Work and Energy

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Work and Energy
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What is work?
Suppose you are moving a desk. What would cause
the amount of work you do to increase Is the work
done the same if the desk is being moved in the
opposite direction?
Work is a scalar quantity that depends on the
amount of force applied and the displacement of
the object
Work W Force x displacement
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W Force x displacement
Suppose you are holding a 10 lb weight at waist
level. Your friend picks up another 10 lb weight
from the floor. Who has done more work?
If the object does not move, no work is been done.
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W Force x displacement
The hockey goals are being moved to resurface the
ice. One goal is pushed with a force of 14.5 N
at an angle of 19o above the horizontal. The
other goal is pushed with the same force directed
along the horizontal. Both goals are moved 5
meters. Is the amount of work the same for each
goal or different?
W Fd cosq
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W Fd cosq
The hockey goals are being moved to resurface the
ice. One goal is pushed with a force of 14.5 N
at an angle of 19o above the horizontal. The
other goal is pushed with the same force directed
along the horizontal. Both goals are moved 5
meters. Calculate the work done on each.
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W Fd cosq
19o
Note that when the force applied is in the same
direction as the displacement, cosq cos(0)1
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What are the units for work?
W Fd cosq
W Newtons x meters Joule
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Suppose you lift the bucket of sand (mass 4.5
kg) in our room and carry it across the room.
Assume you lift it at constant velocity. How much
work do you do when you lift it? When you carry
it 7 meters across the room?
To do work, there must be a force and a
displacement. Only forces in the direction of
displacement do work. Any forces perpendicular
to the displacement do no work, since there is no
displacement in that direction.
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Example
A weightlifter is bench-pressing a barbell whose
weight is 710 N. He raises the barbell a
distance of 0.65m above his chest and lowers it
the same distance. The weight is raised and
lowered at constant velocity. Determine the work
done on the barbell by the weightlifter (a)
during the lifting phase and (b) during the
lowering segment.
Note that work is negative when the force
component points in the opposite
direction of the displacement.
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Example
If a man lifts a 20.0 kg bucket from a well and
does 6.00 kJ of work, how deep is the well?
Assume the speed of the bucket remains constant
as it is lifted.
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Mechanical Energy

• Mechanical energy is the energy which is
  possessed by an object due to
• its motion (kinetic energy)
• its stored energy of position (potential energy)
• Objects have mechanical energy if
• they are in motion, and/or
• if they are at some position relative to a zero
  potential energy position

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Mechanical Energy

• In Physics, work is defined as a force acting
  upon an object to cause a displacement. In order
  for a force to qualify as having done work on an
  object, there must be a displacement and the
  force must cause the displacement.
• Any object which possesses mechanical energy -
  whether it be in the form of potential energy or
  kinetic energy - is able to do work.
• An objects mechanical energy enables that object
  to apply a force to another object in order to
  cause it to be displaced.

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Work-Energy Theorem
When work is done on an object, its energy
changes. We can combine 3 concepts that we
already know to define the relationship between
work and energy.
SF ma
W (Fcosq)d
vf2 vi2 2ad
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Work-Energy Theorem
Assume a constant net, external force acts on an
airplane of mass, m. The force is acting in the
same direction as the displacement.
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Newtons second law tells us SF ma Multiply
both sides of the equation by d SFd mad
If we solve vf2 vo2 2ad for ad and substitute
into the above equation, we can get an equation
relating work to velocity.
Work done by external force
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SFd mad
SFd m (vf2 - vo2)
Simplifying --
W mvf2 mvo2
These terms are the initial and final kinetic
energy terms.
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Kinetic Energy
Kinetic Energy is the energy resulting from the
motion of an object and it is described with the
following equation
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Example
What is the mass of a lacrosse ball that has 110
joules of energy when it is going 22 m/s
Recall that
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Example
A 750-kg compact car moving at 100 km/hr has
approximately 290 000 Joules of kinetic energy.
What is the kinetic energy of the same car if it
is moving at 50 km/hr?
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Work-Energy Theorem
W mvf2 mvi2
W KEf KEi

• A moving object has kinetic energy because work
  was done to accelerate the object from vi to vf
• The unit for kinetic energy is the same as that
  for work, joules.

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Example
A 1400 kg car is being towed. The net forward
force is 4500 N. The car starts from rest and
travels down a horizontal highway. Find the speed
of the car after it has gone 100.0 m. Ignore the
effects of wind resistance and friction.
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Example
Your arm does work on a 6.8 kg bowling ball
increasing its kinetic energy. Assume that you
apply a force over a distance of 1.1 m and
increase the velocity from 0 to 8.5 m/s at the
point of release. What is the magnitude of the
applied force?
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Example
In screeching to a halt, a car leaves skid marks
that are 65m long. The coefficient of kinetic
friction between the tires and the road is mk
0.71. How fast was the car going before the
driver slammed on the brakes?
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Example
A 55 kg skier is coasting down a 25o slope as
shown. A kinetic friction force of magnitude fk
70 N opposes his motion. Near the top of the
slope the skiers speed is vi 3.6 m/s.
Ignoring air resistance, determine the speed vf
at a point that is displaced 57 m downhill.
Draw the free body diagram!
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Kinetic Energy

• If the work done by the force is positive, the
  kinetic energy ____________.
• If the work done by the force is negative, the
  kinetic energy ____________. This occurs when
  the force is in the __________ direction as the
  displacement.
• If the work is zero, the kinetic energy
  _________________.

increases
decreases
opposite
remains the same
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Power
Which engine is more powerful? An 8-cylinder or
a 4-cylinder? Why?
Both engines can accelerate a car, but the 8
cylinder engine can do it faster.
Power is the rate at which work is done.
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Power
Work Time
P
Since Work Change in energy
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Power
Since Work F d
What is d/t ?
Note that this is the average speed!
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Power
A 1100 kg car starting from rest, accelerates for
5 seconds. The magnitude of the acceleration is
4.6 m/s2. Determine the average power generated
by the net force that accelerates the vehicle.