Physics 218 Lecture 10

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Physics 218Lecture 10

• Dr. David Toback

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Overview Chapters 6 7

• Combine Chapter 6 7 into four lectures
• Today well cover Work
• Intuitive understanding
• The math and multiple ways to calculate work
• Next time
• How much energy does it take to accomplish a task?

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Why are we learning this stuff?

• This is Fundamental to Engineering
• How much work can a machine do? (today)
• How much energy does it take to accomplish a
  task? (next time)

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Work

• The word Work means something specific in
  Physics (Kinda like Force)
• The amount of Work we do is the amount of Forcing
  we do over some distance
• Example If we are accelerating a car for 1 mile,
  then there is a force and a distance ? We do Work

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Calculating the work

• Work is done only if the force (or some component
  of it) is in the same (or opposite) direction as
  the displacement
• Work is the force done Parallel to the
  displacement

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Work for Constant Forces

• The Math Work can be complicated. Start with a
  simple case.
• For constant forces, the work is
• (more on this later)

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1 Dimension Example

• Pull a box with a constant force of 30N for 50m
  where the force and the displacement are in the
  same direction
• How much work is done on the box?
• ?W F.d 30N . 50m 1500 N . m
• 1500
  Joules

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• What if the Force and the Displacement arent in
  the same direction?

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2 Dim Force Parallel to Displacement

• W Fd F.d Fdcosq where q is the angle
  between the net Force and the net displacement.
  You can think of this as the force component in
  the direction of the displacement.

Force
Force
Rotate
Displacement
F Fcosq
Displacement
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Work done and Work experienced

• Something subtle The amount of work YOU do on a
  body may not be the same as the work done ON a
  body
• Only the NET force on the object is used in the
  total work calculation
• Add up all the work done on an object to find the
  total work done!

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Examples

• Holding a bag of groceries in place
• Is it heavy?
• Will you get tired holding it?
• Are you doing Work?
• Moving a bag of groceries with constant speed
  across a room
• Is it heavy?
• Will you get tired doing it?
• Are you doing Work?
• Lifting a bag of groceries a height h with
  constant speed?
• Work by you?
• Work on the bag?

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Groceries With the math

• Holding a bag of groceries
• WF.d Fdcosq (0)(0)cosq 0
• Moving a bag of groceries with constant speed
  across a room
• Force exerted by you mg, Net Force on bag 0
• Work on bag F.d Fdcosq 0dcosq 0
• Work exerted by you Fdcosq mgdcos(900)0
• Lifting a bag of groceries a height h with
  constant speed?
• Work on bag Fdcosq (0)h(00) 0
• Work by you Fdcosq (mg)hcos(00)mgh

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Work in Two Dimensions

• You pull a crate of mass M a distance X along a
  horizontal floor with a constant force. Your pull
  has magnitude FP, and acts at an angle of Q. The
  floor is rough and has coefficient of friction m.
  Determine
• The work done by each force
• The net work on the crate

Q
X
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• What if the Force is changing direction?
• What if the Force is changing magnitude?

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What if the force or direction isnt constant?

• I exert a force over a distance for awhile, then
  exert a different force over a different distance
  (or direction) for awhile. Do this a number of
  times. How much work did I do?

Need to add up all the little pieces of work!
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Find the work Calculus
To find the total work, we must sum up all the
little pieces of work (i.e., F.d). If the force
is continually changing, then we have to take
smaller and smaller lengths to add. In the limit,
this sum becomes an integral.
Fancy sum notation?Integral
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Use an Integral for a Constant Force
Assume a constant Force, F, doing work in the
same direction, starting at x0 and continuing
for a distance d. What is the work?
Region of integration WFd
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Non-Constant Force Springs

• Springs are a good example of the types of
  problems we come back to over and over again!
• Hookes Law
• Force is NOT CONSTANT over a distance

Some constant
Displacement
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Work done to stretch a Spring

• How much work do you do to stretch a spring, at
  constant velocity, from x0 to xD?

D
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This Week

• Next Lecture More on Work and Energy
• Finish the reading for Chapter 7
• Recitation on Chapter 5, with HW5 due Monday
• Get caught up on your homework

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• End of Lecture Notes

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Examples

• While you are lifting up a bottle with mass m,
  the bottle moves a distance d with constant
  velocity. As you lift it
• What is the force you exert?
• What is the work done by you?
• What is the work done by gravity?
• What is the net work?
• You push a box with Force F on a rough floor with
  coefficient of friction m for a distance d, and
  the box moves with constant velocity. As it
  moves
• What is the work done by you?
• What is the work done by friction?
• What is the net work?

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Exam 1 Results

• Overall
• Mean50/75 (after bonus) or 66
• This was a hard exam Well probably curve it.
• Preliminary curve will change
• gt85 gt A
• gt75 gtB
• Between 40 and 52 out of 75 gt C
• lt40/75 in the D or F range
• Remember Exam 1 only worth 75 points

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Does the Earth do work on the Moon?
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Simple Case

• Start with our spherical cow
• Constant Forces in a single direction
• Work is the force done Parallel to the
  displacement
• Work is done only if the force (or some component
  of it) is in the same (or opposite) direction as
  the displacement

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Hiker

• A hiker carries a backpack of mass M with
  constant speed up a hill of angle Q and height h.
• Determine
• The work done by the hiker
• The work done by gravity
• The work on the backpack

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Simple Example with Unit Vectors
A woman pulls a box of mass M with Force FP in
the Q direction for a distance d. Ignore
friction Find the work using unit vectors