Transcript Kinetic Energy

CPO Science
Foundations of Physics
Chapter 9
Unit 4, Chapter 10
Unit 4: Energy and Momentum
Chapter 10 Work and Energy
 10.1 Machines and Mechanical Advantage
 10.2 Work
 10.3 Energy and Conservation of Energy
Chapter 10 Objectives
1. Calculate the mechanical advantage for a lever or
rope and pulleys.
2. Calculate the work done in joules for situations
involving force and distance.
3. Give examples of energy and transformation of
energy from one form to another.
4. Calculate potential and kinetic energy.
5. Apply the law of energy conservation to systems
involving potential and kinetic energy.
10.1 Machines and Mechanical
Advantage
Key Question:
How do simple machines
work?
10.1 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
Mechanical
advantage
Input force (N)
𝑭𝒐
𝑴𝑨 =
𝑭𝒊
Output force (N)
10.1 Mechanical Advantage of a Lever
Mechanical
advantage
𝑴𝑨𝒍𝒆𝒗𝒆𝒓
Length of output arm
(m)
𝑳𝒊
=
𝑳𝒐
Length of input arm
(m)
10.1 Calculate position
 Where should the fulcrum of a lever be
placed so one person weighing 700 N
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.
10.1 Wheels, gears, and rotating
machines
 Axles and wheels 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.
10.2 Work
Key Question:
What are the consequences
of multiplying forces in
machines?
10.2 Work
 In physics, work has a
very specific meaning.
 In physics, work
represents a measurable
change in the energy of
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 (g)
Work (joules)
W = mgh
Height object raised (m)
Gravity (m/sec2)
10.3 Why the path doesn't matter
10.3 Calculate work
 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?
10.3 Energy and Conservation of Energy
 Energy is the ability to make things 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 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.
10.3 Potential Energy
Mass (kg)
Potential Energy
(joules)
Ep = mgh
Height (m)
Acceleration
of gravity (m/sec2)
10.3 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
Mass (kg)
Kinetic Energy
(joules)
Ek = ½
mv2
Speed (m/sec)
10.3 Kinetic Energy
 Kinetic energy becomes important in
calculating braking distance.
10.3 Calculate Kinetic Energy
 A car with a mass of 1,300
kg is going straight ahead
at a speed of 30 m/sec (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 and Conservation of
Energy
Key Question:
How is motion on a track
related to energy?
Application: Hydroelectric Power