10.2 work 10.3 energy and conservation of energy · measurable change in a system, caused by a...
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Chapter 10: Work and Energy
10.2 Work
10.3 Energy and Conservation of Energy
10.2 Work
In physics, work
has a very specific
meaning.
In physics, work
represents a
measurable change
in a system, caused
by a force.
10.2 Work
If you push a box with a force of one
newton for a distance of one meter, you
have done exactly one joule of work.
10.2 Work (force is parallel to distance)
W = F x dDistance (m)
Force (N)
Work (joules)
10.2 Work (force at angle to distance)
W = Fd cos (q)
Distance (m)
Force (N)
Work (joules) Angle
10.2 Work done against gravity
W = mghHeight object raised (m)
Gravity (m/sec2)
Work (joules)
Mass (g)
1. You are asked for the work and time it takes to do work.
2. You are given mass, height, and work done per second.
3. Use: W = mgh.
4. Solve: W = (1,500 kg) ( 9.8 N/kg) (50 m) = 735,000 J
5. At a rate of 10,000 J/s, it takes 73.5 s to lift the beam.
Calculate work done against gravity
A crane lifts a steel beam with a mass of 1,500
kg. Calculate how much work is done against
gravity if the beam is lifted 50 meters in the air.
How much time does it take to lift the beam if
the motor of the crane can do 10,000 joules of
work per second?
10.2 Work done by a machine
Work is usually done when a force is applied to
a simple machine.
All machines can be described in terms of input
work and output work.
In any machine, some of the input work goes to
overcoming friction.
The output work is always less than the input
work because of the energy lost to friction.
Chapter 10 Work and Energy
10.2 Work
10.3 Energy and Conservation of Energy
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
Ep = mgh Height (m)
Mass (kg)
Potential Energy
(joules)
Acceleration
of gravity (m/sec2)
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.
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?
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
Ek = 1 mv2
2
Speed (m/sec)
Mass (kg)
Kinetic Energy
(joules)
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
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
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.
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.
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.
Hydroelectric Power
In hydroelectric power, the potential
energy of falling water is converted
to electricity.
No air pollution is produced, nor
hazardous wastes created.
Practice Problem #1.
A 50-kilogram boy and his 100-kilogram father went jogging. Both ran at a
rate of 5 m/sec. Who had more kinetic energy? Show your work and
explain.
Practice Problem #2.
What is the potential energy of a 10-newton book sitting on a shelf 2.5
meters high?