Work, Energy, and Power
Objectives
At the end of this lesson, the learners should be able to
demonstrate an understanding of:
1. Demonstrate the work done by a force acting on a system.
2. Relate the gravitational potential energy of a system or object to the
configuration of the system.
Motivation
• What causes an object to
change its state?
• What affects motion?
Work
Work is the amount of energy by a force through a distance in the
direction of the force. Like energy, it is a scalar quantity, with SI units of
joules (J).
Work
• Work is related to energy.
• You transfer energy to an
object by doing work on it.
Work In Concept
F
F
2F
∑ 𝐹 = 𝐹 + 𝐹 = 2𝐹
Work
In order for work to be done, the following conditions must be
met.
• There must be a force acting on the object.
• The object has to move a certain distance called displacement.
• There must be a movement parallel in the direction of the
force.
Work
For the work done along horizontal, it is calculated by
For the work done along vertical, it is calculated by
Work done at an Angle
Work done by constant force:
where:
= constant force in newton (N)
= displacement in meter (m)
= angle between and
SI unit is joule (J): 1 J = 1 N·m
Example
A man pushes on a car with a force of 300 N and moves it
10m(in the direction of the force). This is shown in the figure
below. How much work is done by the man on the car?
Example
A box whose mass is 45 kg is moved across a
horizontal floor by dragging it with a rope attached to
the front end with a force of 200 N. If the rope makes
an angle of 30 with the horizontal, how much work is
done in dragging the box over a distance of 5.75 m?
Continuation
A box of mass 45 kg is moved across a horizontal floor
by dragging it with a rope attached to the front end,
applying a force of 200 N. The rope makes an angle of
30° with the horizontal. If the coefficient of kinetic
friction between the box and the floor is
what is the acceleration of the box?
,
Work as Area Under the Curve
• What is the work from 0 to 5 m?
• What is the work from 5 to 10m?
• What is the work from 10 to 15m?
• What is the work from 0 to 15m?
Work as an Integral
Energy
Energy is a scalar quantity, a conserved
extensive property of a physical system,
which cannot be observed directly but
can be calculated from its state. It is the
capacity to change the state of a system.
Kinetic Energy, KE
It is the energy in moving matter and wave.
Other forms of Kinetic Energy:
Translational Kinetic Energy
Kinetic
energy
is
the
energy
possessed by moving bodies. If you
push a stationary object and it moves,
it gains kinetic energy. The change in
kinetic energy can be measured from
the work done on the object.
Translational Kinetic Energy
Since the object moves and acquires a velocity, v, from rest, it undergoes
acceleration. Therefore, its final velocity maybe calculated by the equation
. (Equation #1 in Kinematics PPT)
Recall:
Substituting:
Hence,
Work-Energy Theorem
If the object was initially moving, the work done on the object is
equal to the change in its kinetic energy. In symbols,
Example
A bullet, of mass 200g, is fired with a speed of 400 m/s.
If it is stopped in 100m, find (a) KE, and (b) the force
needed to stop it.
Potential Energy, PE
Energy in matter due to arrangements of its parts, its composition, location
and structure. It is commonly considered as a stored energy having the
potential to do mechanical work.
Other forms of Potential Energy:
Gravitational Potential Energy
It is the energy possessed by an
object due to its position (relative
to the ground). Every object on
earth’s surface possess this energy.
Since,
Then,
and
Example
A man walks up from the ground to the 4th floor of a building
whose vertical distance is 15m. The gravitational potential energy
acquired by the person at that height is 8,820 J. If the
acceleration due to gravity is 9.8 m/s², what is the man’s weight?
Work done by gravity
Conservation of Energy
Conservation of Energy
The law of conservation of energy states that energy can
neither be created nor destroyed - only converted from one
form of energy to another.
Conservation of Energy
Kinetic and Potential energy are forms
of mechanical energy. If friction is
negligible, the sum of the kinetic
energy and potential energy of a body
remains constant, and is called total
mechanical energy.
In symbols,
Example
A 5-kg object is raised 50m high. (a) What is its PE? (b)
How far is the object from the ground after 1s of fall?
(c) If the object is released from that height, what is its
PE and KE after 1s of fall? (d) What is its KE before it
hits the ground?
Power, P
It is the amount of work done per unit
of time. The shorter the time required
to do work, the greater the power.
SI unit: 1 watt = 1 J/s
1 hp = 746 watts
Example
A 60-kg man runs up a staircase 3 m high in 2.5 seconds. What
power has he developed?
Example
Mary pushes a 30-kg carton of books across the floor of her
dormitory by exerting constant force of 185 N at an angle of 37
with the horizontal. If the opposing force of friction is 70N, (a)
how much work does she do as she moves the carton 4 m in 15
s? (b) What power in watts has she expended?
Instantaneous Power,
The instantaneous power is the limiting value of the average
power as the time interval
approaches zero.
Example
A worker pulls a 50-kg sled across a flat surface by applying a
force of 250 N at an angle of 30° above the horizontal. The sled
moves at a constant velocity of 4 m/s.