Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 24.
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Transcript of Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 24.
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Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova
Lecture 24
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Ex.6
This is a one dimensional problem. A particle of mass m is attracted to the origin with a force of magnitude
2x
kFx
If a particle starts at x=A, moving to the right with velocity V0, where will it turn around? Could there be no solution?
x=0 x=A xV0
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Quiz
A particle can only move along the x axis. Forces act on it so that its potential energy function is
42
21 4
1
2
1)( xkxkxU
where k1 and k2 are positive. The particle is started at x=a with zero velocity.
a)Where is the velocity a maximum? What is its magnitude?
b) Where else will the velocity be zero?c)What is the force on the particle as a function
of x?
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Second exam Tuesday, October 21
105 Heldenfels
Section 801 and half of 802 start at 7 pm
Section 803 and half of 802 start at 8:15 pm
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Work Energy Theorem
22
222
1
initialfinalr
r
total
mVmVrdFW
22
2222
11
22
11
initialfinalyx
yx
totaly
yx
yx
totalx
mVmVdyFdxF
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If a force can be written as the gradient (slope) of some scalar function, that force is conservative.
U(x) is called the potential energy function for the force F
If such a function exists, then the force is conservative
1D case:dx
dUFx
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)]()([ 12
2
1
2
1
xUxUdxdx
dU
FdxW
x
x
x
x
veconservati
veconservatiW does NOT depend on path!
1D case:dx
dUF
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conW does NOT depend on path!
)]()([ 12 xUxUW con
If Fx(x) is known, you can find the potential energy function as
CdxxFxU x )()(
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or
112221 ,0 UKUKW nc If
112221 UKUKW nc
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Kinematics:
dt
dVa
dt
dVa y
yx
x ;
dt
dyV
dt
dxV yx ;
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If is given, you can find anda
V
r
daVdtaV yyxx ;
dtVydtVx yx ;
ty
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Newton’s 2nd Law
amF
xx maF yy maF
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Work does not depend on the choice of coordinates! You can calculate work of each force in the most convenient system of coordinates.
Do not forget to work with components!
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Usually there are several ways to solve the problem. Indicate the law or the theorem you use!
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We will have a regular class on Wednesday!
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Help Session:When: tonight at 7:00 pm
Where:Room 207 James J. Cain Engineering/Physics Lab Building
Spence St.
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Have a great day!
Hw: Be prepared for the test
Good luck!