Transcript Kinetic and Gravitations Potential Energy

Kinetic & Gravitational Potential
Energy
• Mechanical Energy
• Kinetic Energy
• Work-Energy
Theorem
• Gravitational
Potential Energy
• Energy is Conserved
• Energy Conservation
Application
• Summary
Mechanical Energy
Mechanical Energy is composed of both:
1. Gravitational Potential Energy
2. Kinetic Energy
Kinetic Energy (EK or KE)
• Kinetic energy is energy of
motion
• When we do work on an
object, energy is transferred
into the system
• When the object gains
energy, it begins to move
• If you do work on a car by
pushing it, it gains kinetic
energy and begins to move
Kinetic Energy
• Kinetic energy (Ek or KE) can be found using:
• EK is the kinetic energy of the object in joules,
m is the mass of the object in kilograms, and v
is the speed of the object in metres per
second
• EK is a scalar quantity (no direction)
Check Your Understanding
Find the kinetic energy of a 48-g dart travelling at a speed of 3.4 m/s.
Answer: 0.28 J
Check Your Understanding
A 97-g cup falls from a kitchen shelf and shatters on the ceramic tile
floor. Assume that the maximum kinetic energy obtained by the cup is
2.6 J and that air resistance is negligible. What is the cup’s maximum
speed?
Answer: 7.3 m/s
Work-Energy Theorem
• The total work done on an object equals the
change in the object’s kinetic energy, provided
there is no change in any other form of energy
(for example, gravitational potential energy).
• We can summarize the relationship involving
the total work and the kinetic energy as
follows:
Check Your Understanding
What total work, in megajoules (106), is required to cause a cargo
plane of mass 4.55 x 105 kg to increase its speed in level flight from
105 m/s to 185 m/s?
Answer: 5.28 x 103 MJ
Check Your Understanding
A fire truck of mass 1.6 x 104 kg, travelling at some initial speed, has
-2.9 MJ of work done on it, causing its speed to become 11 m/s.
Determine the initial speed of the fire truck.
Answer: 22 m/s
Gravitational Potential Energy (ΔEg or PE)
• The energy stored in an object due to its elevation
above Earth’s surface
• The potential energy at a height “h” above that point is
equal to the work which was required to lift the object
to that height.
• Like charging a battery. You put energy into a battery
which can be used at a later time.
Gravitational Potential Energy (ΔEg)
• Because gravity acts vertically, we will use h
rather than Δd for the magnitude of the
displacement.
• The force applied to the box to raise it is in the
same direction as the displacement and has a
magnitude equal to mg. Therefore, the work
done by the force on the box is W = mgh
• Since the energy obtained at the top is equal to
the work it took to get there W = ΔEg = mgh
Things to keep in mind
• ΔEg = the change in potential energy from one
height to another
• ΔEg is the change in gravitational potential
energy, in joules; m is the mass, in kilograms;
g is the magnitude of the gravitational field
constant in m/s2; and h is the vertical
component of the displacement, in metres.
• ΔEg = mgh
Check Your Understanding
A diver, of mass 57.8 kg, climbs up a diving board ladder and then
walks to the edge of the board. He then steps off the board and falls
vertically from rest to the water 3.00 m below. Determine the diver’s
gravitational potential energy at the edge of the diving board, relative
to the water.
Answer: 1.70 x 103 J
Check Your Understanding
In the sport of pole vaulting, the jumper’s centre of mass must clear
the pole. Assume that a 59-kg jumper must raise the centre of mass
from 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 where the jumper started to jump?
Answer: 2.0 x 103 J
Check Your Understanding
A 485-g book is resting on a desk 62 cm high. Calculate the book’s gravitational
potential energy relative to
a) the desktop and
b) the floor.
Answer: a) 0 J
b) 2.9 J
Check Your Understanding
The elevation at the base of a ski hill is 350 m above sea level. A ski lift
raises a skier (total mass = 72 kg, including equipment) to the top of
the hill. If the skier’s gravitational potential energy relative to the base
of the hill is now 9.2 × 105 J, what is the elevation at the top of the hill
relative to sea level?
Answer: 1.7 x 103 J
Energy is Conserved
• Energy cannot be created or
destroyed, only converted from
one form to another
• Work is done to move an object
upwards giving it Ek (because it is
moving) and Eg (because it is
gaining height)
• Once v = 0 the object stops
moving up and Ek = 0. The
energy from EK is completely
converted to Eg at its peak
• Once the objects starts to
descend, Eg is converted to EK as
the objects gains speed
Energy Is Conserved
• If you raise an object to the top of a hill, you are giving it
potential energy (Eg)
• As the object moves down the hill, it converts its
potential energy into kinetic energy
• As kinetic energy increases, speed increases. This is why
the object will be going faster at the bottom of the hill
then at the top
Application
• Hydroelectric plants
convert the Eg of the
water at higher
elevations into EK as
water rushes down via
gravity to spin turbines
to create electricity
Summary
• Kinetic energy (EK): The energy of
motion
• Gravitational Potential Energy (ΔEg):
The energy stored in an object due to
its elevation above a reference point
• Energy can be converted from one
form to another (i.e. EK to Eg)
• Mechanical energy is the sum of
potential energy and kinetic energy. It
is the energy associated with the
motion and position of an object.
• Example: If EK = 100 J and Eg = 50 J.
What is the mechanical energy of the
system.
Answer: 150 J