ENERGY AND POWER This ppt is from XI class CBSE board Energy A body which has the capacity to do work is said to possess energy. For example , water in a reservoir is said to possesses energy as it could be used to drive a turbine lower down the valley. There are many forms of energy e.g. electrical, chemical heat, nuclear, mechanical etc. The SI units are the same as those for work, Joules J. In this module only purely mechanical energy will be considered. This may be of two kinds, potential and kinetic. Power Power is the rate at which work is done, or the rate at which energy is used transferred. Equation 3.6 The SI unit for power is the watt W. A power of 1W means that work is being done at the rate of 1J/s. Larger units for power are the kilowatt kW (1kW = 1000 W = 103 W) and the megawatt MW (1 MW = 1000000 W = 106 W). If work is being done by a machine moving at speed v against a constant force, or resistance, F, then since work doe is force times distance, work done per second is Fv, which is the same as power.

1. ENERGY AND
POWER
CLASS :- XI A
MADE BY :- AKSHAT TRIVEDI
SCHOOL :- K.V. IIT POWAI

2. Force, distance and direction
For force to do work, there must be movement
in the direction of the force

3. 1) Work :-
Work is said to be done when a force acts on an object
and the object is displaced in the direction of force.
The work done on an object is the product of the force
applied and the displacement.
Work done = force x displacement
W = F X s
The unit of work is joule (J).
If F is 1 Newton and displacement is 1 metre then the
work done is 1Nm or 1 joule (J).
So 1 joule is the amount of work done when a force of I
Newton displaces an object by 1 metre.
Eg :- If a force of 5 N acts on an object is displaced
through 2 m in the direction of force, then work done is
5 N x 2 m = 10 Nm or 10 J

4. We all are familiar with the word ‘work’. We do a lot of work everyday. But
in science ‘WORK’ has another meaning.
According to science, a work is said to be done only when a force act on an
object which displaces it or which causes the object to move.
Therefore the two conditions required to prove that a work is done :
A force should act on an object.
The object must be displaced.
If any one of the above conditions does not exist, then work is not done.
WORK is a scalar quantity, i.e. it has only magnitude and no direction.
The unit of WORK is Neuton metre (N m) or joule (J).

5. Let a constant force, F act on an object. Let the object be displaced
through a distance, s in the direction of the force. Let W be the work
done.
So we define work to be equal to the product of the force and
displacement.
→ Work done = Force x Displacement
W = FsW = Fs
For Example : If F=1N and s=1m then the work done by the force will be
1Nm.

6. WORK done by a constant force acting on an object is
equal to the magnitude of the force multiplied by the
distance moved in the direction of the force.
If the force and the displacement are in the same
direction, then the WORK done will be equal to the
product of the force and displacement i.e. the WORK
done will be positive. W=Fs.
If the force acts opposite to the direction of
displacement, then the WORK done will be negative i.e.
W=F x (-s) or (-F x s).

7. force exerted by
the gas when it
expands
F = p A
work done is
W = p A s
movable piston
P =
force
area
_____
A s ???
Change in
volume, ΔV
W = p Δ V
Work done by gas

8. Arya pushed a large piece of
rock and the rock moved
through a distance.
Akhil pulled a box and the
table moved through a
distance.
Megha kicked a football and
the ball moved a little.
Ashish tried to pushed a
refrigirator in his room, but it did
not move.
Anandu tried to lift a bench lying
on the floor, but it did not move.
Harsha kicked a tank full of
water, but it did not get displaced.
Here, WORKis done because the
applied force displaced the object or
cause the object to move.
Here, WORKis not done because
the applied force could not move
the object orcause displacement.

9. When the gas EXPANDS,
work is done BY the gas.
When the gas
CONTRACTS, then work
is done ON the gas.

10. The work done by a force may be positive or negative.
The work done by a force is positive if the force and displacement are in
the same direction.
The work done by a force if negative if the force and displacement are in
opposite directions.
The work done by a force is zero if there is no displacement.
The work done by a force is zero if the force is perpendicular to the
displacement.
Eg :- When we lift an object the object moves upward in the direction of
force. Here the work done is positive. But there is the force of gravity
acting downward on the object. The work done by the force of gravity is
negative.
Eg :- A porter lifts a luggage of 15 kg from the ground and puts it on his
head 1.5 m above the ground. Calculate the work done by him on the
luggage.
Mass of luggage m = 15 kg, displacement = 1.5 m,
Acceleration due to gravity = 10 ms
Work done W = F x s = mg x s = 15 kg x 10 ms x 1.5 m
= 225 kg ms = 225 N m = 225 J
-2
-2
-2

11. ENERGY is the capability of doing work.
An object having the capability to do work is said to posses energy.
The object which does the work loses energy and the object on which
the work is done gains energy.
An object that possesses energy can exert a force on another object.
When this happens, energy is transferred from the former to the later.
The second object may move as it receives energy and therefore do some
work.
Any object that possesses energy can do work.
The unit of energy is the same as that of work. i.e. joule (J)

12. We have many different forms of ENERGY. The various forms
include:
Mechanical Energy (Potential Energy + Kinetic Energy)
Heat Energy
Chemical Energy
Electrical Energy
Light Energy

13. 2) Energy :-
The energy of an object is its capacity for doing work.
The unit of energy is the same as that of work that is
joule(J).
1 joule is the energy required to do 1 joule of work.
1000 J = 1 kilo joule (kJ).
There are different forms of energy. They are heat energy, light
energy, electrical energy, chemical energy, mechanical energy
(potential energy + kinetic energy) etc.
3) Kinetic energy :-
The kinetic energy of an object is the energy possessed by the
object due to its motion.
All moving objects possess kinetic energy. A falling coconut, a
speeding car, a flying aircraft, flowing water, blowing wind, a
running athlete etc. possess kinetic energy.
The kinetic energy of an object depends upon its speed. An
object moving faster has more kinetic energy than an object
moving slower.

14. The kinetic energy of an object is the energy which it possesses due to
its motion. It is defined as the work needed to accelerate a body of the
given mass from rest to its current velocity. Having gained this energy
during its acceleration, the body maintains this kinetic energy unless its
speed changes. The same amount of work would be done by the body in
decelerating from its current speed to a state of rest.
The speed, and thus the kinetic energy of a single object is completely
frame-dependent (relative): it can take any non-negative value, by choosing
a suitable inertial frame of reference. For example, a bullet racing past an
observer has kinetic energy in the reference frame of this observer, but the
same bullet is stationery, and so has zero kinetic energy, from the point of
view of an observer moving with the same velocity as the bullet.

15. The kinetic energy possessed by an object of mass m and
moving with uniform velocity v is
E = mv
Eg :- An object of mass 15 kg is moving with a uniform
velocity of 4 ms . What is the kinetic energy possessed by
the object ?
Mass of the object m = 15 kg.
Velocity of the object v = 4 ms
E = mv
= x 15 kg x 4 ms x 4 ms
= 120 J
The kinetic energy of the object is 120 J
2
k
-1
-1
1
2
2
k
1
2
1
2
-1 -1

16. When a fast moving ball hits a stationary wicket, the wicket
is thrown away.
When a raised hammer falls on a nail placed on a piece of
wood, it drives the nail into the wood.
When an air filled balloon is pressed, it will change its
shape. If we press the balloon hard it will explode
producing a blasting sound.

17. James Prescott Joule ( 24 December 1818 – 11 October 1889) was an
English physicist and brewer, born in Salford, Lancashire. Joule studied the
nature of heat, and discovered its relationship to mechanical
work (see energy). This led to the theory of conservation of energy, which led
to the development of the first law of thermodynamics. The SI derived unit of
energy, the joule, is named after him. He worked with Lord Kelvin to develop
the absolute scale of temperature, made observations onmagnetostriction, and
found the relationship between the current through a resistance and the heat
dissipated, now called Joule's law.

18. By contrast, the total kinetic energy of a system of objects
cannot be reduced to zero by a suitable choice of the inertial
reference frame, unless all the objects have the same velocity. In
any other case the total kinetic energy has a non-zero minimum,
as no inertial reference frame can be chosen in which all the
objects are stationery. This minimum kinetic energy contributes
to the system's invariant mass, which is independent of the
reference frame.
According to classical mechanics (i.e. ignoring relativistic
effects) the kinetic energy of a non-rotating object
of mass m traveling at a speed v is mv2/2. This will be a good
approximation provided v is much less than the speed of light.

19. The unit of POWER is watt [in honour of James Watt (1736-1819)]
having the symbol W. 1 watt is the power of an agent, which does work at
the rate of 1 joule per second.
1 watt = 1 joule/second or 1W = 1 J sˉ¹.
We express larger rates of energy transfer in kilowatts (kW).
1 Kilowatt = 1000 watts
1 kW = 1000 W
1 kW = 1000 J sˉ¹
The power of an agent may vary with time. This means that the agent
may be doing work at different rates at different intervals of time.
Therefore the concept of average power is useful. We obtain average power
by dividing the total energy consumed by the total time taken.
Average power = Total energy consumed/Total time taken

20. 4) Potential energy :-
The potential energy of an object is the energy possessed
by the object due to its position or shape.
Eg :- If a rubber band is stretched and then released it
regains its original position. When the rubber band is
stretched, energy is transferred to it and stored as potential
energy.
If we wind the key of a toy car and place it on the ground
it moves. When we wind the key of the car, energy is
transferred to the spring inside and stored as potential
energy.
If we lift an object to a height and release it, it falls down.
When the object is lifted energy is transferred to it and
stored as potential energy.

21. Potential energy is energy that is stored within a system. It exists when there is
a force that tends to pull an object back towards some lower energy position. This
force is often called a restoring force. For example, when a spring is stretched to the
left, it exerts a force to the right so as to return to its original, unstretched position.
Similarly, when a mass is lifted up, the force of gravity will act so as to bring it back
down. The action of stretching the spring or lifting the mass requires energy to
perform. The energy that went into lifting up the mass is stored in its position in
the gravitational field, while similarly, the energy it took to stretch the spring is
stored in the metal. According to the law of conservation of energy, energy cannot be
created or destroyed; hence this energy cannot disappear. Instead, it is stored as
potential energy. If the spring is released or the mass is dropped, this stored energy
will be converted into kinetic energy by the restoring force, which is elasticity in the
case of the spring, and gravity in the case of the mass. Think of a roller coaster. When
the coaster climbs a hill it has potential energy. At the very top of the hill is its
maximum potential energy. When the car speeds down the hill potential energy turns
into kinetic. Kinetic energy is greatest at the bottom.

22. The more formal definition is that potential energy is the energy difference
between the energy of an object in a given position and its energy at a
reference position.
There are various types of potential energy, each associated with a
particular type of force. More specifically, every conservative force gives rise
to potential energy. For example, the work of an elastic force is called elastic
potential energy; work of the gravitational force is called gravitational
potential energy; work of the Coulomb force is called electric potential
energy; work of the strong nuclear force or weak nuclear force acting on
the baryon charge is called nuclear potential energy; work of intermolecular
forces is called intermolecular potential energy. Chemical potential energy,
such as the energy stored in fossil fuels, is the work of the Coulomb force
during rearrangement of mutual positions of electrons and nuclei in atoms
and molecules. Thermal energy usually has two components: the kinetic
energy of random motions of particles and the potential energy of their
mutual positions.
As a general rule, the work done by a conservative force F will be
W = -ΔU
where ΔU is the change in the potential energy associated with that
particular force. Common notations for potential energy are U, Ep, and PE.

23. 5) Potential energy of an object at a height :-
When an object is raised to a height, its energy increases
because work is done on it against gravity. The energy present in
such an object is called gravitational potential energy.
If an object of mass m is raised to a height h from the ground, the force
required to raise the object is equal to the weight of the object mg
Work done = Force x displacement
or W = mg x h
= mgh
Potential energy gained by the object
E = mgh
Eg :- Find the energy possessed by an object of mass 10 kg when it is at a
height of 6m above the ground. Given g = 9.8 ms .
Mass of the object m = 10 kg, displacement (height) h = 6 m
Acceleration due to gravity g = 9.8 ms
Potential energy E = mgh
= 19 kg x 9.8 ms x 6 m
= 588 J
p
-1
-1
p
-1

24. An object increases its energy when raised throughout a height. This is because work
is done on it against gravity while it is being raised. The energy present in such an
object is the gravitational potential energy.
The gravitational potential energy of an object at a point above the ground is defined
as the work done in raising it from the ground to that point against gravity.
It is easy to arrive at an expression for the gravitational potential energy of an object
at a height.
Consider an object of mass m. Let it be raised through a height, h from the ground. A
force is required to do his. The minimum force is required to raise the object is equal to
the weight of the object, mg. The object gains energy equal to the work done on it. Let
the work done on the object against gravity be W. That is
Work done = Force x Displacement
= mg x h
= mgh
Since work is done on the object is equal to mgh, an energy equal to mgh unit is gained
by the object. This is the potential energy (E ) of the object.
E = mgh
It is useful to note that work done by gravity depends on the difference in vertical
heights of the initial and final positions of the object and not on the path along which
the object is moved.
p

25. The law of conservation of energy states that energy cannot be created
or destroyed., and that neither one appears without the other. Thus in
closed systems, both mass and energy are conserved separately, just as
was understood in pre-relativistic physics. The new feature of relativistic
physics is that "matter" particles (such as those constituting atoms) could
be converted to non-matter forms of energy, such as light; or kinetic and
potential energy (example: heat). However, this conversion
does not affect the total mass of systems, since the latter forms of non-
matter energy still retain their mass through any such conversion.

26. Today, conservation of “energy” refers to the conservation of the total system
energy over time. This energy includes the energy associated with the rest mass of
particles and all other forms of energy in the system. In addition, the invariant
mass of systems of particles (the mass of the system as seen in its center of
mass inertial frame, such as the frame in which it would need to be weighed) is
also conserved over time for any single observer, and (unlike the total energy) is
the same value for all observers. Therefore, in an isolated system, although matter
(particles with rest mass) and "pure energy" (heat and light) can be converted to
one another, both the total amount of energy and the total amount of mass of such
systems remain constant over time, as seen by any single observer. If energy in any
form is allowed to escape such systems (see binding energy), the mass of the
system will decrease in correspondence with the loss.
A consequence of the law of energy conservation is that perpetual
motion machines can only work perpetually if they deliver no energy to their
surroundings.

27. 6) Transformation of energy :-
The conversion of energy from one form into another
form is called transformation of energy.
When energy is converted from one form into another, the
total energy always remains the same.
Law of conservation of energy :-
The law of conservation of energy states that energy can
only be converted from one form into another, it can neither
be created nor destroyed. The total energy before and after
the transformation remains the same.
Eg :- Let an object be allowed to fall freely from a height. At the start the
potential energy is more. As it falls down the potential energy changes
into kinetic energy. The potential energy decreases and the kinetic
energy increases. When the object is about to reach the ground the
kinetic energy is the largest and the potential energy is the least. But the
sum of the potential energy and kinetic energy is the same at all points.
So potential energy + kinetic energy = constant. The sum of the potential
energy and kinetic energy is the total mechanical energy.

28. 7) Rate of doing work (Power) :-
Power is the rate of doing work.
If W is the work done in time t, then
work done W
Power = ---------------- or P = ---
time taken t
The unit of power is watt (W).
1 watt is the power of an agent which does work at the
rate of 1 joule per second.
1 watt = 1 joule / second or 1 W = 1 J s
1 kilowatt = 1000 watts
1 kW = 1000 W
1 kW = 1000 J s
-1
-1

29. All of us do not work at the same rate. All machines do not
consume or transfer energy at the same rate. Agents that transfer
energy do work at different rates.
A stronger person may do certain work in relatively less time. A
more powerful vehicle would complete a journey in a shorter
time than a less powerful one. We talk of the power of motorbikes
and motorcars. The speed with which these vehicles change
energy or do work is a basis for their classification. Power
measures the speed of work done, i.e. how fast or slow work is
done. Power is defined as the rate of transfer of energy. If an
agent does a work W in time t, then power is given by:
Power = Work/Time
i.e. P = W/t

30. Power
Power =
work done
time taken
J
s
Watts (W)
- is the rate of working 1
joule per second ( scalar
just like energy )

31. 8) Commercial unit of power :-
The commercial unit of energy is kilowatt hour (kW h).
1 kilowatt hour is the energy used in one hour at the rate
of 1 kilowatt (or 1000 J s ).
1 kW h = 1 kW x 1 h
= 1000 W x 1 h
= 1000 W x 3600 s
= 3600000 J
1 kW h = 3.6 x 10 J
The electrical energy used in homes and industries are
expressed kilowatt hour. The electrical energy used during
a month is expressed in ‘units’. Here 1 unit means 1
kilowatt hour.
-1
-6

32. What is the kinetic energy of an object?
The kinetic energy of an object is the energy which it possesses due to
its motion.
An object of mass 15 kg is moving with a uniform velocity of 4 m sˉ².
What is the kinetic energy possessed by the object?
Mass of the object, m = 15 kg
Velocity of the object = 4 m sˉ¹
→ E = ½ m v²
= ½ x 15 kg x 4 m sˉ¹
= 120J
The kinetic energy of the object is 120 J.
k

33. A force of 7N acts on an object. The displacement is, say 8m, in the
direction of the force. Let us take it that the force acts on the object
through the displacement. What is the work done in this case?
The applied = 7N
Its displacement = 8m
Work done = Force x displacement
= 7N x 8m
= 56 N m = 56J.
Therefore the work done is 56J.

34. The unit joule is too small and is inconvenient to express large quantities
of energy. We use a bigger unit called kilowatt hour (kW h). For example,
we have a machine that uses 1000 J of energy every second. If this machine
is used continues for an hour, it will consume 1 kW h of energy. Thus 1 kW
h of energy is the energy used in one hour at the rate of 1000 J sˉ¹ (or 1 kW).
1 kW h = 1 kW x 1 h
= 1000 W x 3600 s
= 3600000 J
1 kW h = 3.6 x 10 J.⁶
The energy used in households, industries and commercial establishments
are usually expressed in kilowatt hour. For example, electrical energy used
during a month is expressed in terms of ‘units’. Here 1 unit means
1kilowatt hour.

35. What is the work to done to increase the velocity of a car from 30 km hˉ¹ to 60
km hˉ¹ if the mass of the car is 1500 kg ?
Mass of car, m = 1500 kg
Initial velocity of the car, u = 30 km hˉ¹
= 30 x 1000m
60 x 60s
= 8.33 m sˉ¹ .
Similarly the final velocity of the car, v = 60 km hˉ¹ = 16.67 m sˉ¹.
Therefore, the initial kinetic energy of the car.
E = ½ m u²
= ½ x 1500 kg x (8.33 m sˉ¹)² = 52041.68 J
The final kinetic energy of the car,
E = ½ x 1500 kg x (16.67 m sˉ¹)² = 208416.68 J
Thus, the work done = Change in kinetic energy
= E - E
= 156375 J
ki
kf
kikf

36. Find the energy possessed by an object of mass 10 kg when it is at a height of 6
m above the ground. Given, g = 9.8 m sˉ².
Mass of object, m = 10 kg
Its displacement (height), h = 6 m
Acceleration due to gravity, g = 9.8 m sˉ²
Potential energy = mgh
= 10 kg x 9.8 m sˉ² x 6 m = 588 J.
The potential energy is 588 J.
An object of mass 12 kg is at a certain height above the ground. If the potential
energy of the object is 480 J, find the height at which the object is with respect
to the ground. Given, mg = 10 m sˉ².
Mass of the object, m = 12 kg
Potential energy, E = 480 J.
E = mgh
489 J = 12 kg x 10 m sˉ² x h
h = 480J = 4m
120 kg msˉ²
The object is at the height of 4 m.
p
p

37. Two girls, each of weight 400 N climb up a ro[e through a height of 8 m. We
name one of the girls A and the other B. Girl A takes 20 s while B takes 50 s
to accomplish this task. What is the power expended by each girl ?
(i) Power expended by girl A:
Weight of the girl, mg = 400 N
Displacement (height), h = 8 m
Time taken, t = 20 s
Power, P = Work done/Time taken = mgh/t = 400N x 8 m
20 s
= 160 W.
(ii) Power expended by girl B:
Weight of the girl, mg = 400 N
Displacement (height), h = 8 m
Time taken, t = 50 s
Power, P = mgh/t = 400 N x 8 m
50 s
= 64 W
Power expended by girl A is 160 W.
Power expended by girl B is 64 W.

38. A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each
step is 15 cm, find his power. Take g = 10 m sˉ².
Weight of the boy, mg = 50 kg x 10 m sˉ²
= 500 N
Height of the staircase, h = 45 x 15/100 m
= 6.75 m
Time taken to climb, t = 9 s
Power, P = Work done/Time taken = mgh/t = 500 N x 6.75 m
9 s
= 375 W.
Power is 375 W.
An electric bulb of 60 W is used for 6 h per day. Calculate the ‘units’ of energy
consumed in one day by the bulb.
Power of electric bulb = 60 W = 0.06 kW.
Time used, t = 6 h
Energy = Power x Time taken
= 0.06 kW x 6 h
= 0.36 kW h = 0.36 ‘units’.
The energy consumed by the bulb is 0.36 ‘units’.

39. Quick review: Doing/Not Doing work????
F
d

40. Θ = 35o
F
=
120
N
Fx = ?
d = 6.0 m
An airport passenger is
pulling his luggage with a
force F = 120 N along a
level floor. The pulling
force makes an angle of
35o
measured from the
floor and the passenger
moves through a distance
d of 6.0 m, what is the
work done on the
luggage?

41. horizontal
component (Fx)
of 50 N
Fx = F cos 30o
=50 cos 30o
= 43. 301270189
Work done = (Fx) x s
= 43. 301270189 x 10
= 433.01270189
= 4.3 x 102
J

42. The diagram shows a child on a swing. The
mass of the child is 35 kg. The child is
raised to point A and then released. She
swings downwards through point B.
a) Calculate the change in
gravitational potential energy of the
child between A and B.
b) Assuming that air resistance is
negligible, calculate the speed of the
child as she passes through the
equilibrium position B.
c) The rope stays taut throughout.
Explain why the work done by the
tension in the rope
is zero.

43. 3. Calculate the increase in kinetic energy of
a mass 800 kg when it accelerates from 20
m/s to 30 m/s.
4. Calculate the change in KE of a ball of
mass 200 g when it bounces. Assume that it
hits the ground with a speed of 15.8 m/s
and leaves it at 12.2 m/s.Change in KE = 10 J
Change in KE = 200 kJ

44. A bullet of mass 30 g and travelling at a
speed of 200 m s−1
embeds itself in a
wooden block. The bullet penetrates a
distance of 12 cm into the wood. Using
the concepts of work done by a force and
kinetic energy, determine the average
resistive force acting on the bullet.
Work done by resistive force = initial kinetic energy of bullet
2
200030.0
2
1
12.0 ××=×F
kN)(5.0N100.5
12.02
200030.0 3
2
×=
×
×
=F

45. Work done against friction = 6.06 × 103
− 3.99 × 103
= 2.07 × 103
J
Since work done is given by:
work done = force × distance
we have:
friction N100N104
20
1007.2 3
≈=
×
=

46. Work done by tension in the rope = F cos θ × x
= 350 × cos 30° × 20
= 6.06 × 103
J
Gain in gravitational potential energy = mgh
= 50 × 9.81 × 20 sin 24°
= 3.99 × 103
J

47. h
v Y
X
An object of mass m passes a point X with a
velocity v and slides up a frictionless incline to stop
at point Y which is at a height h above X
A second ball of mass 0.5m passes X with a
velocity of 0.5v. To what height will it rise?

48. 10.0 m
1.0 m
A body of mass 1.0 kg initially at rest slides down an incline
plane that is 1.0 m high and 10.0 m long. If the body
experiences a constant resistive force of 0.5 N over the slope,
what is the KE of the body at the base of the plane?
Gain in KE = loss in PE – Work against resistive force
4.8J

49. Doing work against gravity
A 80.0 kg man is climbing
a stair as shown in the
diagram on the right. Given
the dimensions calculate
for the work done by the
man upon reaching the last
step above.

50. A stunt person slides down a cable that is attached between a tall
building and the ground.
The stunt person has a mass of 85 kg. The speed
of the person when reaching the ground
is 20 m s−1
. Calculate:
a)the change in gravitational potential energy of
the person
b) the final kinetic energy of the person
c) the work done against friction
d) the average friction acting on the person.

51. Try these:
1. Calculate how much gravitational potential
energy (GPE) is gained if you climb a flight of
stairs. Assume that you have a mass of 52 kg
and that the height you lift yourself is 2.5 m.
2. A climber of mass 100 kg (including all the
equipment he is carrying) ascends from sea level
to the top of a mountain 5500 m high. Calculate
the change in her gravitational potential energy
(GPE)

52. 45o
100 N
70 N
100 N
30 N
The figure on
the right shows
the forces
acting on a
box which is
being pushed
up a slope.
Calculate the work done by each force if the box
moves up 0.5 m up the slope.

53. Test yourself
3. A stone of weight 10 N falls from
the top of a 250 m high cliff.
a) Calculate how much work is
done by the force of gravity in pulling
the stone to the foot of the hill.
b) How much energy is
transferred to the stone?
2500 J
2500 J

54. The diagram shows a 50 kg crate
being dragged by a cable up a ramp
that makes an angle of 24° with the
horizontal.
The crate moves up the ramp at a constant speed and travels a
total distance of 20 m up the ramp. Determine the magnitude of
the friction between the crate and the surface of the ramp.

55. Test yourself
1. In each of the following examples, explain whether or
not any work is done by the force mentioned.
a) You pull a heavy sack along the ground.
b) The force of gravity pulls you downwards when you
fall.
c) The tension in a string pulls on a stone when you
whirl it around at a steady speed.
d) The contact force of the bedroom floor stops you
from falling into the room below.
2. A man of mass 70 kg climbs stairs of vertical height 2.5
m. Calculate the work done against the force of gravity.
YES
YES
NO
NO
1716.75 = 1.7 kJ