Transcript Energy and Work

ENERGY AND WORK
SPH4C/SPH3U
Findlay
Energy


Energy can be defined as the capacity to work or
to accomplish a task.
Example: burning fuel allows an engine to do the
work of moving a car.
Forms of Energy

Radiant Energy
 Components
of the electromagnetic spectrum have
characteristics of waves, such as wavelengths,
frequencies, and energies; they travel in a vacuum at
the speed of light (3.0 x 108 m/s).
Forms of Energy

Kinetic Energy
 Energy
of motion, every moving object has this energy
Forms of Energy

Gravitational Potential Energy
A
raised object has stored energy due to its position
above some reference level
Forms of Energy

Elastic Potential Energy
 Is
stored in objects that are stretched or compressed.
Forms of Energy

Chemical Potential Energy
 In
chemical reactions, new molecules are formed and
chemical potential energy is released or absorbed.
Forms of Energy

Nuclear Potential Energy
 The
nucleus of every atom contains energy.
 Nuclear
fission – The breaking down of atoms
 Nuclear fusion – the joining of atoms
Forms of Energy

Electrical Potential Energy
 Electrons
in a electric circuit can transfer energy to the
components of the circuit.
Forms of Energy

Thermal Energy
 The
more rapidly atoms and molecules move, the
greater their total thermal energy.
Forms of Energy

Sound Energy
 Produced
by vibrations; the energy travels by waves
through a material to the receiver.
Energy Transformations


The 9 forms of energy listed above are able to
change from one to another; this change is called
energy transformation. A energy transformation
equation can be used to summarize the changes in
a transformation. Example: a microwave
Electrical energy  Radiant Energy  Thermal
Energy
Energy Transformation Technology

A device used to transform energy for a specific
purpose.
Mechanical Work


Mechanical work is done on an object when a force
displaces the object in the direction of the force or
a component of the force.
Work is not energy itself, but rather it is a transfer
of mechanical energy.
Mechanical Work

The mechanical work, W, done by a force on an
object is the product of the force, F, and the
displacement, Δ𝑑,
𝑊 = 𝐹Δ𝑑


The magnitude of the force must be constant.
The force and displacement must be in the same
direction.
Is this an example of work?



A teacher applies a force to a wall and becomes
exhausted.
A book falls of a table and free falls to the ground.
A waiter carries a tray full of meals above his head
by one arm straight across the room at constant
speed.
Example: Pushing a cart
How much mechanical work does a store manager do
on a grocery cart if she applies a force with
magnitude 25 N in the forward direction and
displaces the cart 3.5 m in the same direction?
𝐹𝑎𝑝𝑝 = 25 N forward
Δ𝑑 = 3.5 m forward
𝑊 =?
𝑊 = 𝐹Δ𝑑
𝑊 = 25N 3.5m
𝑊 = 88 Nm = 88 J
∴ the work done to move the cart is 88 J.
Example: Work done to change the
speed
A curler applies a force of 15 N on a curling stone and
accelerates the stone from rest to a speed of 8.00 m/s in 3.5 s.
Assuming that the ice surface is level and frictionless, how much
mechanical work does the curler do on the stone?
𝐹𝑎𝑝𝑝 = 15 N
𝑣𝑖 = 0 m/s
𝑣𝑓 = 8.00 m/s
Δ𝑡 = 3.5 s
𝑊 =?
Δ𝑑 = ?
𝑣𝑖 + 𝑣𝑓
Δ𝑡
2
0 m/s + 8.00 m/s
Δ𝑑 =
2
Δ𝑑 = 14 m
Δ𝑑 =
𝑊 = 𝐹Δ𝑑
𝑊 = 15 N 14 m
𝑊 = 210 J
∴ the work done by the curler is 210 J.
3.5 s
Negative Work

If the force is opposite in direction to the displacement, the
work done is negative.
𝑊 = −𝐹Δ𝑑


Consider the previous example of the shopping cart but this
time a second employee exerts a horizontal force in the
opposite direction to the 25 N force.
Since the force is in the opposite direction to the
displacement, the work done by the second employee on the
carts is negative.
Work Done by Friction

Negative work can also occurs with kinetic friction
because the force of kinetic friction always happens
in the direction opposite to the direction of motion
of the object.
𝑊 = −𝐹𝑘 Δ𝑑

𝐹𝑘 is the magnitude of the force of Kinetic Friction.
Example
A toboggan carrying two children (total mass 85kg)
reaches its maximum speed at the bottom of a hill. It
then glides to a stop 21 m along a horizontal surface.
The coefficient of friction between the toboggan and
the snowy surface is 0.11.
A.
Calculate the magnitude of the force of kinetic
friction acting on the toboggan
B.
Calculate the work done by the force of kinetic
friction on the toboggan
Example
A.
𝑚 = 85 kg
𝑔 = 9.8 N/kg
𝜇𝑘 = 0.11
𝐹𝑘 = ?
𝐹𝑘 = 𝜇𝑘 𝐹𝑁 = 𝜇𝑘 𝑚𝑔
𝐹𝑘 = 0.11 85 9.8
𝐹𝑘 = 92 N
B.
Δ𝑑 = 21 m
𝑊=?
𝑊 = −𝐹𝑘 Δ𝑑
𝑊 = − 92 21
𝑊 = −1.9 × 103 J
Friction

The work done by friction has been transformed into
thermal energy. This is observed as a increase in
temperature.
Zero Work


Sometimes an object can experience a force, a displacement,
or both, yet no work is done on the object.
Example: Holding a box in your hands. The box is not moving
so no work is done so the displacement is zero.

A puck on an air hockey table is moving but it does not have
force acting parallel to the movement as friction is negligible.
Positive, Negative, or Zero?
Force and Displacement in Different
Directions

An object may experience a force in one direction
while it moves in a different direction. This occurs
when a person pulls on a suitcase with wheels and a
handle.
𝐹𝑎𝑝𝑝
𝜃
𝐹𝑥
𝐹𝑦
Horizontal Component causes
Horizontal Displacement



The applied force makes an angle, Θ,
with the horizontal displacement. The
force acting in the same direction as the
displacement is the horizontal component
of the applied force.
𝑊 = 𝐹Δ𝑑
𝑊 = 𝐹𝑥 Δ𝑑
𝑊 = 𝐹𝑎𝑝𝑝 cos 𝜃 Δ𝑑
This force is the only force that causes the suitcase to move along the
floor. The work done by this force is,
𝑊 = 𝐹𝑐𝑜𝑠 Θ Δ𝑑
The vertical force, 𝐹𝑦 , is perpendicular to the displacement and does
not do work on the suitcase.
Example

Calculate the mechanical work done by a custodian on a
vacuum cleaner if the custodian exerts an applied force of
50.0 N on the vacuum hose and the hose makes a 30.0o with
the floor. The vacuum cleaner moves 3.00 m to the right on a
level, flat surface.
Total Work Done by Many Forces

In many cases, objects can experience many forces
at a time. The total work done, 𝑊𝑛𝑒𝑡 , on the object
is the sum of the work done by all of the forces
acting on the object.
𝑊𝑛𝑒𝑡 = 𝑊1 + 𝑊2 + ⋯ = 𝐹𝑛𝑒𝑡 cos(Θ) Δ𝑑
Example
A shopper pushes a shopping cart on a horizontal
surface with horizontal applied force of 41.0 N for
11.0 m. The cart experiences a force of friction of
35.0 N. Calculate the total mechanical work done on
the shopping cart.
MECHANICAL ENERGY
SPH4C/SPH3U
Findlay
Work





Energy is the capacity to do work and provides
objects with the ability to do work.
Work is not energy itself, but rather a transfer of
energy.
A force does work on an object if it causes the
object to move.
Work is always done on an object and results in a
change in the object.
The work done is equal to the change in energy.
Mechanical Energy

The mechanical work on an object is the amount of
mechanical energy transferred to that object by a
force.
𝑊 = Δ𝐸

The mechanical energy of an object is that part of
its total energy which is subject to change by
mechanical work.
Kinetic and Potential Energy

Kinetic energy is the energy of motion and
potential energy is the energy to, potentially, do
something else.
Kinetic Energy

Energy due to the motion of an object.
Kinetic Energy

1.
2.

Objects energy depends on two
factors:
Mass
Speed
When a force is applied to
accelerate an object from
speed 𝑣1 to speed 𝑣2 , the work
done on the object can be
written as,
𝑊 = 𝐹Δ𝑑 = 𝑚𝑎Δ𝑑
Change in Energy


We are interested in the kinetic energy, which
means we want to see how the speed affects the
energy.
Using the following equations from kinematics, we
can find the change in kinetic energy.
Δ𝑣 𝑣2 − 𝑣1
𝑎=
=
Δ𝑡
Δ𝑡
𝑣1 + 𝑣2
Δ𝑑 = 𝑣𝑎𝑣 Δ𝑡 =
Δt
2
Change in Energy
𝑣2 − 𝑣1
𝑊 = 𝑚𝑎Δ𝑑 = 𝑚
Δ𝑡
𝑣1 + 𝑣2
Δ𝑡
2
1
1
2
𝑊 = 𝑚𝑣2 − 𝑚𝑣12 = Δ𝐸𝑘
2
2
A change in speed represents a change in kinetic
energy and the work done to change the speed
represents a transfer of kinetic energy.
Kinetic Energy
The kinetic energy can be found from,
1
𝐸𝑘 = 𝑚𝑣 2
2
Where
 𝐸𝑘 is the kinetic energy in joules ( J )
 𝑚 is the mass in kg
 𝑣 is the speed in m/s
Example
A car of mass 1500 kg is travelling at a speed
of 24 m/s. Calculate the kinetic energy of the
car.
Example
An object of mass 5.0 kg is travelling at a speed of 4.0 m/s.
27 J of work is done to increase the speed of the object.
Calculate its final kinetic energy and final speed.
𝑚 = 5.0 kg
𝑣1 = 4.0 m/s
𝑊 = 27 J
𝐸𝑘2 = ?
𝑣2 = ?
𝑊 = 𝐸𝑘2 − 𝐸𝑘1 or 𝐸𝑘2 = 𝑊 + 𝐸𝑘1
1
𝐸𝑘2 = 27 J + 5.0 4.0 2
2
𝐸𝑘2 = 67 J
𝑣2 =
2𝐸𝑘2
𝑚
2 67
𝑣2 =
5.0
𝑣2 = 5.2 m/s
Gravitational Potential Energy



The type of energy that an object possess because
of its position above some level.
The energy is called potential because it can be
stored and used at a lower level for work.
When an object falls, its potential energy is
transformed into kinetic energy as its speed
increases.
Gravitational Potential Energy


Since the force (𝐹) required to lift an object without
accelerating is the same as the objects weight (𝑚𝑔), the
energy (𝐸𝑔 ) required to lift an object is the same as its
potential energy from the height it was lifted from.
Since 𝐹𝑔 = 𝑚𝑔, we can make a common equation for
gravitational potential energy.
𝐸𝑔 = 𝐹𝑔 Δh = mgΔh

Energy is measured in joules and height is measured in
meters.
Gravitational Potential Energy


The potential energy in a system must be based
against a Reference Level – The level to which the
object may fall.
It is important to note that when answering questions
about relative potential energy, it is important to
state the reference level.
Example
In the sport of pole vaulting, the jumper’s point of
mass centralization, called the centre of mass, must
clear the pole. Assume that a 59 kg jumper must raise
the centre of mass 1.1 m off the ground to 4.6 m off
the ground. What is the jumper’s gravitational
potential energy at the top of the bar relative to the
point at which the jumper started the jump?
Example
ℎ = 4.6 − 1.1 = 3.5 m
𝑚 = 59 kg
𝑔 = 9.8 N/kg
𝐸𝑔 = ?
𝐸𝑔 = 𝑚𝑔Δℎ
𝐸𝑔 = 59 9.8 3.5
𝐸𝑔 = 2.0 × 103 J
Mechanical Energy

The sum of gravitational potential energy and
kinetic energy is called mechanical energy.
𝐸𝑚𝑒𝑐ℎ = 𝐸𝑘 + 𝐸𝑔