UNIT 1 - ENERGY & MOTION
Lesson 1.
Overview
Lesson 1.1 deals with energy, work and power. On
completion of the lesson, you should be able to describe
different forms of energy. You should be able to
calculate the kinetic energy of a moving object, the
gravitational potential energy of an object above a
certain point of reference and the amount of power when
energy is used at a particular rate. You should also be
able to estimate the speed of an object from its kinetic
energy.
ToDo
Watch the video presentation.
Carry out the activities.
Read through the lesson notes and do the exercises.
Refer to the solutions and check your answers.
At
home: Prepare for
Lab 1.1 by reading the instructions and collecting the necessary
materials and equipment.
Similarly, prepare for the two activities
in Lesson 1.2 and
test the equipment.
Lesson 1.1 Activities
- Match
Rockets (Optional) : Show how chemical energy
stored in the compounds in a match head can be
converted to pressure energy when gasses form
during ignition. The pressure energy is then
converted to kinetic energy in the match rocket
as it accelerates away from the launching point.
- Pendulum:
Use
pendulum to show conversion between gravitational
potential energy and kinetic energy
ACTIVITY
1.1.1 MATCH ROCKETS
What this illustrates
The chemical energy stored in the compounds in a
match head can be converted to pressure energy when
gasses form during ignition. The pressure energy is then
converted to kinetic energy in the match rocket as it
accelerates away from the launching point.
WARNING: Do not attempt this activity
without adult supervision. The activity should be
conducted outside on a paved area with minimum dimensions
of 3m x 3m (10ft x10ft) and away from any combustible
materials. Read the Safety Precautions below.
What you will need:
- 2 matches
- Small square of
aluminum foil
- Paper clip
- Safety pin
Procedure:
- Take one match and
wrap a small piece of aluminum foil around the
match-head. Wrap the foil tightly.
- Make a small opening
in the foil wrapped around the match head by
inserting the point of a safety pin and bending
upward slightly.
- Bend the paper clip
to form a launch pad as shown in the diagrams.
Erect the match stick rocket on the pad. Make
sure the pad is set up on a surface that will not
be damaged by the rocket's exhaust such as a lab
table. Several layers of foil on the lab table
work well.
- Ignite the match by
holding a second lighted match under the foil
until its combustion temperature is reached.
Safety
Precautions
The match rockets could travel in unexpected directions.
Wear eye protection during the activity. All observers
must wear eye protection.
The match heads - and the aluminum foil - will be hot
after ignition and could cause burns if handled without
adequate hand protection. Also, if the match rockets land
on combustible material before ignition is complete, they
could set the material on fire.
Ensure that the match rockets are pointed away from
people. Use canvas gloves when handling the rocket after
it has been used. The foil head of the rocket will be
very hot!
Activity
1.1.2 - PENDULUM
What this illustrates
When the pendulum bob is pulled to side (before it is
released to start swinging) it gains gravitational
potential energy. As the bob swings towards it's lowest
point it gains kinetic energy. At the lowest point, all
of the gravitational potential energy that it had to
start with, will have been converted to kinetic energy.
The bob will be travelling at it's maximum speed. The
kinetic energy then carries the bob up to nearly the same
height as it started from. Some energy is lost due to
friction with the air.
What you will need:
String / twine. (Roughly 1 meter long.)
A small metal weight. (The mass of the weight should be
large compared to the mass of string used.)
Nail, hook or screw to fix string to wall, roof or board
Procedure:
- Fix the nail or screw
to a suitable mounting device.
- Attach the weight to
the string and the string to the nail or screw.
- Cause the pendulum to
swing back and forward and show how it speeds up
as it moves towards its lowest point and then
slows down as it approaches one of the extremes.
- For a particular
cycle (i.e. one swing forward and one swing back),
measure the difference in height between the
highest and lowest points during the cycle.
- Measure the mass of
the bob.
- Calculate the
gravitational potential energy of the bob at its
highest point in the cycle – relative to its
lowest point in the cycle.
- Calculate the kinetic
energy of the bob when it reaches its lowest
point in the first part of the cycle.
What to measure
Measure the difference in height between the point at
which the pendulum starts to swing and its lowest point.(difference
in height - in meters)
Determine the mass of the bob. (in kilograms)
What to calculate
Assuming that all of the pendulum's mass is in the bob
and that the energy loss due to friction is negligible:
1) Determine the gravitational potential energy of the
bob (relative to the lowest point of the swing) at the
point at which it starts to swing.
The gravitational potential energy (in Joules) = m.g.h =
the mass of the bob (in kilograms) x the gravitational
field vector (9.81 N/kg) x the difference in height (in
meters).
2) Estimate the maximum
speed of the bob at it's lowest point. The mass of the
bob does not need to be known for this calculation.
At the lowest point, the kinetic energy = the initial
gravitational potential energy.
0.5 x mass of bob x (speed)2 = mass of bob x g x
difference in height.
Speed = square root of (2 x difference in height)
For
example
- A pendulum bob with a
mass of 50 grams starts swinging at a height that
is 20 centimeters above the lowest point that it
reaches during it's cycle.
What is the gravitational potential energy of the
bob at the point at which it starts to swing -
relative to the lowest point?
- If no energy is lost
due to friction, how much kinetic energy will the
bob contain at its lowest point?
Answers
- The mass of the bob
in kilograms is 50/1000 = 0.05 kg.
Its height above the lowest point in meters is 20/100
= 0.2 meters.
The GPE = mgh = 0.05 x 9.81 x 0.2 = 0.0981 Joules.
- relative to the lowest point?
- If no energy is lost
due to friction, all of the GPE will have been
converted to kinetic energy when it reaches the
lowest point. The KE will thus be equal to 0.0981
Joules.
- Energy is the
capacity to do work.
- There are many
different forms of energy. These include kinetic
energy, mechanical energy, pressure energy,
chemical potential energy, electromagnetic
potential energy, elastic potential energy,
molecular potential energy etc.
- If a force acts on an
object, work is done if the object moves or
changes shape.
- Work is also done on
an object when energy is transferred to the
object. Work is needed to increase the
temperature of an object, change a solid to
liquid or a liquid to vapor.
- Kinetic energy is the
energy that an object has as a result of its
speed.
- Potential energy is
the energy that an object has as a result of its
position in a force field.
- Power is the capacity
to do work at a particular rate. Power is a
combination of energy and time. Power is the
quantity of energy used divided by the time taken.
- The SI unit of Power
is the Watt. It is equivalent to 1 Joule per
second.
(Power in Watts = Energy in Joules divided by
Time in seconds)
Everything we do involves energy. People around the world
spend billions of dollars each year on fuels for
transportation, fuels to keep warm in winter and energy
to keep cool in summer. We need foods to provide energy
for life and we need fuels for transportation, for
electrical energy and for industry.
What is Energy?
The simple definition of energy is that it is the
capacity to do work. Energy cannot be created or
destroyed (except in nuclear reactions). Work occurs when
energy is converted from one form to another.
Work
A simple definition of work is that work is done when a
force is used to move an object in the presence of an
opposing force - such as friction, gravity etc.
The amount of
work is calculated by multiplying the size of the force
times the distance moved.
W = F
x d : Work = Force x distance.
Where: W = work in
Joules (J)
F = force in Newtons (N)
and d = distance in meters (m)
In more
general terms, work is done when energy is converted from
one form to another. For example, when work is done by
lifting an object against gravity, the energy used is
coverted to gravitational potential energy. If work is
done against friction, the surfaces that rub against each
other experience an increase in temperature (and an
increase in thermal energy).
When
electrical energy is used to heat water or to create
light, energy is converted and work is done.
Energy
and Mechanics
The branch of physics that is concerned with the motion
of bodies is called Mechanics. Mechanics deals with the
simple and obvious ways in which material objects and
forces interact with each other.
Acceleration
Acceleration occurs when an object changes speed and/or
it's direction of movement. Forces can cause acceleration.
A moving object will not change it's speed or direction
unless acted upon by an external force.
Forces
The simplest definition of a force is that it is a push
or a pull. Work is done when an object moves as a result
of an applied force.
A force is needed to change the velocity of (or
accelerate) an object. Newton's First Law states that a
body that is at rest or that is moving at constant speed
in a straight line will continue to do so unless acted
upon by an externally applied force.
The SI unit of force is the Newton (N).
1 Newton is the force needed to accelerate 1 kilogram by
1 meter per second per second.
(1 N = 1 kg.m/s2)
Gravity
Gravity is a force that causes attraction between objects
(or bodies). The gravitational force that acts on 1
kilogram at the Earth's surface force is roughly 9.81
Newtons.
The
Joule & The Newton
The Joule is a unit that we use to measure energy and/or
work. Since energy is the capacity to do work, the Joule
is also the SI unit of energy.
The Joule (J) is defined
as the energy needed move a force of 1 Newton through a
distance of 1 meter.
1 Joule = 1 Newton-meter.
(1J = 1N.m)
Potential
Energy is the
energy an object or system has as a result of its
position in a force field. For example, any object that
is not at the center of the earth has gravitational
potential energy as a result of its position in the earth’s
gravitational field. It has the capacity to do work when
it moves closer to the the center of the earth. Force
fields can be caused by gravity, magnetic forces,
electric forces etc.
How to
Calculate Gravitational Potential Energy
Gravitational potential energy is defined as the energy
that an object has as a result of its height above a
certain reference point in the earth’s gravitational
field. The amount of energy always depends on the point
of reference that has been selected. Although the earth’s
gravitational force on an object changes with distance
from the earth’s center, for most purposes, we may
assume that the gravitational force at the earth's
surface is constant at 9.81 Newtons per kilogram. The
value of 9.81 Newtons per kilogram is called the Gravitational
Field Vector.
The equation used to
calculate the relative gravitational potential energy of
an object is as follows:
PEg
= mgh : Gravitational potential energy = mass x
gravitational field vector x height above reference point.
Where: PEg
= gravitational potential energy in Joules
m = mass in
kilograms (kg)
g = gravitational
field vector (9.81 N/kg)
and h = height in
meters (m)
Kinetic
energy is
energy that an object or system has as a result of its
speed. Kinetic energy is a combination of mass and speed.
How to
Calculate Kinetic Energy
The kinetic energy of an object is proportional to its
mass and the square of its speed.
The equation used to
calculate kinetic energy is as follows:
KE = ½mv2
: Kinetic energy = ½
mass x (speed squared)
Where: KE = kinetic
energy in Joules (J)
m = mass in
kilograms (kg)
and v = speed in
meters per second (m/s)
Mechanical
Energy
Mechanical energy is usually regarded as a combination of
kinetic energy and gravitational potential energy. When
working with fluids, pressure energy is also included in
mechanical energy.
Power
Power is defined as the rate at which work is done or can
be done.
Power is rated in Joules per second or Watts. 1 Watt = 1
Joule per second.
The older, British, unit
of power is horsepower. This was originally used by James
Watt to compare the power of a steam engine with that of
a horse. It was defined by the rate at which a horse
could pull a rope connected via a pulley to a heavy
object suspended in a well.
One horsepower is
equivalent to 745.7 Watts.
Power is a combination of
energy and time. A machine or motor has more power if it
can do a certain amount of work in a shorter period of
time. The amount of energy converted is the power
consumed multiplied by the time taken.
Energy (Joules) = Power in Watts x Time taken in seconds.
Example
1.1.1: Kinetic Energy. What is the kinetic energy of a 10
kilogram cannon ball traveling at 50 meters per second?
Solution
KE = ½mv2
KE = 0.5 x 10 x (50)2 Joules (kg.m2/s2)
KE = 12500 J.
Example
1.1.2: Kinetic Energy. What is the kinetic energy of an 80 gram
bullet traveling at 600 meters per second?
Solution
KE = ½mv2
The mass must be expressed in kilograms:
80 g = 0.08 kg.
KE = 0.5 x 0.08 x (600)2 Joules (or kg.m2/s2)
KE = 14400 J.
Example
1.1.3: Gravitational Potential Energy: What is the gravitational
potential energy of an 80 gram object relative to ground
level if it is 20 meters above ground?
Solution
PEg = mgh
Where: PEg = gravitational
potential energy in Joules
m = mass in kilograms (kg)
g = gravitational field vector (9.81 N/kg)
and h = height in meters (m)
The mass of the object is 0.08 kilograms and the height
relative to the ground is 20 meters.
PEg = 0.08
x 9.81 x 20 = 15.7 Joules
Example
1.1.4: Work:
An electric motor connected to a small crane lifts a bag
of cement with a mass of 25 kg vertically against the
force of gravity through a distance of 3 meters. The
force of gravity can be taken as 9.81 N/kg.
How much work is done on the bag of cement?
Solution
Work = force x distance.
The force used = 25 kg x 9.81
N/kg
Force used = 245.25 N.
Work = 245.25 N x 3 m.
Work = 735.75 N.m
Example
1.1.5: Power:
An electric motor is rated at 500 Watts. How much work
can it do in 1 minute?
Solution
An electric motor rated at 500 W that is 100% efficient
can provide 500 Joules of work per second.
In 1 minute it can do (500 J/s)(60 s) = 30,000 Joules of
work.
REVIEW QUESTIONS
- A motor vehicle with
a mass of 2000 kg accelerates from rest to a
speed of 20 meters per second in 4 seconds. How
much kinetic energy does it gain during this 4-second
period?
- 300 cubic meters of
water with a mass of 300 tons (300 000 kg) is
stored in a tank that is roughly 30 meters above
ground level. If the average height of the water
above ground level is 33 meters, what is the
gravitational potential energy of this quantity
of water?
- If an electric motor
converts electrical energy to mechanical energy
at a rate of 2000 Joules per second, what is the
power consumption of the motor?
- How much electrical
energy will a light bulb that is rated at 75
Watts consume in 10 minutes?
- Utility companies
sell electrical energy in Units. Each unit is
equivalent to 1 kilowatt-hour. If there are 1000
Joules per second in a kilowatt and there are
3600 seconds in an hour, how many Joules are
supplied in a Unit of electricity?
- An electric motor is
rated at 500 Watts. How much work could it do in
10 seconds?
- A weightlifter lifts
200 kg from floor level to a height of 2.5 meters
above floor level in 1.5 seconds. How much power
is applied?
- What is the
horsepower of the weightlifter in the above
example?
- If a Unit of
electricity costs 12 cents, how much does it cost
to use three 100-Watt light bulbs for 24 hours?
- An electric motor is
rated at 1.5 horsepower. How much will it cost to
run this motor at its rated capacity for 24
hours?
(Assume that the cost of electricity is 12 cents
per unit.)
- A motor vehicle with
a mass of 2000 kg accelerates from rest to a
speed of 20 meters per second in 4 seconds. How
much power is used to accelerate the vehicle?
HANDS-ON
HOMEWORK
Prepare for the recommended activities for Lesson 1.2. Collect the items needed and test
the procedures before demonstrating the activities during
the next theory lesson.
W = F
x d : Work = Force x distance.
Where: W = work in
Joules (J)
F = force in Newtons (N)
and d = distance in meters (m)
KE = ½mv2
: Kinetic energy = ½
mass x (velocity squared)
Where: KE = kinetic
energy in Joules (J)
m = mass in kilograms (kg)
and v = velocity in meters per second (m/s)
PEg
= mgh
Gravitational
potential energy = mass x gravitational acceleration x
height above reference point.
Where: PEg
= gravitational potential energy in Joules
m = mass in kilograms (kg)
g = acceleration due to gravity in meters per
second squared (m/s2)
and h = height in meters (m)
Energy: The
capacity to do work.
Joule: The SI unit
of energy and of work. 1 Joule = 1 Nm (1 Newton-meter)
Work: Force x
distance
Force: A push or a
pull. A force influences the motion and/or the shape of
an object.
Power: The rate at
which work is done or energy is converted to a different
form.
Watt: The unit of
power. 1 watt = 1 J/s (Joule per second)
Kinetic energy:
Energy resulting from motion.
Potential energy:
Energy resulting from position in a force field.
Gravity: A force
that results from a force field that exists around every
object.
g:
The symbol for the acceleration due to gravity at the
earth’s surface. g = 9.81 m/s2 (meters
per second squared)
g: The
gravitational field vector. The gravitational force on an
object in a vertical direction towards the earth. At the
earth’s surface this is equivalent to 9.81 N/kg.
Vector quantity: A
quantity that has magnitude and direction.
Vector: A line,
arrow or set of coordinates that represents a quantity
and its direction.
ANSWERS TO REVIEW QUESTIONS
- KE = ½.m.v2 Kinetic energy = 0.5 x 2,000 x 202
= 400,000 Joules.
- PEg
= mgh. Gravitational potential energy =
300,000 kg x 9.81 N/kg x 33
= 97,119,000 Joules. (97,119 kilojoules)
- 2000 Joules per
second = 2000 Watts or 2 kilowatts.
- 75 Watts = 75 Joules
per second. In 10 minutes (600 seconds) the light
bulb will consume 75 x 600 = 45,000 Joules or 45
kilojoules.
- 1 kWh = 1000 Joules
per second x 3600 seconds = 3,600,000 Joules or 3,600
kJ
or 3.6 MJ.
- 500 Joules per second
x 10 seconds = 5000 Joules.
- Work = force x
distance. Force = 200 kg x 9.81 N/kg = 1962 J.
Work = 1962 N x 2.5 m = 4905 J.
4905 J in 1.5 s is equivalent to 4905 / 1.5 =
3270 J/s = 3270 Watts.
- 1 horsepower = 745.7
Watts. The Horsepower of the weightlifter is:
3270/745.7 = 4.385 hp.
- 3 light bulbs use 300
J every second. In 24 hours there are 60 x 60 x
24
= 86,400 seconds.
The electricity consumed = 300 x 86,400 = 25,920,000
J or 25.92 MJ.
From Question 5 above, there are 3.6 MJ in a Unit.
The number of Units used is therefore = 25.92/3.6
= 7.2 Units.
If each Unit costs 12 cents, the cost of running
the light bulbs is:
7.2 x $ 0.12 = $ 0.86
- 1 horsepower = 745.7
Watts. 1.5 hp = 745.7 x 1.5 = 1118.55 J/s.
In 86,400 seconds (24hrs) this will consume 86,400
x 1118.55
= 96,642,720 J or 96.64MJ.
(Note: The least-accurate number used in this
calculation contains 2 significant figures i.e. 1.5hp.
The answer will therefore be somewhere between 1.45
x 745.7 x 86,400 = 93,421,296 J and 1.55 x 745.7
x 86,400 = 99,864,144 J.
or between 93 and 100 MJ.)
If there are 3.6 MJ in a Unit and each unit costs
$ 0.12, the cost of electricity will be = 96.64 /
3.6 * $ 0.12 = $ 3.22
- The kinetic energy
developed in 4 seconds is 400,000 J. (See
Question 2) The power used is therefore 400,00 J
/ 4 s = 100,000 J/s.
|
