• An object can store energy as the result of its
position. For example, the heavy ball of a demolition
machine is storing energy when it is held at an
elevated position. This stored energy of position is
referred to as potential energy.
• Just like a drawn bow is able to store energy as the
result of its position.
• When assuming its usual position (i.e., when not
drawn), there is no energy stored in the bow. Yet
when its position is altered from its usual equilibrium
position, the bow is able to store energy by virtue of
its position.
• This stored energy of position is referred to as
potential energy. Potential energy is the stored
energy of position possessed by an object.
Gravitational Potential Energy
• The two examples above illustrate the two forms of
potential energy to be discussed in this course gravitational potential energy and elastic potential
energy.
• Gravitational potential energy is the energy stored in an
object as the result of its vertical position or height.
• The energy is stored as the result of the gravitational
attraction of the Earth for the object. The gravitational
potential energy of the massive ball of a demolition
machine is dependent on two variables - the mass of the
ball and the height to which it is raised.
•There is a direct relation between gravitational
potential energy and the mass of an object. More
massive objects have greater gravitational potential
energy.
•There is also a direct relation between gravitational
potential energy and the height of an object. The
higher that an object is elevated, the greater the
gravitational potential energy.
•These relationships are expressed by the following
equation:
•PEgrav = mass • g • height
• Use this principle to determine the blanks in the
following diagram. Knowing that the potential energy
at the top of the tall platform is 50 J, what is the
potential energy at the other positions shown on the
stair steps and the incline?
• A: PE = 40 J (since the same mass is elevated to
4/5-ths height of the top stair)
• B: PE = 30 J (since the same mass is elevated to
3/5-ths height of the top stair)
• C: PE = 20 J (since the same mass is elevated to
2/5-ths height of the top stair)
• D: PE = 10 J (since the same mass is elevated to
1/5-ths height of the top stair)
• E and F: PE = 0 J (since the same mass is at the
same zero height position as shown for the
bottom stair).
PE going to KE
QUIZ
AGAIN
• 1. A cart is loaded with a brick and pulled at
constant speed along an inclined plane to the
height of a seat-top. If the mass of the loaded
cart is 3.0 kg and the height of the seat top is
0.45 meters, then what is the potential energy
of the loaded cart at the height of the seattop?
• 2. If a force of 14.7 N is used to drag the
loaded cart (from previous question) along the
incline for a distance of 0.90 meters, then how
much work is done on the loaded cart?
Answer #1
• PE = m*g*h PE = (3 kg ) * (9.8 m/s/s) * (0.45 m)
• PE = 13.2 J
Answer #2
• W = F * d * cos Theta W = 14.7 N * 0.9 m * cos (0 degrees)
• W = 13.2 J
• In the following descriptions, the only forces
doing work upon the objects are internal
forces - gravitational and spring forces.
• Thus, energy is transformed from KE to PE (or
vice versa) while the total amount of
mechanical energy is conserved.
• Read each description and indicate whether
energy is transformed from KE to PE or from
PE to KE.
• A ball falls from a height of 2 meters in the
absence of air resistance.
• PE to KE
• The ball is losing height (falling) and gaining
speed. Thus, the internal or conservative force
(gravity) transforms the energy from PE
(height) to KE (speed).
• A skier glides from location A to location B
across a friction free ice.
• PE to KE
• The skier is losing height (the final location is
lower than the starting location) and gaining
speed (the skier is faster at B than at A). Thus,
the internal force or conservative (gravity)
transforms the energy from PE (height) to KE
(speed).
• A baseball is traveling upward towards a man
in the bleachers.
• KE to PE
• The ball is gaining height (rising) and losing
speed (slowing down). Thus, the internal or
conservative force (gravity) transforms the
energy from KE (speed) to PE (height).
• A bungee cord begins to exert an upward
force upon a falling bungee jumper.
• KE to PE
• The jumper is losing speed (slowing down)
and the bunjee cord is stretching. Thus, the
internal or conservative force (spring)
transforms the energy from KE (speed) to PE
(a stretched "spring"). One might also argue
that the gravitational PE is decreasing due to
the loss of height.
• The spring of a dart gun exerts a force on a
dart as it is launched from an initial rest
position.
PE to KE
•The spring changes from a compressed state
to a relaxed state and the dart starts moving.
So, the internal or conservative force (spring)
transforms the energy from PE (a compressed
spring) to KE (speed).
Kinetic Energy
• The word 'kinetic' is derived from the modern
Greek word, 'kinesis', meaning 'to move'. In
physics, if an object has energy then we say it
has the ability to work (more on work later).
Kinetic energy is the energy of motion and it
follows that any object with a velocity or
which is moving is producing kinetic energy.
• The faster the body moves the more kinetic
energy is produced. The greater the mass and
speed of an object the more kinetic energy
there will be. As a car accelerates down a hill,
its velocity increases and so does the kinetic
energy it is producing. The potential energy
posseses by the car at the top of the hill is
being changed into kinetic energy.
• Kinetic energy is often defined informally as
energy of motion. It is better defined as the
work it would take to get an object of mass,
m, moving with velocity, v, and is given by the
formula:
• Ek = ½mv2
• Ek = ½mv2
• Where:
• Ek = kinetic energy in joules (J),
m = mass of the object in kilograms (kg),
v = the velocity of the object in metres per
second (ms-1).
• The net work done on an object is equal to the
change in its kinetic or potential energy.