Work and Power

1
Work and Power

• More relationships between forces, time and motion

2
What is work?

• Work is defined as a force acting on an object to
  cause a displacement in the direction of the
  force

3
Be careful!

• The force you use is not the net force! It is the
  particular force you are considering.
• The displacement is only the displacement while
  the force is acting.
• For instance, you hit a hockey puck with your
  stick and it slides 20 m. The displacement is
  only the distance you moved the puck while it was
  in contact with the stick!

4
Work vs. Impulse

• Compare this to impulse which is a force acting
  on an object for a time to cause a change in
  momentum
• Note that work has absolutely nothing to do with
  the time it takes to do it!!

5
Which of these is work?

• A weightlifter lifts a 100 Kg barbell 2 meters
  straight up
• A baby pushes a wagon 10 feet along the floor
• A weightlifter holds a bar bell still above his
  head
• A waiter carries a tray full of food while
  walking horizontally

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Simple CaseParallel Force and Displacement
When force and displacement are in the same
direction
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Parallel Force and Displacement

• Examples
• Pushing something along a floor
• Lifting something straight up
• Pushing something up a hill or ramp while
  measuring the displacement along the hill

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Simple CasePerpendicular Force and Displacement
When force and displacement are perpendicular
there is no component of the force along the
displacement
Example The waiter carrying a tray while
walking horizontally
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The General Case
The dot symbolizes a type of vector
multiplication called the dot product. It says
multiply the magnitude of one vector by the
component of the other vector that is in the same
direction.
Component of force in direction of displacement
F cos ?
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An example
I pull up and to the right on the leash to pull
Darkest to the right Only the horizontal
component of the force contributes to the work!
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Another Simple CaseAnti-Parallel Force and
Displacement
When force and displacement are in opposite
directions
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Which of these is work?

• Mr. Gangluff lifts his baby straight up from his
  crib
• A baby pulls a wagon 10 feet along the floor with
  the handle at a 45 angle
• A man pushes against a wall without moving it
• Mr. Gangluff walks down the hall holding his baby
  above his head.

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Calculating Work

• Work is a scalar
• Units of work are force X distance or Nm
• New unit 1 Nm1 Joule

5 N
A 5 N force is used to push a box 10 m
horizontally at a constant speed. How much work
was done? 5 N 10 m cos(0) 50 Nm 50 J
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Calculating Work
5 N
30
A 5 N force is applied to a handle at 30 to pull
a box 10 m horizontally at a constant speed. How
much work was done? 5 N 10 m cos(30) 50
.87 Nm 43.5 J
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Calculating Work
5 N
A 5 N force is used to pull a box 10 m
horizontally at constant speed. How much work
was done by the applied force? 5 N 10 m
cos(0) 50 Nm 50 J How much work was done by
the frictional force? 5 N 10 m cos(180) -50
Nm -50 J
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Time for practice!

• Try the problems on your worksheet.
• Some useful information
• cos (0) 1
• cos (90) 0
• cos(180) -1
• Be sure your calculator is set up in degrees!
• To check, try entering 90 then cos. Answer should
  be zero. If not, switch mode.

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What is Power?

• Power is the rate at which work is done
• Power is a scalar
• Units of power are J/s Watts
• Another unit of power is horsepower
• 745 Watts 1 hp

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Understanding the Power Equation

• If I do the same amount of work in less time,
  power increases
• If I do more work in the same amount of time,
  power increases
• More power means you can do more work in the same
  amount of time!

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Calculating Power

• I do 1000 J of work dragging Darkest on his walk
  in 100 s. What is my power?

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Thinking About Power a Different Way
Displacement /time velocity

• Power can also be thought of as the dot product
  of force and velocity

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Calculating Your Personal Power

• Run up a flight of stairs at a constant velocity
• The force you exert is your body weight in N
• Weigh yourself and convert using 1 lb 2.2 N
• Measure your upwards velocity
• Count the steps
• Measure the steps in m
• Time yourself
• V steps X height of step/time
• Power Weight X Velocity
• Are you more powerful than a 100 W light bulb?