Transcript P221_2009_week6

Exam I
P221 Exam 1 Histogram
Average: 58.9 = 75.5%
8
7
Frequency
6
5
Frequency
4
3
2
1
0
36
39
42
45
48
51
54
57
60
Bin
63
66
69
72
75
78
More
Power
• We are often concerned with not only how
much energy it takes to do something (say
get a car up to a certain kinetic energy) but
also how quickly that energy can be
transferred.
• POWER : the rate at which energy is
transferred.
• P = dW/dt Pavg = W/Dt
•
The Rolls-Royce "Trent 800" series of jet engines have a thrust rating of up to
420 kNewtons. Two of these engines power some versions of the Boeing 777
aircraft. If such an aircraft is traveling at 240m/s (854 km/hr) with both of its
engines operating at full capacity, what is the power being generated by each
engine? What happens to all this energy? ( 16 correct; 12 incorrect (mainly
silly mistakes, units etc.); 29 no answ.)
• W=F*d =› W=854km/hr*420000N=358680000J. P=W/t =›
358680000J/1sec=358680000watts. Due to conservation of energy, all
this energy does not disappear.
• The aircraft expends 1.008 x 10^8 watts of energy.
Most of the energy is transformed into heat,
motion, sound and other forms of energy.
• Two questions:
– Does gravity do any work in this situation?
– What does the work done by drag do???
Variable Forces
• IF the force is not constant, we have to look at:
–
dW = Fx(x) dx (increment of work performed is the
product of the x Force component and the
incremental displacement)
• We have seen that springs provide forces whose
magnitude increases as the spring is
compressed or expanded more
• F = - k (x-xo) ; k is the spring constant
(what is the significance of the -?)
• W = -½ k (x-xo)2
• What is the property that a force must possess if
it is possible to define a potential energy
associated with that force? (6 said “conservative”
but only a few people explained what that means;
22 were off the mark 26 no answers)
• There were a large number of seemingly random suggestions. I
guess people have not yet looked at chapter 8 (my mistake).
Chapter 7 problems
• In class, I will use the expression U = 1/2k (x-x_o)^2 for
the potential energy of a spring. Comment briefly on the
difference between this and U = 1/2kx^2, which is the
form given in most texts. What is the significance of the
term xo? Which form would you find more useful? (24
“initial position” 7 “equilibrium position” 1 Other 23 no
reply)
• I don’t know if this reflects confusion, or just
careless wording of responses, but be careful.
Simlar symbols can, unfortunately, mean
different things in different contexts!!
Chapter 8: Potential Energy
•A conservative force is one for which the work done around ANY closed circuit
is ZERO
•A VERY important consequence of this is that:
•The work done by a conservative force in going from a to b depends ONLY
on the two points a and b, NOT on the path taken between them!!!
•Note: this allows us to define a CHANGE IN ENERGY associated with the
CHANGE IN POSITION (from a to b).
Chapter 8: Potential Energy
Check point 1 is the force acting here conservative?
Chapter 8: Potential Energy
Check point 1 is the force acting here conservative?
NO!!!
Chapter 8: Potential Energy
Check point 1 is the force acting here conservative?
NO!!!
But it could be conservative if the bottom path was -60 J rather than + 60J.
-
Chapter 7 examples
Chapter 8 Examples
g. How fast would the car be moving at point C?
Potential Energy Curves and
Conservative Forces
F(x) = - dU/dx
Chapter 8 Problems (cont.)
•
•
•
•
•
A parachutist is drifting downward at a constant speed of
roughly 1m/s after his chute has opened. If the combined
mass of the parachutist and his equipment is 85.0 kg, at
what rate is he losing gravitational potential energy?
Where is this lost potential energy going?
(833 W: 17, but 5 had units wrong; others 8 no answer
28)
He is losing gravitational energy at a rate 1666.67 J/s.
This lost potential energy is going into kinetic energy. (I
have no idea where this number came from? Think: the
PE is decreasing, but is the KE increasing??)
He is losing gravitational potential energy at a rate of 833.85 Newtons per second The potential energy is
converted into the kinetic energy of him falling. (watch
your units)
Energy of potential energy due to gravity: E=mgy=
85x9.8(1) 833 j/s The energy is being transferred by way
of the dissipative drag force to thermal energy which is
distributed throughout the environment. (very good)