Transcript work done by the machine

Chapter 13
Work and Energy
Work, Power, and Machines
• Work:
– Is done only when force is applied to an object
and the object moves in the same direction as
the applied force
– Is calculated by multiplying the force by the
distance over which the force is applied
– Work = force x distance
– W = F x d
– Work is 0 when an object is not moving
Work, Power, and Machines
• Work is measured in Joules
– Because work is calculated as force times distance, it is
expressed in newtons times meters (N x m)
• 1 Nm = 1 J = 1 Kg x m2/s2
• Because all of these units are equivalent, when
solving a particular problem, you can choose
which unit to use
– Substituting equivalent units will often help you cancel
out other units in a problem
Work, Power, and Machines
• In order to lift the barbell
above his head the weight
lifter need to apply a force
which opposes the
downward acting force of
gravity on the mass of the
barbell. The distance from
the floor to above the
lifters head is 2 meters.
Work, Power, and Machines
• Mass of barbell = 25 + 25
= 50kg
Weight of barbell = mass
x acceleration due to
gravity
F=mxg
F = 50Kg x 9.8m/s2 = 490
Newtons
Work done = force x
distance
Work done = 490Kgm/s2
x 2m = 980Kgm2/s2 = 980
Joules
Work, Power, and Machines
• In the example above the work done by the weight
lifter in lifting the weights was 980 joules. In order
to do this work energy had to be transferred. 980
joules of chemical energy from food eaten by the
weight lifter was transferred to 980 joules of
gravitational potential energy to the barbell. Thus
the amount of work done is equal to the energy
transferred from one form to another.
Work, Power, and Machines
• Is any work being
done?
Work, Power, and Machines
Work, Power, and Machines
• Power: is the rate at which work is done, or how
much work is done in a given amount of time
• Power = work / time
•
P = W / t
• Power is measured in watts
– One watt is the amount of power needed to do 1 joule
of work in 1 second
– Do not confuse the symbol for work (W) which is
italic, with the symbol for watt, W
Work, Power, and Machines
Work, Power, and Machines
• When doing a chin-up,
a physics student lifts
her 42.0-kg body a
distance of 0.25
meters in 2 seconds.
What is the power
delivered by the
student's biceps?
Work, Power, and Machines
• To raise her body upward
at a constant speed, the
student must apply a force
which is equal to her
weight (m•g). The work
done to lift her body is
• W = F * d = (411.6 N) *
(0.250 m) W = 102.9 J
• The power is the
work/time ratio which is
(102.9 J) / (2 seconds) =
51.5 Watts (rounded)
Work, Power, and Machines
• Your household's monthly electric bill is
often expressed in kilowatt-hours. One
kilowatt-hour is the amount of energy
delivered by the flow of l kilowatt of
electricity for one hour. Use conversion
factors to show how many joules of energy
you get when you buy 1 kilowatt-hour of
electricity.
Work, Power, and Machines
• Using conversion factors, it can be shown
that 1 kilo-watt*hour is equivalent to 3.6 x
106 Joules. First, convert 1 kW-hr to 1000
Watt-hours. Then convert 1000 Watt-hours
to 3.6 x 106 Watt-seconds. Since a Wattsecond is equivalent to a Joule, you have
found your answer.
Work, Power, and Machines
• Machines help do work by changing the
size of an input force, the direction of the
force, or both
Work, Power, and Machines
• Mechanical advantage:
– Is the ratio between the output force and the
input force
– Also, it is equal to the ratio between the input
distance and the output distance
– If friction is ignored
Work, Power, and Machines
• Mechanical advantage =
– Output force / input force = input distance / output distance
• Machine with a mechanical advantage greater than 1
– Multiplies the input force
– Helps you move or lift a heavy object
• Machine with a mechanical advantage less than 1 does
not multiply force but increases distance and speed
Simple Machines
• Machines are either modifications of simple
machines or combinations of several simple
machines
• Six types of simple machines:
–
–
–
–
–
–
Simple lever
Pulley
Wheel and axle
Simple inclined plane
Wedge
Screw
Simple Machines
• First-class lever: fulcrum
located between the points
of application of the input
and output forces
• Second-class lever:
fulcrum is at end of the
arm, and the input force is
applied to the other end
• Third-class lever:
multiplies distance rather
force. Mechanical
advantage of less then 1
Simple Machines
Simple Machines
Simple Machines
Simple Machines
Simple Machines
Simple Machines
Simple Machines
• Pulleys are modified
levers
– Point in the middle of a
pulley is like the
fulcrum of a lever
Simple Machines
Simple Machines
• A wheel and axle is a lever connected to a shaft
Simple Machines
Simple Machines
• Inclined plane:
pushing an object up
an inclined plane
requires less input
force than lifting the
same object does.
Simple Machines
Simple Machines
Simple Machines
• Wedge: formed when
two inclined planes are
placed back to back
– Like pushing a ramp
instead of pushing
something up a ramp
– Turns a single
downward force into
two forces directed out
to the sides
Simple Machines
Simple Machines
• Screw is an inclined plane wrapped around
a cylinder
– The threads on a screw are inclined planes
• Gentle sloping threads requires a small force to act
over a long distance
• Steeper slopes requires more force over less distance
– Drill bits
– Jar lids
Simple Machines
• Compound machines
– Many devices that you use
everyday are made of more
than one single machine
– Machine that combines two
or more simple machines
• Example: a pair of scissors
uses two 1st class levers
joined at a common
fulcrum
– Each lever arm has a
wedge that cuts into the
paper
What is Energy?
• Energy:
– Ability to do work
– Whenever work is done, energy is transformed
or is transferred from one system to another
system
– Measured in Joules (same as in Work)
What is Energy?
• Potential Energy (PE):
– Energy of position
because it results from
the relative positions of
objects in a system
What is Energy?
• Gravitational potential
energy depends on
both mass and height
• PE = mass x free-fall
acceleration x height
• PE = mgh
– Note: mg is the weight
of the object in
Newtons
What is Energy?
What is Energy?
What is Energy?
What is Energy?
• Kinetic Energy: energy of motion
–
–
–
–
Depends on both the mass and speed of an object
KE = ½ x mass x speed squared
KE = ½mv2 = ½ kg x m2/s2
Why are car crashes more dangerous at high speeds?
• Depends on speed more than it depends on mass
• Speed is squared, so a small change in speed causes a large
change in KE
What is Energy?
What is Energy?
• Mechanical energy: sum of the kinetic
energy and potential energy in a system
– Mechanical engineering
• Design machines
• Chemistry: chemical potential energy
• Photosynthesis: energy from the sun
Conservation of Energy
• The total amount of energy in the universe
never changes, although energy may change
from one form to another
• Energy cannot be created or destroyed
– Potential becomes kinetic
– Kinetic becomes potential
Conservation of Energy
• Efficiency of machines:
– Not all work done by a machine is useful work
• Friction generates heat
– Measured as a percentage: ratio of useful work
output to work input
– Efficiency = useful work output/work input
Conservation of Energy
• A diesel engine with an efficiency of 0.39 requires
750 J of work to be done on its pistons.
• How much useful work is done by the diesel
engine?
• 1. List the given and unknown values.
• Given: efficiency = 0.39
• work done on the machine (input) = 750 J
• Unknown: useful work done by the machine
(output) = ? J
Conservation of Energy
• 2. Use the efficiency equation, and rearrange it to solve for
useful work done by the
• machine (output).
• Efficiency = useful work done by the machine output /
work done on the machine input
• efficiency × work done by the machine (input)= × useful
work done by the machine output/work done on the
machine input x work done on the machine input
• = useful work done by the machine (output)
Conservation of Energy
• 3. Substitute the values for the work done
on the machine and the efficiency into the
• equation, and solve.
• useful work done by the machine (output) =
(0.39) × (750 J)
• useful work done by the machine (output) =
290 J
Conservation of Energy