Download work, energy and power

WORK, ENERGY AND
POWER
WHY ARE
WE
WORKING
SO HARD?
GET the FACTS.
• Work is done when a force acts on an object
and it moves in the direction of the force.
work done W = F.Δx.cosӨ
• Work is a scalar quantity.
• The unit for work is the joule (J) or the
newton metre (N.m).
• 1 joule = 1 N.m = 1 kg.m.s-2. m = 1 kg.m2.s-2
If a force acts on an object but the object
does not move, no work is done on the
object.
If an object moves at constant velocity
across a frictionless surface, no force acts
on the object and so no work is done.
Force
Weight
This man is doing work against the force of
gravity, but is doing no horizontal work on
the suitcase, because he is exerting a force
vertically and not horizontally.
WORK DONE BY FORCES ACTING AT AN
ANGLE TO THE HORIZONTAL
The force doing the work and the motion
must be in the same direction.
If the force doing the work acts at an angle,
first determine the horizontal component of
the force acting at an angle.
Use the horizontal component of the force
to determine the amount of work done.
Fvertical
Fapplied
θ
θ
Fhorizonal
FH = F cos θ, where θ is the angle between
the applied force and the horizontal.
work done = Fhorizontal .Δx
where Δx = distance moved
The Inuit man pulling the sledge exerts a
force of 200N and moves the sledge 20m
along the level ground. The rope is inclined
at an angle of 30o to the horizontal.
Determine the work done by the man, while
he moves the penguins.
The horizontal component of the force can
be calculated as follows:
FH = F cos 30o = 173,21N
Work done = F.Δx
= 173,2 X 20
= 3 464,10J
OR
W = FΔx.cosӨ
= 200(20).cos 30°
= 3464,10J
Work done on an inclined plane
• The diagram is important and learners
must be able to draw:
ENERGY
• Energy is defined as the capacity to do work.
• The energy of an object or a system is
determined by calculating the amount of
work that it can do.
• The unit of energy is the joule (J) and it is a
scalar quantity.
• Energy is transferred when work is done.
•The object doing the work loses energy.
•The object on which work is done, gains
energy.
•When an object is lifted in the earth’s
gravitational field, the work is done against the
force of gravity.
•When an object is moved across a rough
surface, the work is done against the force of
friction.
THE LAW OF CONSERVATION OF
MECHANICAL ENERGY
Mechanical energy (or any other energy)
cannot be created or destroyed, only
changed from one form to another.
The mechanical energy of an object is the
sum of it’s gravitational potential energy
(Ep) and it’s kinetic energy (Ek).
Gravitational Potential Energy
Gravitational Potential energy is the energy
an object possesses due to its position in
the earth’s gravitational field.
Ep = mgh
m = mass
g = gravitational acceleration
h = height above the earth
An object gains gravitational potential energy
when it is lifted up in the earth’s gravitational field.
Deriving an equation for calculating
gravitational potential energy
•
•
•
•
Lifting an object at constant velocity to a
height h:
Force applied = weight of the object = mg
Distance (s) = h
Work = F.s = gain in Ep
h
Ep = mgh
Fg = mg
Deriving an equation for calculating Ek
• A force (F) accelerates an object
across a frictionless surface for a
distance s.
F
s
•Work done = F.s
•Fres = m.a
Work done = m.a.s (m x a x s)
The object accelerates, velocity increases
and the energy is transferred as Ek.
•For this movement:
vf2 = vi2 + 2as and vi = 0
as = ½ vf2
• Ek = ½ mvf2
Conservation of energy during free fall
Mechanical energy = Ep = mgh
X
h
Mechanical energy = Ep + Ek
= mg(h – x) + ½ mvf2
= Ep at top
Mechanical energy = Ek = ½ mv2
= Ep at top
Conservation of energy during the swing of
a pendulum
At the top of its swing the bob stops for an
instant, and so has no kinetic energy.
The total energy at the top of the swing is
given by
Ep = mgh
(where h is the height above the lowest point)
At the bottom of the swing Ep = 0
and all the energy is kinetic energy.
Ek = ½ mv2.
v is the maximum speed of the bob.
Ep at the top = Ek at the bottom
mgh = ½ mv2
v2 = 2gh
v = √2gh
V is the maximum velocity of the bob and
occurs at the bottom of its swing.
POWER
• Power is the rate at which work is done.
• p = work done/t or energy transferred/t
• The unit for power is joule per second, or
J/s, also called a watt (W)
Apply your knowledge
A boy of mass 40kg is traveling at 8m.s-1
on a skateboard when he reaches a ramp
of height 1,2m and of length 5m. A
constant force of friction of 16N acts
between the skateboard and the surface
of the ramp.
Calculate his velocity when he reaches the
top of the ramp.
This is how your answer should look:
Ek at the bottom of the ramp = ½ mv2
Ek = ½ x 40 x (8)2 = 1280J
This is the total amount of energy at the beginning
Ep gained during journey up ramp = mgh
Ep gain = 40 x 10 x 1,2 = 480J
Energy lost due to friction = F.s = 16 x 5 = 80J
Ek remaining = 1280 – (480 + 80) = 720J
720 = ½ mv2
720 = ½ x 40 x v2
v = 6 m.s-1
Apply your knowledge 2
A woman, shopping in a hurry, applies a
force of 60N and moves her trolley at a
constant speed of 3m.s-1. What is her
power?
This is how your answer should look:
Work done = Fcosθ
Because the force is horizontal, cos θ = 1
Work done = f.s and P = work done/t
power = f.s/t but s/t = v
DO NOT
power = f.v = 60 x 3 = 180W
CONFUSE
POWER (P) AND
MOMENTUM (p).
RATHER WRITE
OUT “POWER. “