Physics 121

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Physics 121
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6. Work and Energy
6.1 Work 6.3 Kinetic Energy 6.4 Potential
Energy 6.5 Conservative and Non-conservative
forces 6.6 Mechanical Energy / Problem
Solving 6.8 Conservation of Energy 6.9
Dissipative Forces / Problem Solving 6.10 Power
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Work
Work Force x Distance W F . d
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Example 6.1 . . . Work for Slackers!
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 6.1 . . . Work for Slackers!
W F.d W 200x3 W 600 Nm W 600 J
Note A Joule (J) is just another term for newton
. meter (N m)
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Energy
Energy is the capacity to do work
Kinetic Energy (motion)
Potential Energy (position)
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Kinetic Energy
K.E. 1/2 mv2
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Example 6.2 . . . Kinetic Energy
The K.E. of a car is 600 J and its mass is 1000
kg. What is its speed?
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Solution 6.2 . . . Kinetic Energy
K.E. 1/2 m v2 600 1/2(1000)(v2) v 1.1 m/s
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Example 6.3 . . . Save your work!
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 6.3 . . . Save your work!
(a) W F.d W mgh W 2x10x3 W 60
J (b) Work was stored as Potential Energy
(hidden). So gravitational P.E. mgh
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Example 6.4 . . . Downhill
A 65 kg bobsled slides down a smooth (no
friction) snow-laden hill. What is its speed at
the bottom?
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Solution 6.4 . . . Downhill
P.E. K.E. mgh 1/2 mv2 9,555 (1/2)(65) v2 v
17.1 m/s
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Example 6.5 . . . Sticky bobsled
Suppose the speed of the bobsled was actually
measured to be 14.8 m/s instead of 17.1 m/s (a)
What could have caused that? (b) What was the
work done by the bobsled against friction?
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Solution 6.5 . . . Sticky bobsled
(a) Not all the P.E. was converted to K.E.
because some work was lost (heat energy) in doing
work against friction P.E. K.E. Wf (b)
mgh 1/2 mv2 Wf 9,555 1/2(65) (14.8)2
Wf Wf 2,436 J
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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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Example 6.7 . . . 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 6.7 . . . Body building
W F . d W (kx)(x) W kx2 W (120)(0.3)2 W
10.8 J X ?
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Correct Solution 6.7 . . . Body building
W F . d We must use the AVERAGE Force! W
(1/2)(kx)(x) W 1/2 kx2 W (1/2)(120)(0.3)2 W
5 .4 J ? ? P.E. of a Spring 1/2 kx2
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Example 6.8 . . . Lugging the Luggage

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

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Solution 6.8 . . . 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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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!
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Example 6.9 . . . Playing with Power
Power is the rate of doing work P W / t A
pump can lift at most 5 kg of water to a height
of 4 m every minute. What is the power rating of
this pump?
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Solution 6.9 . . . Playing with Power
W mgh W (5)(10)(4) W 200 J P W / t P
200 J / 60 s P 3.3 J / s P 3.3 W
Note Watt (W) is just another term for Joules /
second (J / s)
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Thats all folks!