GRADE 12
2022
WORK, ENERGY AND POWER –
EXTRA QUESTIONS
DEFINITIONS (SAGS)
Work: The product of the displacement and the component of the force parallel to the
displacement.
Gravitational potential energy: The energy an object possesses due to its position relative to a
reference point.
Kinetic energy: The energy an object has as a result of its motion.
Mechanical energy:
The sum of an objects gravitational and kinetic energy at a point.
The principle of conservation of mechanical energy:
The law of conservation of energy:
The work-energy theorem:
In the absence of air resistance or any
external forces, the mechanical energy of an
object is constant.
The total energy in a system cannot be created or
destroyed. It can only be transformed from one form to
another.
The work done by a net force on an object is equal to the change in
the object’s kinetic energy.
Power:
The rate at which work is done / The rate at which energy is transferred.
One watt:
The power when one joule of work is done in one second.
Efficiency:
The ratio of output power to input power.
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GRADE 12
2022
FORMULAE (SAGS)
𝑾 = 𝑭𝜟𝒙. 𝒄𝒐𝒔 𝜽 where 𝑊 is the work done (J), 𝐹 is the force (N), ∆𝑥 is the distance (m) and 𝜃 is the
angle between the force and the distance.
𝑬𝒑 = 𝒎𝒈𝒉 where 𝐸𝑝 is the potential energy (J), 𝑚 is the mass of the object (kg), 𝑔 is gravitational
acceleration (9,8 m.s-2) and ℎ is the height above the reference point (m).
𝟏
𝑬𝒌 = 𝟐 𝒎𝒗𝟐 where 𝐸𝑘 is the kinetic energy (J), 𝑚 is the mass of the object (kg) and 𝑣 is the speed of
the object (m.s-1).
𝑬𝑴 = 𝑬𝒑 + 𝑬𝒌 where 𝐸𝑀 is the mechanical energy (J), 𝐸𝑝 is the potential energy (J) and 𝐸𝑘 is the
kinetic energy (J).
(𝑬𝑷 + 𝑬𝒌 )𝒊 = (𝑬𝒑 + 𝑬𝒌 )𝒇 , where 𝐸𝑘 is the kinetic energy (J), 𝐸𝑝 is the potential energy (J), i means
the original position of the object, f means the final position of the object.
𝑾𝒏𝒆𝒕 = ∆𝑬𝒌 = 𝑬𝒌𝒇 − 𝑬𝒌𝒊 where 𝑊𝑛𝑒𝑡 is the net work done (J) and Δ𝐸𝑘 is the change in kinetic
energy (J). This is known as the work-energy theorem.
𝑾𝒏𝒄 = 𝜟𝑬𝒌 + 𝜟𝑬𝒑 where 𝑊𝑛𝑐 is the work done by a non-conservative force (J), Δ𝐸𝑝 is the change
in potential energy (J) and Δ𝐸𝑘 is the change in kinetic energy (J).
𝑾
𝑷 = 𝒕 where 𝑃 is the power (W), 𝑊 is the work done (J) and 𝑡 is the time (s).
𝑷 = 𝑭𝒗 where 𝑃 is the power (W), 𝐹 is the force (N) and 𝑣 is the speed of the object (m.s-1).
𝑝𝑜𝑤𝑒𝑟
% 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑝𝑜𝑤𝑒𝑟𝑜𝑢𝑡 x100
𝑖𝑛
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GRADE 12
2022
EXTRA QUESTIONS
1)
The diagram shows a crate of mass 90 kg sliding down a rough surface inclined at 20° to
the horizontal. A constant force F, parallel to the incline, is applied to the crate. The crate
moves down the incline at constant velocity.
The magnitude of the kinetic frictional force (fk) between the crate and the surface of the
inclined plane is 266 N.
1.1)
Draw a labelled free-body diagram showing all the forces acting on the crate.
1.2)
Friction is a non-conservative force. What is meant by the term non- conservative
force?
(2)
1.3)
What is the magnitude of the net work done on the crate?
(1)
1.4)
Calculate the magnitude of the force F.
(4)
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(4)
GRADE 12
2022
If the crate is released from rest without force F being applied, it moves 3 m down the
incline.
1.5)
2)
Using energy principles only, calculate the speed of the block after the 3 m.
(6)
A skateboarder is practising a sequence of tricks at the local skate park on a halfpipe. The
total mass of the skateboarder and skateboard is 75 kg. The skater leaves point A, 2,4 m
above the ground. He skates down the ramp towards point B. He reaches Point B, 1,6 m
above the ground, with a speed of 3,75 m.s-1 just by rolling along and without using his
feet to push himself along the half-pipe.
The skateboarder has not oiled the wheels of his skateboard for some time, so there is
significant friction between the axles and the wheels of the skateboard.
2.1)
State in words, the work-energy theorem.
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(2)
GRADE 12
2.2)
2.3)
Calculate the work done by the gravitational force on the skateboarder as he
moves from Point A to Point B.
2022
(4)
Using the work-energy theorem, determine the work done by the frictional force
exerted on the skateboard.
(6)
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GRADE 12
2.4)
2022
The skateboarder thinks about constructing an inclined plane to join Points A
and B to provide an alternative route between these two points.
2.4.1) How would the work done by the gravitational force change if he were
to roll from Point A to Point B along the inclined plane instead of
following the curved track? Answer only INCREASE, DECREASE or
REMAINS THE SAME.
(1)
2.4.2) Explain your answer to QUESTION 2.4.1
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(2)
GRADE 12
3)
2022
A health care worker, while pushing a patient on a wheelchair, approaches an incline plane
of length 10 m and height 1,5 m, as shown in the diagram below.
The combined mass of the patient and the wheelchair is 120 kg. A constant frictional force
of 50 N acts on the wheelchair as it moves down the incline. The rotational effects of the
wheels of the wheelchair may be ignored.
The worker exerts a force on the wheelchair, which is parallel to the plane, so that the
wheelchair moves down the incline at constant speed of 1,25 m.s−1.
3.1)
Is the mechanical energy of the wheelchair conserved while it moves down the
incline? Give a reason for your answer.
(3)
3.2)
What is meant by a conservative force?
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(2)
GRADE 12
2022
3.3)
Draw a labelled free body diagram showing the forces that act on the wheelchair
as it moves down the incline. Indicate the following on your diagram:
•
Normal force. Label this force A.
•
Frictional force. Label this force B.
•
The component of weight that acts parallel to the incline. Label this
force C.
•
The component of weight that acts perpendicular to the incline. Label this
force D.
•
The force exerted by the healthcare worker on the wheelchair parallel to
the incline. Label this force E.
(5)
3.4)
Calculate the magnitude of the force C.
(3)
3.5)
Write down, without doing a calculation, the amount of work done on the
wheelchair by force D. Give a reason for your answer.
(2)
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GRADE 12
3.6)
State, in words, the work-energy theorem.
3.7)
Calculate the work done on the wheelchair as it moves down the incline by the
force labelled:
2022
(2)
3.7.1) B
(3)
3.7.2) C
(2)
3.8.1) Use the work-energy theorem to calculate the work done on the wheelchair by
the force labelled E.
(4)
3.8.2) Determine the average power output of the health care worker as he takes the
wheel chair down the incline.
(6)
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GRADE 12
4)
2022
A box is held stationary at point A, the top of a plane ABC, inclined at an angle to the
horizontal. The portion AB of the plane is smooth while the portion BC is rough.
4.1)
State the principle of conservation of mechanical energy in words.
(2)
4.2)
Calculate the speed of the box at position B.
(4)
4.3)
The box experiences a kinetic frictional force of 14,7 N as it moves with a
constant velocity, from B to C, down the plane.
4.3.1) State the Work-Energy Theorem in words.
(2)
4.3.2) Draw a free-body diagram showing ALL forces acting on the box at B.
(3)
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GRADE 12
4.4)
2022
4.3.3) Use the work-energy principle to calculate the distance d, between B
and C, if the box has a mass of 3 kg.
(5)
The angle between the incline and the horizontal is decreased. How will this
decrease affect the kinetic friction acting on the box? Write only INCREASE,
DECREASE or REMAIN THE SAME. Explain your answer.
(4)
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GRADE 12
5)
2022
A 5 kg rigid crate moves from rest down path ABC as shown in the diagram below
(diagram not drawn to scale). Section AB of the path is frictionless whilst section BC is a
rough surface. Assume that the crate moves in a straight line down the path.
5.1)
State, in words, the principle of the conservation of mechanical energy.
(2)
5.2)
Use the principle of the conservation of mechanical energy to calculate the
velocity of the crate when it reaches point B.
(4)
On reaching point B, the crate continues to move down the section BC of the path. It
experiences an average frictional force of 10 N and reaches point C with a speed
of 4 m.s-1.
5.3)
Apart from friction, write down the names of TWO other forces that act on the
crate as it moves down section BC.
(2)
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GRADE 12
5.4)
2022
In which direction does the net force act on the crate as it moves down section
BC? Write down only B to C or C to B.
(1)
Another crate of mass 10 kg now moves from point A down path ABC.
5.5)
6)
How will the velocity of this 10 kg crate at point B compare to that of the 5 kg
crate at B? Write down only GREATER, SMALLER or EQUAL TO.
(1)
A block of wood, mass 1,595 kg, is placed on the edge of a table 1,5 m above the floor.
The block is struck by a bullet, mass 0,005 kg, moving at an UNKNOWN, horizontal
velocity. After the impact, the bullet is embedded in the block, which falls to the floor.
The block strikes the floor with a speed of 5,6 m.s-1. Ignore all types of friction.
6.1)
State the principle of conservation of mechanical energy in words.
(2)
6.2)
Use the principle of conservation of mechanical energy to calculate the
magnitude of the velocity with which the block leaves the table.
(5)
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GRADE 12
7)
2022
6.3)
State the principle of conservation of momentum in words.
(2)
6.4)
Calculate the magnitude of the velocity with which the bullet strikes the block. (4)
During a fire extinguishing operation, a helicopter remains stationary (hovers) above a
dam while filling a bucket with water. The bucket, of mass 80 kg, is filled with 1 600 kg of
water. It is lifted vertically upwards through a height of 20 m by a cable at a CONSTANT
SPEED of 2 m.s-1. The tension in the cable is 17 000 N. Assume there is no sideways motion
during the lift. Air friction is NOT ignored.
7.1)
State the work-energy theorem in words.
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(2)
GRADE 12
2022
7.2)
Draw a labelled free body diagram showing ALL the forces acting on the bucket
of water, while being lifted upwards.
(3)
7.3)
Use the WORK ENERGY THEOREM to calculate the work done by air friction on
the bucket of water after moving through the height of 20 m.
(5)
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GRADE 12
8)
2022
A constant force, F, applied at an angle of 20° above the horizontal, pulls a 200 kg block,
over a distance of 3 m, on a rough, horizontal floor as shown in the diagram below.
3m
The coefficient of kinetic friction, μk, between the surface of the floor and the block is 0,2.
8.1)
Give a reason why the coefficient of kinetic friction has no units.
(1)
8.2)
State the work-energy theorem in words.
(2)
8.3)
Draw a free-body diagram indicating ALL the forces acting on the block while it
is being pulled.
(4)
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GRADE 12
2022
8.4)
Show that the work done by the kinetic frictional force (Wfk) on the block can be
written as Wfk = (-1 176 + 0,205F) J.
(4)
8.5)
Calculate the magnitude of the force F that has to be applied so that the net
work done by all forces on the block is zero.
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(4)
GRADE 12
9)
2022
In order to measure the net force involved during a collision, a car is allowed to collide
head-on with a flat, rigid barrier. The resulting crumple distance is measured. The crumple
distance is the length by which the car becomes shorter in coming to rest.
In one of the tests, a car of mass 1 200 kg strikes the barrier at a speed of 20 m.s−1. The
crumple distance, (x1 – x2), is measured as 1,02 m. Ignore the effects of frictional forces
during crumpling.
9.1)
Draw a labelled free-body diagram showing ALL the forces acting on the car
during the collision.
(3)
9.2)
State the work-energy theorem in words.
(2)
9.3)
Assume that the net force is constant during crumpling.
9.3.1) USE THE WORK-ENERGY THEOREM to calculate the magnitude of the
net force exerted on the car during crumpling.
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(4)
GRADE 12
9.3.2) Calculate the time it takes the car to come to rest during crumpling.
10)
2022
(4)
A block of mass 10 kg is sliding along a uniform rough surface. The surface is horizontal
from A to B and inclined at 35° to the horizontal from B to C.
The block is travelling at a speed of 12 m.s−1 as it passes A.
10.1)
Define the term kinetic energy.
(2)
10.2)
Calculate the kinetic energy of the block as it passes A.
(3)
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GRADE 12
2022
The frictional force acting on the block as it slides from A to B is 54,9 N.
10.3)
State the work-energy theorem.
(2)
10.4)
Calculate the speed of the block (v) as it reaches B.
(4)
The block slides up the incline from B and comes to rest at C. The frictional force
acting on the block as it slides from B to C is 45,0 N.
10.5)
Write an expression for the potential energy of the block at C in terms of x.
(2)
10.6)
Calculate the distance, x, that the block slides up the slope before coming to
rest at C.
(5)
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GRADE 12
10.6)
2022
The frictional force experienced by the block on the inclined plane is less than the
frictional force experienced on the horizontal surface even though the surfaces
are made of the same material. Explain by making use of a relevant equation. (3)
At point C, the object only just manages to remain at rest.
10.7)
Draw a labelled free-body diagram of the block at rest at C.
(3)
10.8)
Calculate the frictional force acting on the block at C.
(3)
10.9)
Hence calculate the coefficient of static friction.
(3)
10.10) Explain why the frictional force calculated in QUESTION 10.8 is greater than the
frictional force of 45,0 N acting while the block was sliding.
(2)
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