Physics 101: Lecture 13

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Physics 101 Lecture 13

• Chapter 6 Work and Energy

• Quick Review of Last Time, Example Problems
• Power, Work done by a variable force
• Reminders
• Exam I, Tuesday, September 30th at 5 PM
• See PHY101 Web page for room assignments
• Please do not forget to bring your UB ID card !

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Work done by a constant Force

• W F s F s cos ? Fs s
• F magnitude of force
• s s magnitude of displacement
• Fs magnitude of force in
• direction of displacement
• Fs F cos ?
• angle between displacement and force
• vectors
• Kinetic energy Ekin 1/2 m v2
• Work-Kinetic Energy Theorem

F
s
?Ekin Wnet
3
Work Done by Gravity

• Example 1 Drop ball

Wg (mg)(S)cos? S h0-hf Wg mg(h0-hf)
cos(00) mg(h0-hf) Epot,initial
Epot,final
S
S
mg
mg
y
y
x
x
4
Work Done by Gravity

• Example 2 Toss ball up

Wg (mg)(S)cos? S h0-hf Wg
mg(h0-hf)cos(1800) -mg(h0-hf)
Epot,initial Epot,final
S
mg
y
x
5
Work Done by Gravity

• Example 3 Slide block down incline

h0
Wg (mg)(S)cos? S h/cos? Wg
mg(h/cos?)cos? Wg mgh with h h0-hf
?
h
S
mg
hf

• Work done by gravity is independent of path
• taken between h0 and hf
• gt The gravitational force is a conservative
  force.

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Concept Question

• Imagine that you are comparing three different
  ways of having a ball move down through the same
  height. In which case does the ball reach the
  bottom with the highest speed?
• 1. Dropping2. Slide on ramp (no friction)3.
  Swinging down4. All the same

In all three experiments, the balls fall from the
same height and therefore the same amount of
their gravitational potential energy is converted
to kinetic energy. If their kinetic energies are
all the same, and their masses are the same, the
balls must all have the same speed at the end.
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Conservation of Mechanical Energy

• Total mechanical energy of an object remains
  constant
• provided the net work done by
  non-conservative forces
• is zero
• Etot Ekin Epot constant
• or
• Ekin,fEpot,f Ekin,0Epot,0
• Otherwise, in the presence of net work done by
• non-conservative forces (e.g. friction)
• Wnc Ekin,f Ekin,0 Epot,f-Epot,i

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Example Problem

• Suppose the initial kinetic and potential
  energies of a system are 75J and 250J
  respectively, and that the final kinetic and
  potential energies of the same system are 300J
  and -25J respectively. How much work was done on
  the system by non-conservative forces?
• 1. 0J 2. 50J 3. -50J 4. 225J 5.
  -225J

Work done by non-conservative forces equals the
difference between final and initial kinetic
energies plus the difference between the final
and initial gravitational potential energies. W
(300-75) ((-25) - 250) 225 - 275 -50J.
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Power

• Average power is the average rate at which a net
  force
• does work
• Pav Wnet / t
• SI unit P J/s watt (W)
• Or Pav Fnet s /t Fnet vav

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Work done by a Variable Force

• The magnitude of the force now depends on the
• displacement Fs(s)
• Then the work done by this force is equal to the
• area under the graph of Fs versus s, which can be
  
• approximated as follows
• W S DWi S Fs(si) Ds
  (Fs(s1)Fs(s2)) Ds