Download Kinetic Energy - BakerMath.org

10.3 Energy and Conservation of
Energy
Chapter 10 Objectives

Calculate the mechanical advantage for a lever or rope
and pulleys.

Calculate the work done in joules for situations involving
force and distance.

Give examples of energy and transformation of energy
from one form to another.

Calculate potential and kinetic energy.

Apply the law of energy conservation to systems
involving potential and kinetic energy.
Chapter Vocabulary
 chemical energy
 kinetic energy
 output force
 closed system
 lever
 potential energy
 law of
conservation
 machine
 pressure energy
 mechanical
 radiant energy
 advantage
 ramp
 mechanical energy
 rope and pulley
 mechanical system
 screw
 nuclear energy
 simple machine
 output
 thermal energy
 output arm
 work
 of energy
 electrical energy
 fulcrum
 gears
 input
 input arm
 input force
Inv 10.3 Energy and Conservation of
Energy
Investigation Key Question:
How is motion on a track
related to energy?
10.3 Energy and Conservation of Energy
 Energy describes a system’s ability to cause
change.
 A system that has energy has the ability to do
work.
 Energy is measured in the same units as work
because energy is transferred during the
action of work.
10.3 Different forms of energy
 Mechanical energy is the energy possessed by
an object due to its motion or its position.
 Radiant energy includes light, microwaves,
radio waves, x-rays, and other forms of
electromagnetic waves.
 Nuclear energy is released when heavy atoms
in matter are split up or light atoms are put
together.
 The electrical energy we use is derived from
other sources of energy.
The workings of the universe can be
viewed as energy flowing from one
place to another and changing back
and forth from one form to another.
10.3 Potential Energy
 Objects that have potential energy do not use
the energy until they move.
 An object’s potential energy comes from the
gravity of Earth.
 Technically, energy from height is called
gravitational potential energy.
 Other forms of potential energy also exist, such
as potential energy stored in springs.
10.3 Potential Energy
Mass (kg)
Potential Energy
(joules)
Ep = mgh
Height (m)
Acceleration
of gravity (m/sec2)
Calculating potential energy
A cart with a mass of 102 kg is pushed up a ramp.
The top of the ramp is 4 meters higher than the
bottom. How much potential energy is gained by
the cart? If an average student can do 50 joules of
work each second, how much time does it take to
get up the ramp?
1.
You are asked for potential energy and time.
2.
You are given mass, height and work done per second.
3.
Use: Ep = mgh.
4.
Solve for Ep = (102 kg) (9.8 N/kg) (4 m) = 3,998 J.
5.
At a rate fof 50 J/s, it takes 80 s to push the cart up the
ramp.
10.3 Kinetic Energy
 Energy of motion is called kinetic energy.
 The kinetic energy of a moving object
depends on two things: mass and speed.
 Kinetic energy is proportional to mass.
10.3 Kinetic Energy
 Mathematically, kinetic energy increases as
the square of speed.
 If the speed of an object doubles, its kinetic
energy increases four times (mass is
constant).
10.3 Kinetic Energy
Mass (kg)
Kinetic Energy
(joules)
Ek = 1 mv2
2
Speed (m/sec)
10.3 Kinetic Energy
 Kinetic energy becomes important in
calculating braking distance.
10.3 The formula for kinetic energy
 A force (F) is applied to mass (m) and
creates acceleration (a).
 After a distance (d), the ball has reached speed (v),
therefore the work done is its mass times acceleration
time distance:
 W= fd = (ma) x d = mad
 Also: d = ½ at2
 Replace d in the equation for work, combine similar
terms:
 W= ma (½ at2) = ½ ma2t2
 Also: v = at, so v2 = a2t2
 Replace a2t2 by v2 shows that the resulting work is the
formula for kinetic energy:
 W = ½ mv2
Calculating kinetic energy
A car with a mass of 1,300 kg is going straight ahead at a speed
of 30 m/s (67 mph). The brakes can supply a force of 9,500 N.
Calculate:
a) The kinetic energy of the car.
b) The distance it takes to stop.
1.
You are asked for kinetic energy and stopping distance
2.
You are given mass, speed and force of brakes.
3.
Use Ek = 1/2mv2 and W= fd
4.
Solve for Ek = ½ (1,300 kg) ( 30 m/s)2 = 585,000 J

To stop the car, work done by brakes = Ek of car, so W = Ek

Solve for distance = W ÷ f = 585,000J ÷ 9,500 N = 62 m
10.3 Law of Conservation of Energy
 As energy takes different forms and changes
things by doing work, nature keeps perfect
track of the total.
 No new energy is created and no existing
energy is destroyed.
10.3 Energy in a closed system
 The conservation of energy is most useful when
it is applied to a closed system.
 Because of the conservation of energy, the total
amount of matter and energy in your system
stays the same forever.
10.3 Energy in a closed system
 The total energy in the system is the potential
energy of the ball at the start.
 Later, the ball is at a lower height (h) moving
with speed (v) and has both potential and kinetic
energy.
Hydroelectric Power
 Every day in the United States the average person uses
about 90 million joules of electrical energy.
 This energy comes from many sources, including burning
coal, gas and oil, nuclear power, and hydroelectric power.
 In hydroelectric power, the potential
energy of falling water is converted
to electricity.
 No air pollution is produced, nor
hazardous wastes created.