Chapter 3: Energy Part 1

1
Chapter 3 Energy Part 1

• Alyssa Jean-Mary
• Source The Physical Universe by Konrad B.
  Krauskopf and Arthur Beiser

2
Energy and Force

• In general, energy is the ability to accomplish
  change
• Almost everything that happens in the physical
  world involves energy
• Any change that takes place in the physical world
  is from forces
• All forces dont cause a change

3
Work

• Definition of work The work done by a force
  acting on an object is equal to the magnitude of
  the force multiplied by the distance through
  which the force acts when both are in the same
  direction.
• If a force is applied to an object, but that
  object does not move, then no work is done on the
  object, no matter how much force is applied. But
  if a force is applied to an object and the object
  does move, then there is work being done on the
  object.
• The equation for work is
• W Fd
• where W is the work done, F is the applied
  force, and d is the distance through which the
  force acts
• In the equation for work, the F used is always in
  the direction of the motion
• A force that is perpendicular to the direction of
  the motion of the object does no work on the
  object (i.e. the force of gravity doesnt do work
  on an object that is moving horizontally on the
  earths surface)

4
The Joule

• The Joule (J) is the SI unit of work
• Since the equation for work is W Fd, and the
  unit for F is Newton and for d is meter, a Joule
  is equal to a (Newton x meter) OR J Nm
• The Joule was named for the English scientist
  James Joule

5
Work Done Against Gravity

• To determine the work done against gravity, start
  with the equation W Fd
• Since the work is done against gravity, the force
  is the force of gravity, so F mg
• Also, since the motion is vertical, the distance
  it moves is referred to as a height, so d h
• Thus, the work done against gravity is W mgh
  OR Work weight x height
• In the equation W mgh, the height is the total
  height the route taken to reach this height is
  not taken into account
• The work done BY gravity on an object that is
  falling can also be calculated by the equation W
  mgh

6
Example Calculations using Work

• Work Example How much work is done by 67N in
  3.2m?
• Answer
• 1. Given 67N, 3.2m
• 2. Looking for work
• 3. Equation W Fd
• 4. Solution W Fd (67N)(3.2m) 214.4J

• Work done against gravity Example How much work
  is done by an object with a mass of 54kg at a
  height of 45m above the earth?
• Answer
• 1. Given 54kg, 45m
• 2. Looking for work
• 3. Equation W mgh
• 4. Solution W mgh (54kg)(9.8m/s2)(45m)
  23814J

7
Power

• The amount of time needed to do something is as
  important as the amount of work needed. Anything
  can accomplish the work needed - even a small
  engine could, as long as there is enough time. A
  larger engine could also accomplish the work it
  would just do so in less time.
• Power is the rate at which work is being done
• The more power something has, the faster it can
  do work
• The equation for power is
• P W/t
• where P is the power, W is the work done, and t
  is the time interval
• The SI unit of power is the watt (W), where a
  watt is equal to a Joule/second OR W J/s, since
  the equation for power is P W/t, and the unit
  for W is Joule and for t is second
• A kilowatt is also often used as a unit to
  express power 1 kW 1000 W
• A person in good physical condition is capable of
  a continuous power output of about 75 W
• At times, an athlete can output 2 or 3 times more
  than this
• For a period of less than a second, the power
  output could be as high as 5 kW

8
Example Calculations using Power

• Example What is the power if 43J of work is done
  in 78 seonds?
• Answer
• 1. Given 43J, 78s
• 2. Looking for power
• 3. Equation P W/t
• 4. Solution P W/t 43J/78s 0.55W

9
Energy

• Definition of Energy Energy is that property
  something has that enables it to do work
• If something has energy, it is able to exert a
  force on something and perform work
• If work is done on something, energy is added to
  it
• The SI unit of energy is the Joule (J) remember
  a Joule (J) is equal to a (Newton x meter) (Nm)

10
Kinetic Energy

• Kinetic energy (KE) is the energy of motion
  i.e. the energy a moving object has
• Because of their motion, all moving objects have
  energy
• A moving object has the ability to exert a force
  on another object and thus perform work on that
  object (i.e. move it, etc.)
• The kinetic energy of an object depends on its
  mass and its speed
• KE (mv2)/2
• Thus, according to this equation, if the mass of
  an object is greater, the kinetic energy will
  also be greater, AND if the speed of an object is
  greater, the kinetic energy will also be greater
  (i.e. both mass and speed are directly
  proportional to kinetic energy)
• Since the kinetic energy varies by v2, but it
  only varies by m, a change in speed affects the
  amount of kinetic energy more than a change in
  mass i.e. if the mass is increased by 10, then
  the kinetic energy is also increased by 10, but
  if the speed is increased by 10, then the kinetic
  energy is increased by 102, or 100

11
Example Calculations using Kinetic Energy (KE)

• Example What is the kinetic energy of an object
  with a mass of 92kg is moving at 3.2m/s?
• Answer
• 1. Given 92kg, 3.2m/s
• 2. Looking for kinetic energy
• 3. Equation KE (mv2)/2
• 4. Solution KE (mv2)/2 ((92kg)(3.2m/s)2)/2
  471.04 J

12
Potential Energy

• Potential energy is the energy of position i.e.
  the energy that an object could have if it was in
  motion
• Because of its position, anything that has the
  ability to move toward the earth under the
  influence of gravity has potential energy
• For example, water on the top of a waterfall has
  potential energy since once it falls, it will do
  work
• Even though the influence of gravity is the most
  common source for potential energy, it is not
  necessary for an object to have potential energy
• For example, a stretched spring has potential
  energy since it will do work when it is let go

13
Gravitational Potential Energy

• The gravitational potential energy of an object
  is equal to the work that was done against
  gravity to lift it to a certain height above the
  ground
• Since the work done against gravity is equal to
  W mgh, gravitational potential energy is equal
  to PE mgh
• The gravitational potential energy of an object
  depends on the reference used to identify the
  height of the object usually the earth is the
  reference used
• For example, if a book is raised above a table,
  the book has a certain potential energy relative
  to the table, but it also has a certain potential
  energy relative to the floor, that would actually
  be greater than the potential energy relative to
  the table because the height of the object
  compared to the floor is greater.
• Thus, since gravitational PE depends on the
  reference, it is a relative quantity i.e. there
  is no true PE

14
Example Calculations using Potential Energy (PE)

• Example What is the potential energy of an
  object that is 45m above the earth and has a mass
  32kg?
• Answer
• 1. Given 45m, 32kg
• 2. Looking for potential energy
• 3. Equation PE mgh
• 4. Solution PE mgh (32kg)(9.8m/s2)(45m)
  14112 J

15
Energy Transformation

• Potential energy can be changed into kinetic
  energy and then back again
• Some examples of energy transformations
• For a car to get to the top of a hill, work is
  done by the engine of the car. At the top of the
  hill, the car has potential energy. Without the
  engine, the car rolls down the hill, and the
  cars potential energy is converted to kinetic
  energy. The amount of kinetic energy the car has
  is equal to the amount of potential energy it had
  at the top of the hill.
• When a planet is close to the sun, its kinetic
  energy is high and its potential energy is low.
  This is because, since the planet is close to the
  sun, the gravitational force between the planet
  and the sun is greater, so the planet moves
  faster so that it is not pulled into the sun. In
  the same way, when a planet is far from the sun,
  its kinetic energy is low and its potential
  energy is high. Since the gravitational force
  between the planet and the sun is less when the
  planet is far from the sun, so the planet needs
  less kinetic energy to not be pulled into the
  sun. The total energy of the planet is always
  constant i.e. the kinetic energy added to the
  potential energy is always the same amount, with
  some times the kinetic energy being more and
  other times the potential energy being more.
• A pendulum consists of a ball on a sting. If the
  ball is pulled to one side, before it is
  released, it has potential energy. Once it is
  released, the potential energy is changed to
  kinetic energy, with the maximum amount of
  kinetic energy occurring at the bottom. After it
  reaches the bottom, the ball continues in motion
  to the other side until it has reached the same
  height as it had initially. At this height, there
  is potential energy again since the ball is
  momentaliy at rest. The ballthen begins to
  retrace its path.

16
Other Forms of Energy

• There are other forms of energy besides potential
  energy and kinetic energy
• Chemical energy this is the energy in food that
  enables our bodies to perform work
• Heat energy this energy from burning coal is
  used to form the steam that drives the turbines
  of power stations
• Electric energy this is the energy that turns
  motors
• Radiant energy this energy from the sun is used
  to form clouds from the evaporation of water from
  the earths surface and to promote chemical
  reactions in plants
• Just as potential energy and kinetic energy can
  be converted into each other, these other forms
  of energy can also be converted into each other
• For example, the gasoline in a car has chemical
  energy. Once it is ignited by the spark plugs,
  the chemical energy becomes heat energy. The heat
  energy is then converted to kinetic energy as the
  pistons are pushed down by the expanding gases of
  the gasoline. Most of the kinetic energy goes to
  move the car, but some of the kinetic energy is
  changed to electric energy to charge the battery
  and to heat energy by friction in bearings.

17
Conservation of Energy

• When it appears as if energy has been loss, it
  actually has not been loss it was just
  converted to another form of energy
• For example, a skier at the top of a hill has a
  certain amount of potential energy. Once the
  skier starts skiing, the potential energy becomes
  kinetic energy. When the skier is at the bottom
  of the hill, it appears as if the skier has lost
  some potential energy since the skier is no
  longer at the same height from the earth, when
  the skier has actually gained heat.
• The Law of Conservation of Energy Energy cannot
  be created or destroyed, although it can be
  changed from one form to another.