Transcript Calculating potential energy

Chapter 10: Work and Energy
 10.1 Machines and Mechanical Advantage
 10.2 Work
 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 10.1 Machines and Mechanical
Advantage
Investigation Key Question:
How do simple machines work?
10.1 Machines and Mechanical
 The ability of humans to build Advantage
buildings and move mountains
began with our invention of
machines.
 In physics the term “simple
machine” means a machine
that uses only the forces
directly applied and
accomplishes its task with a
single motion.
10.1 Machines
 The best way to analyze what a machine does
is to think about the machine in terms of input
and output.
10.1 Mechanical Advantage
 Mechanical advantage is the ratio
of output force to input force.
 For a typical automotive jack the
mechanical advantage is 30 or
more.
 A force of 100 newtons (22.5
pounds) applied to the input arm
of the jack produces an output
force of 3,000 newtons (675
pounds)— enough to lift one
corner of an automobile.
10.1 Mechanical Advantage
Output force (N)
Mechanical
advantage
Input force (N)
MA = Fo
Fi
10.1 Types of simple machines
 The lever, wheel and axle,
rope and pulleys, screw, ramp,
and gears are the most
common simple machines.
 Complex machines, combine
many simple machines into
mechanical systems.
 A mechanical system is an
assembly of simple machines
that work together to
accomplish a task.
10.1 Mechanical Advantage of a Lever
 The essential features of a lever are the input
arm, output arm, and fulcrum.
10.1 Three types of levers
 The three types of levers are
classified by the location of
the input and output forces
relative to the fulcrum:
 first class lever
 second class lever
 third class lever
10.1 How a lever works
 A lever works by rotating about its fulcrum.
 The mechanical advantage can be deduced by
calculating the torques created by the input and output
forces.
 The input force creates a (positive) counterclockwise
torque.
 The torque created by the reaction force is clockwise
(negative).
 When the lever is in equilibrium the net torque must be
zero.
10.1 Torque and mechanical advantage
Calculating the position of the
fulcrum
Where should the fulcrum of a lever be placed so one person weighing 700N
can lift the edge of a stone block with a mass of 500 kg? The lever is a steel
bar three meters long. Assume a person can produce an input force equal to
their own weight. Assume that the output force of the lever must equal half
the weight of the block to lift one edge.
1.
2.
3.
You are asked for the location of the fulcrum
You are given input force, lever length, mass to be lifted
Since you are told to assume Fo = ½ Fw , use:
 Fw = mg , MA = Fo ÷ Fi , MA = Li÷ Lo
4. Solve for Fo = (.5) (500 kg) (9.8 N/kg) = 2,450 N
5. Solve for MA = 2,450 N ÷ 700 N = 3.5
6. Since Li = 3.5 Lo , and Li + Lo = 3m, then Lo = .67m
10.1 Mechanical advantage of ropes
and pulleys
 A tension force is a pulling force acting along
the direction of a rope or string.
 Ropes and strings carry tension forces
throughout their length.
 If friction is small, the tension force in a rope is
the same everywhere.
 If you were to cut a rope in tension and insert a
force scale, the scale would measure the same
force at any point along the rope.
10.1 Rope & Pulleys
 The block-and-tackle
machine is a simple
machine using one rope
and multiple pulleys.
 The rope and pulleys can
be arranged to create
different amounts of
mechanical advantage.
10.1 Wheels, gears, & rotating machines
 Wheels and axles provide advantages.
 Friction occurs where the wheel and axle touch or where
the wheel touches a surface.
 Rolling motion creates less wearing away of material
compared with two surfaces sliding over each other.
 With gears the trade-off is
made between torque and
rotation speed.
 An output gear will turn with
more torque when it rotates
slower than the input gear.
10.1 Ramps and Screws
 Ramps reduce input force by
increasing the distance over
which the input force needs to
act.
 A screw is a simple machine
that turns rotating motion into
linear motion.
 A thread wraps around a screw
at an angle, like the angle of a
ramp.
Chapter 10 Work and Energy
 10.1 Machines and Mechanical Advantage
 10.2 Work
 10.3 Energy and Conservation of Energy
Inv 10.2 Work
Investigation Key Question:
What is the trade-off for
multiplying forces in a
machine?
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)
Force (N)
Work (joules)
W=Fxd
Distance (m)
10.2 Work (force at angle to distance)
Force (N)
Work (joules)
W = Fd cos (q)
Angle
Distance (m)
10.2 Work done against gravity
Mass (kg)
Work (joules)
W = mgh
Height object raised (m)
Gravity (m/sec2)
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?
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.
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
 10.1 Machines and Mechanical Advantage
 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
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.