 2.0-kilogram mass is placed on a frictionless track at point A and released from rest. Assume the gravitational potential energy of the system to be zero at point E. [WEP 2] Set B Q14
Which graph best represents the relationship between potential energy (PE) and height above ground (h) for a freely falling object released from rest? [WEP 2] Set B Q15
A simple pendulum has a 2.0-kilogram bob and a length of 10. meters. The pendulum is released from rest at position 1 and swings without friction through position 4 [WEP 2] Set B Q16
As the pendulum swings from position A to position B as shown in the diagram below, what is the relationship of kinetic energy to potential energy? [Neglect friction.] [WEP 2] Set B Q17
Three people of equal mass climb a mountain using paths A , B, and C shown in the diagram below. Along which path(s) does a person gain the greatest amount of gravitational potential energy from start to finish? [WEP 2] Set B Q18
A 10-kilogram block starts from rest at point A and slides along the track. What is the approximate speed of the block at point B? [WEP 2] Set B Q19
Which graph best represents the relationship between the gravitational potential energy of a freely falling object and the object’s height above the ground near the surface of Earth? [WEP 2] Set B Q20
How much work is done on a downhill skier by an average braking force of 9.8 × 102 Newtons to stop her in a distance of 10 meters? [WEP 2] Set B Q21
A box is pushed to the right with a varying horizontal force. The graph below represents the relationship between the applied force and the distance the box moves. [WEP 2] Set B Q22
As shown in the diagram below, a child applies a constant 20-newton force along the handle of a wagon which makes a 25° angle with the horizontal. [WEP 2] Set B Q23
A box is dragged up an incline a distance of 8 meters with a force of 50 Newtons. If the increase in potential energy of the box is 300 joules, the work done against friction is [WEP 2] Set B Q24
In the diagram below, 55 joules of work is needed to raise a 10 N weight 5.0 m. How much work is done to overcome friction as the weight is raised? [WEP 2] Set B Q25
A block weighing 15 N is pulled to the top of an incline that is 0.20 meter above the ground, as shown below. [WEP 2] Set B Q26
A constant force is used to keep a block sliding at constant velocity along a rough horizontal track. As the block slides, there could be an increase in its [WEP 2] Set B Q27
As shown in the diagram below, a student exerts an average force of 600. newtons on a rope to lift a 50.0-kilogram crate a vertical distance of 3.00 meters. [WEP 2] Set B Q28
A motor has an output of 1,000 watts. When the motor is working at full capacity, how much time will it require to lift a 50-newton weight 100 meters? [WEP 2] Set B Q29
A student running up a flight of stairs increases her speed at a constant rate. Which graph best represents the relationship between work and time for the student's run up the stairs? [WEP 2] Set B Q30
A force of 70 Newtons must be exerted to keep a car moving with a constant speed of 10 meters per second. What is the rate at which energy must be supplied? [WEP 2] Set B Q31
A boat weighing 9.0 × 102 N requires a horizontal force of 6.0 × 102 Nto move it across the water at 1.5 × 101 m/s. The boat’s engine must provide energy at the rate of [WEP 2] Set B Q32
If a boy of mass 90 kg takes 3 minutes to run up a flight of 60 steps of height 20 cm each, what is his average power? [WEP 2] Set B Q33
A force of 5 N exerted on an object causes it to accelerate from a velocity of 0 m s-1 to 8 m s-1 in 10 s. Determine the power of this force. [WEP 2] Set B Q34 method 1
A force of 5 N exerted on an object causes it to accelerate from a velocity of 0 m s-1 to 8 m s-1 in 10 s. Determine the power of this force. [WEP 2] Set B Q34 method 2
A baseball bat strikes a ball with an average force of 2.0 × 104 N. If the bat stays in contact with the ball for a distance of 5.0 × 10–3 meter, what kinetic energy will the ball acquire from the bat? [WEP 2] Set B Q35
Sixteen joules of work was required to lift a 2.0-kilogram object from the floor to a table. How much potential energy was gained by the 2.0-kilogram object? [WEP 2] Set B Q36
In the diagram below, an average force of 20. Newtons is used to pull back the string of a bow 0.60 meter. As the arrow, leaves the bow, its kinetic energy is [WEP 2] Set B Q37
At a height of 10 meters above the earth's surface, the potential energy of a 2-kilogram mass is 196 joules. After the mass which starts at rest falls 5 meters, its kinetic energy will be [WEP 2] Set B Q38
When object M is swung to a height of h and released, it passes through the rest position at a speed of 10 meters per second. The height h from which the object was released is approximately [WEP 2] Set B Q39
The diagram represents a 1.00 kilogram object being held at rest on a frictionless incline. [WEP 2] Set B Q40
A ball of mass 400 g rolls down a hill 2.0 m above the bottom of the hill, the speed of the ball is 3.0 m/s. [WEP 2] Set B Q41
The wrecking crane shown below is moving toward a brick wall which is to be torn down. At what point in the swing of the wrecking ball should the ball make contact with the wall to make a collision with the greatest kinetic energy? [WEP 2] Set B Q42
An electric motor is required to haul an object of weight 600 N up a vertical height of 100 min 2.0 minutes. What will be the electrical power required if the overall efficiency of the motor is 80%? [WEP 2] Set B Q43
The motor which drives a lift is working at 80% of its maximum power. The mass of the lift and its load is 500 kg and they are moving vertically upwards at a constant speed of 2 ms-1. [WEP 2] Set B Q44
A motorcar of mass 500 kg generates a power of 10,000 W. How much time does the motorcar need to accelerate from a speed of 10 m s-1 to 20 m s-1? [WEP 2] Set B Q45
A motorcar of mass 500 kg generates a power of 10,000 W. How much time does the motorcar need to accelerate from a speed of 10 m s-1 to 20 m s-1? [WEP 2] Set C Q1
A pendulum bob, swinging down swiftly is obstructed by a nail. Neglecting friction, the bob will then swing up to point [WEP 2] Set C Q2
A ball is allowed to roll along an undulating plane as shown. It is at rest at R. Neglecting air resistance and assuming the plane is smooth, [WEP 2] Set C Q3
On braking, 500 kJ of thermal energy was produced when a vehicle of total mass 1 600 kg was brought to rest on a level road. The speed of the vehicle before the brakes were applied was [WEP 2] Set C Q4
Walking up the top of the steep slope usually seems to be easier if a zigzag path is used instead of climbing by the steepest route. Why is this so? [WEP 2] Set C Q5
An electric motor is used to lift a 5 N load through 3 m as shown in the diagram. The total electrical energy used by the motor is 27 J. What amount of energy is wasted by the motor ? [WEP 2] Set C Q6
A 0.2 kg mass is thrown vertically upwards so that it reaches a height of 3 m above the point of projection. What is its kinetic energy when it is 2 m above the point of projection? [WEP 2] Set C Q7
A crate is pushed along a horizontal surface by a force of 80 N. The frictional force opposing the motion is 60 N. How much of the work done is converted into kinetic energy and internal energy of the crate? [WEP 2] Set C Q8
A cyclist travels along a horizontal track at constant speed. The work done by the cyclist is equal to [WEP 2] Set C Q9
A lorry of mass 10 000 kg takes 5000 kg of sand to the top of a hill 50 m high, unloads the sand and then returns to the bottom of the hill. The gravitational field strength is 10 N/kg. What is the overall gain in potential energy? [WEP 2] Set C Q10
A wooden block of mass of 30 kg is pulled up a rough inclined plane at a constant speed by a force of 70 N parallel to the plane. When the distance moved along the plane is 12 m, the increase in height is 1.0 m. [WEP 2] Set C Q11
An object of mass 20 kg is pulled up a slope of 15 m long. The frictional force between the object and the slope is 30 N. The minimum work done by the pulling force is [WEP 2] Set C Q12
A weight is to be lifted from a level X to a high level Y along different paths labelled L, M and N. [WEP 2] Set C Q13
How much work is done when a person raises a 3 kg lead ball by a vertical distance of 1.5 m and throws it horizontally with an initial velocity of 10 m s-1 ? [WEP 2] Set C Q14
A girl weighing 400 N takes 4.0 s to run up the stairs as shown in the diagram below. Which of the following gives the values of her average speed and power? [WEP 2] Set C Q15
A lorry of mass 2000 kg has an engine which can deliver a maximum power of 50 kW. What is the minimum time in which the car can be accelerated from rest to a speed of 100 km h-1 on level ground? [WEP 2] Set C Q16
A car of mass M = 800 kg decelerates from 80 km h-1 to rest in 12 5. At what average rate must the braking surfaces lose heat if their temperature is not to rise significantly? [WEP 2] Set C Q17
An electric motor runs with a steady input of 250 V and 4 A while raising a load of 1 000 N. Assuming that the motor and transmission is 100 % efficient, how much time is taken to lift the load vertically through a distance of 10 m? [WEP 2] Set C Q18