Physics
Jan. 2015
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The ability of humans to build
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.
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The best way to analyze what a machine does
is to think about the machine in terms of
input and output.
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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.
Output force (N)
Mechanical
advantage
Input force (N)
MA = Fo
Fi
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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.
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The essential features of a lever are the input
arm, output arm, and fulcrum.
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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
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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.
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.
4.
5.
6.
◦
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
Solve for Fo = (.5) (500 kg) (9.8 N/kg) = 2,450 N
Solve for MA = 2,450 N ÷ 700 N = 3.5
Since Li = 3.5 Lo , and Li + Lo = 3m, then Lo = .67m
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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.
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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.
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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.
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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.
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A force acts upon
an object to cause a
displacement of the
object. Forces
make things move.
(energy transfer)
Work is only done
when a force moves
an object through a
distance.
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We do work when we lift a load or push a box
across the floor. The force is in the same
direction as the displacement.
Two things enter into every case where work
is done
1. The application of a force
2. The movement of something in the same
direction as that force.
◦ A person pushing a shopping cart through the
store.
 YES. The force of the person causes the cart to get displaced.
◦ A weightlifter lifting a barbell above his head.
 YES. The force of the weightlifter displaces the barbell upward.
◦ A person applies a force to a wall and
becomes exhausted.
 NO. The wall is not displaced.
◦ A book falls off a table and free falls to the
ground.
 YES. The force of gravity acts on the book which causes it to be
displaced in a downward direction (fall).
◦ You finish your physics homework before you
leave class.
 NO. The is a not the scientific form of work, this is work done in an
everyday sense!
Force (N)
Work (joules)
W=Fxd
Distance (m)
Straight line
force
W = Fd cos ()

Force acts at an angle
Angle
Mass (kg)
Work (joules)
W = mgh
Height object raised (m)
Gravity (m/sec2)
Remember that F = mg
1.
A 10.5 g hockey puck is sliding across
the ice. A player exerts a constant force
of 4.5 N over a distance of 0.15 m. How
much work does the player do on the
puck?
W=Fxd
W = 4.5 N x 0.15 m = __________?
0.675 J
1.
A sailor pulls a boat 30 m along a dock
using a rope that makes a 25° angle with
the horizontal. How much work does the
sailor do on the boat if he exerts a force of
255N on the rope?
W = Fd cos(θ)
W = 255N x 30m (cos 25°) = _______?
6933J
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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.
Sections 10.3 and 11.3
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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.
Mechanical energy is the total energy
possessed by an object due to its motion
or its position.
Kinetic Energy (motion)
Potential Energy (position)
 Gravitational
 Elastic

ME = KE + PEg + PEe
Definition: energy associated with an
object due to its position.
 An object has the potential to move and
change its position.
 It is a SCALAR quantity, it does not have
a direction.
 SI unit for PE is also the Joule (N•m).
 Two types of PE:
1) Gravitational PEg
2) Elastic PEe
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Definition: The energy associated with an
object due to the object’s position relative to
a gravitational source.
PEg depends on an object’s MASS, HEIGHT,
and free-fall acceleration (GRAVITY).
Equation:
PEg = mgh
 m is mass of the object (kg)
 g is the free-fall acceleration (m/s2)
 h is the height (m)
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A cart with a mass of 200 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?
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m= 200kg
g = 9.8 m/s2
h=4m
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PE = (200 kg)(9.8 m/s2)(4 m) = 7840 J
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Definition: the PE stored in
any compressed or stretched
elastic object (springs,
strings)
When external forces
compress or stretch the
spring, elastic potential
energy is stored.
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The amount of
energy depends on
the distance the
spring is
compressed or
stretched from its
relaxed length and
its spring constant.
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Equation:
PE(elastic) = ½ k x2
◦ k is a symbol for the spring constant (N/m)
◦ x is the distance compressed or stretched (m).
◦ Remember: spring constant is the force constant or
how resistant a spring is to being stretched or
compressed.
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A 70 kg stuntman is
attached to a bungee
cord with an
unstretched length of
15m. He jumps off a
bridge and when he
finally stops, the cord
has a stretched length
of 44 m. The spring
constant of the bungee
cord was calculated to
be 71.8N/m. What is
the elastic potential
energy of the bungee
cord?
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Definition: The energy of an object due to its
motion
KE depends on both an object’s MASS and its
SPEED.
It is a SCALAR quantity, it does not have a
direction.
SI unit for KE is the Joule (N • m).
Equation:
KE = ½ mv2
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m is the mass (kg)
v represents speed, not velocity (m/s)
A 7.0 kg bowling ball moves at 3.0
m/s. How much kinetic energy does
the bowling ball have?
•
3.
KE = ½ (7.0kg)(3.0m/s)2 = 31.5 J
How fast must a 2.45 g table-tennis
ball move in order to have the same
kinetic energy as the bowling ball?
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When work is done by external forces (push,
pull, friction, etc), the energy of the object is
altered.
The net work done on an object is equal to
the change in kinetic energy of the object.
◦ If the force and the displacement are in the same
direction, then positive work is done on the object
and the object gains KE.
◦ If the force and the displacement are in the
opposite direction, then negative work is done on
the object; the object loses KE.
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Megan drops the ball and hits it with her
tennis racket. The racket is moving
horizontally as the strings apply a horizontal
force while in contact with the ball.
Work is Positive
KE increases (ball gains speed)
The frictional force between highway and tires
pushes backwards on the tires of a skidding
car.
Work is Negative
KE decreases (car slows down)
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Equation:
A 1150 kg truck speeds up from 15
m/s to 30 m/s while passing another
truck. How much work was done on
the truck to increase its speed?
∆KE = KEf - KEi
5.
KEf = 1/2(1150kg)(30m/s)2 =517500J
KEi = 1/2(1150kg)(15m/s)2 =129375J
∆KE = 517500J - 129375J = 388000 J
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No new energy is created and no existing
energy is destroyed.
As energy takes different forms and changes
things by doing work, nature keeps perfect
track of the total.
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Mechanical energy (ME) is the total of the
kinetic and potential energies acting on
an object.
ME is conserved when the only type of
force doing work upon an object is an
internal force (gravity or spring forces).
◦ The object’s energy changed from:
PE →KE or KE → PE.
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A ball falls from a height of 2 meters in
the absence of air resistance.
◦ Change in PE to KE
◦ Internal force: gravity
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A bungee cord begins to exert an upward
force upon a falling bungee jumper.
◦ Change in KE to PE
◦ Internal force: spring force
http://www.physicsclassroom.com
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A pendulum bob is swinging to and fro on the
end of a string.
There are only two forces acting upon the
pendulum bob.
◦ Gravity (an internal force)
acts downward
◦ Force of Tension(an external force)
pulls upwards towards the pivot point.
 The external force does not do work since it is
perpendicular to the motion.
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As the pendulum bob swings, its height above
the table top and in its speed is constantly
changing.
As the height decreases, PE is lost; and KE is
gained.
At all times, the SUM of the PE and KE of the
bob remains constant.
There is NO loss or gain of mechanical energy;
only a transformation from KE to PE (and vice
versa).
100
E
PEg
N
E
R
G
Y
KE
(J)
0
0
http://www.physicsclassroom.com/mmedia/energy/pe.cfm
100
TIME (s)
Think about this carefully – you will see it again.
http://www.physicsclassroom.com/mmedia/energy/ce.cfm
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Mechanical energy is the total of the kinetic and
potential energies acting on an object.
The initial mechanical energy is equal to the final
mechanical energy, in the absence of friction.