Physics 221 Chapter 7

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Physics 221Chapter 7
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Problem 1 . . . Work for slackers!

• WORK Force x Distance
• W F . D
• Units Nm J Newton meters Joules
• Problem 1 You push a car with a force of 200 N
  over a distance of 3 m. How much work did you
  do?

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Solution 1 . . . Work

• W F.d
• W 200x3
• W 600 J

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Problem 2 . . . Energy

• Energy is the capacity to do work
• Units Joules (J)
• Kinetic Energy Energy due to motion
• Problem 2 What is the kinetic energy of the car
  in Problem 1?

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Solution 2 . . . Kinetic Energy

• Kinetic Energy Work done (if no friction)
• K.E. 600 J
• Problem 3 Given that m 1000 kg, what is the
  speed of the car?

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Solution 3 . . . Speed and K.E.

• F ma
• 200 1000 a
• a 0.2 m/s2
• Vf 2 Vi 2 2ad
• Vf 2 0 2(0.2)(3)
• Vf 2 1.2
• Vf 1.1 m/s

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Kinetic Energy Formula

• K.E. 1/2 m v2
• Problem 4 The K.E. of a car is 600 J and its
  mass is 1000 kg. What is its speed?

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Solution 4 . . . more K.E.

• K.E. 1/2 m v2
• 600 1/2(1000)(v2)
• v 1.1 m/s
• Does this look familiar?
• Moral of the story We can find the speed either
  by using Newtons Laws or Energy Principles.

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Problem 5 . . . Lugging the Luggage

• What is the speed when the distance is 3 m?

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Solution 5 . . . Lugging the Luggage

• What is the speed when the distance is 3 m?
• F.d 1/2 m v2
• (40 cos 600)(3) (1/2)(10)(v2)
• v 3.5 m/s
• Moral of the story
• W (F)(d)(cos?)

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Scalar Product (Dot Product)

• A . B A B cos ?
• i . i 1
• i . j 0
• W F . d

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Problem 6 . . . work is a scalar !

• F 3 i 2 j acts on an object and causes a
  displacement of 7 i
• (a) How much work was done?
• (b) What is the angle between F and d?

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Solution 6 . . . work is a scalar !

• (a) W F.d
• W (3 i 2 j) . 7 i
• W 21 0
• W 21
• (b) F 5 and d 7 and F.d 21
• F.d F d cos ?
• 21 (5)(7) cos ?
• cos ? 3/5
• ? 53 0

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Stretching Springs
Hookes Law The amount of stretch is directly
proportional to the force applied. F k x
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Example 6.6 . . . Springy Spring
The spring constant (k) of a spring is 20 N/m.
If you hang a 50 g mass, how much will it stretch?
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Solution 6.6 . . . Springy Spring
F k x mg kx (50 /1000)(9.8) (20)(x) x 2.5
cm
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Problem 8 . . . Body building

• How much work would you have to do to stretch a
  stiff spring 30 cm (k 120 N/m)?

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Solution 8 . . . Body building

• W F . d
• W (kx)(x)
• W kx2
• W (120)(0.3)2
• W 10.8 J
• ?

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Correct Solution 8 . . . Body building

• F is a variable force so integration must be
  performed.
• W ?F . dx
• W ? kx . dx
• W 1/2 kx2
• W (1/2)(120)(0.3)2
• W 5 .4 J
• ?

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Problem 1 . . . Potential Energy

• You lift a 2 kg book and put it on a shelf 3
  meters high.
• A. How much work did you do?
• B. Was the work lost?

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Solution 1 . . . Hidden Energy (P.E.)

• A.
• W F.d
• W mgh
• W 2x10x3
• W 60 J
• B.
• Work is stored as Potential Energy (hidden).

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Problem 2 . . . In other words

• In other words, if the 2 kg book fell down from
  the top of the bookshelf (3m), what would its
  K.E. be?

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Solution 2 . . . In other words

• The K.E. would be equal to the P.E.
• K.E. 600 J.
• In other words, energy was converted
  (transformed) from one form (P.E.) to another
  (K.E.)

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Conservative Forces

• If the work done against a force does not depend
  on the path taken then that force is called a
  conservative force. Examples are gravity and
  spring force. The total mechanical energy (P.E.
  K.E.) will remain constant in this case.
• If the work done against a force depends on the
  path taken then that force is called a
  non-conservative force. Example is friction.
  The total mechanical energy (P.E. K.E.) will
  not remain constant in this case.
• Vote Democrat . . . Just kidding!