Transcript Work - Effingham County Schools

Mechanics
Work and Energy
Chapter 6
Work
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What is “work”?
Work is done when a force moves an object some distance
The force (or a component of the force) must be parallel to
the object’s motion
W = F ║d
W = Fdcosθ
Work is measured in Joules (J); 1 J = 1 N·m
Work is the bridge between force (a vector) and energy (a
scalar)
Work
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SI unit for Work & Energy:
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Joule (N·m)
 1 Joule of work is done when 1 N acts on a body, moving it
a distance of 1 meter
Other units for Work & Energy:
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British: foot-pound
Atomic Level: electron-Volt (eV) ← we’ll use this later!
Work
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A 5-N force pushes a box 1-m. How much
work was done?
A 5-N force pushes a box, but the box
doesn’t budge. How much work was
done?
A 5-N force pushes upward on a box, and
the box moves 1-m to the right. How
much work was done?
Work
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There is NO WORK done by a force if it causes NO
DISPLACEMENT!
 Forces perpendicular to displacement can do no work. The
normal force and gravity do no work when an object is slid
on a flat floor, for instance.

Forces can do positive, negative, or zero work
Work
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A person pulls a rolling suitcase at an angle of 30° with
the horizontal, with a force of 200 N. How much work
does she do to pull it 160 m along a flat surface?
More Work Practice
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Jane uses a vine wrapped around a pulley to lift a 70-kg
Tarzan to a tree house 9.0 meters above the ground
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How much work does Jane do when she lifts Tarzan?
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How much work does gravity do when Jane lifts Tarzan?
Work & Energy
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Work transfers energy to an object or a system
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If a force does positive work on a system, the mechanical
energy of the system increases
If a force does negative work on a system, the energy of
the system decreases
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The two forms of mechanical energy are Potential Energy
and Kinetic Energy
Kinetic Energy
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Moving objects have Kinetic Energy.
K = ½ mv2
K is measured in Joules (J)
Constant Force and Work
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If force is
constant over the
distance
traveled:
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W = FΔr
can be used to
calculate the
work done by the
force when it
moves an object
some distance r
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For a Force vs. distance graph, the
area under the curve can be used
to calculate the work done by the
force
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This is true even if force is not
constant!
Work and graphs
The area under the curve
of a graph of force vs
displacement gives the
work done by the force in
performing the
displacement.
F(x)
xa
xb
x
The Work-Energy Theorem
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Wnet = DKE
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When net work due to all forces acting on an object is positive,
the kinetic energy of the object will increase (positive
acceleration).
When net work due to all forces is negative, the kinetic energy
of the object will decrease (deceleration).
When there is no net work due to all forces acting on an
object, the kinetic energy is unchanged (constant speed).
Kinetic Energy
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A 10.0 g bullet has a speed of 1.2 km/s.
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What is the kinetic energy of the bullet?
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What is the bullet’s kinetic energy if the speed is halved?
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What is the bullet’s kinetic energy if the speed is doubled?
Work & Energy
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A 0.25-kg ball falls for 5 seconds.
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What force does work on the ball?
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Find the work done on the ball after
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1.0 second, 3.0 seconds, and 5.0 seconds
Find the kinetic energy of the ball after
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1.0 second, 3.0 seconds, and 5.0 seconds
Work & Energy
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Where did the ball get the energy to
speed up?
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Potential Energy (PE or U) is energy
stored in an object from its position
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The ball had stored energy due to its
height
Potential energy
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Energy an object possesses by virtue of its position
or configuration.
Represented by the letter U.
Examples:
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Gravitational Potential Energy
Spring Potential Energy
Energy
Gravitational Potential Energy (PEg – measured in
Joules): energy stored in any object that has the ability to
fall
PEg = mgh
h is the height of the object
Find the gravitational potential energy of the falling ball if it
was originally 10.0 m above the ground.
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Energy
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Elastic Potential Energy: stored in objects that can stretch
or compress
It takes force to stretch or compress a spring: FP = kx,
where k is the spring constant, or resistance to stretching,
and x is the distance stretched/compressed
Remember Hooke’s Law! The force
of the spring is opposite the
direction of displacement
F = -kx
Springs
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A spring does NEGATIVE WORK on an object, since it
pushes or pulls opposite the direction of
stretch/compression
The force doing the stretching/compressing does positive
work, equal but opposite the work done by the spring
Springs: stretching
0
Fapp = kx
F(N)
200
m
100
m
x
F
00
1
2
3
4
-100
-200
Wapp = ½ kx2
5
x (m)
Springs:compressing
0
m
Fapp = kx
F(N)
200
100
m
0
x
-100
F
-200
-4
-3
-2
-1
Wapp = ½ kx2
0
x (m)
Spring Practice
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It takes 180 J of work to compress a certain spring 0.10 m
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What is the force constant of the spring?
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To compress the spring an additional 0.20 m, does it take 180 J,
more than 180 J, or less than 180 J? Verify your answer with a
calculation.
More Spring Practice/Review
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A physics student hangs various masses on a spring using
a 0.050 kg hanger. He determines the spring constant to
be 18.2 N/m. He then hangs a 0.400 kg mass on the
spring, and a few seconds later, the mass falls off and the
hanger is propelled upward by the restoring force of the
spring.
Find the energy stored in the spring when it is stretched.
When it is stretched, what force does it exert on the
mass and hanger?
When the hanger is launched upward, it has kinetic
energy. Where did that energy come from?
Energy Review
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Moving objects have kinetic energy
K = ½ mv2

Objects at some height have gravitational potential
energy
PEg = mgy

Compressed/Stretched objects have elastic potential
energy
Elastic PE = ½ kx2
Power
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Power is the rate at which work is done
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Remember: Work is a transfer of energy!
P = W/Δt
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W: work in Joules
Δt: elapsed time in seconds
P = F V
 (force )(velocity)
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The SI unit for Power is the Watt (W)
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1 Watt = 1 Joule/second
The British unit is horsepower (hp)
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1 hp = 746 W
Power
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The rate of which work is done.
When we run upstairs, t is small so P is big.
When we walk upstairs, t is large so P is small.
Power Practice Problem
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A record was set for stair climbing when a man ran up the
1600 steps of the Empire State Building in 10 minutes and
59 seconds. If the height gain of each step was 0.20 m,
and the man’s mass was 70.0 kg, what was his average
power output during the climb? Give your answer in
both watts and horsepower!
Work & Energy
Force Types
Force Types
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Forces acting on a system can be divided into two types
according to how they affect potential energy:
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Conservative forces can be related to potential energy changes
Non-conservative forces cannot be related to potential energy
changes
Conservative and Nonconservative Forces
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Forces like friction “use up” energy. It cannot be
recovered later as kinetic energy. It is converted to
other forms of energy (like heat)
Work done by a nonconservative force cannot be
recovered later as kinetic energy.
Nonconservative forces are “path dependent” - knowing
starting and ending points is not sufficient – you have to
know the total distance traveled
Conservative and
Nonconservative Forces
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Other forces CAN be recovered as kinetic
energy later, and are Conservative Forces.
Gravity is also a conservative force.
Gravitational potential energy is stored in
objects and can be released at a later
time.
Conservative forces are “path
independent”
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Work can be calculated from the starting
and ending points – the actual path can be
ignored
Law of Conservation of Energy
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In any isolated system, the total energy remains
constant
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Energy can neither be created nor destroyed, but can only
be transferred to other objects or transformed from one
type of energy to another
Law of Conservation of Mechanical Energy
Pendulums and Energy Conservation
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Energy goes back and forth between K and U
At the highest point, all energy is U
As it drops, U transforms into K
At the bottom, energy is all K
Pendulums:
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A 5.0-kg swinging pendulum
encounters a frictional force from
air resistance. The pendulum is
released from rest at a height of
0.50 m above its lowest point.
After making one complete swing
forward and back, the pendulum
only reaches a height of 0.49 m.
What amount of mechanical
energy was lost to air resistance?
Springs and Energy Conservation
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Energy is transformed
back and forth between K
and U
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When fully stretched, all
energy is U
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When passing through equilibrium, all energy is K
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At other points, energy is a mixture of U and K
Mechanical Energy
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Along an ideal rollercoaster (with no friction) the
mechanical energy of the car will always remain constant.
Realistically, frictional forces transform kinetic energy into
thermal energy.
Mechanical energy is not conserved, but friction does work
to transform KE into heat
Nonconservative Forces
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The work done by a nonconservative force is equal to the
change in mechanical energy:
WNC = ΔKE + Δ PE
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The work done by the frictional force is:
WNC = -Ffrd
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So,
Δ KE + Δ PE = -Ffrd
Energy Conservation in Oscillators
(general)
K+U
 K1
= constant
+ U1 = K2 + U2
 ΔK = -ΔU
Energy Conservation in Springs
 K1 + U1
= K2 + U2
1
2
 K = /2mv
1
2
 U = /2kx
x
Energy Conservation in Pendulums
 K1
+ U1 = K2 + U2
 K = 1/2mv2
 U = mgh
h