University of Waterloo
Department of Physics and Astronomy
ECE 105 - OKTOBERTEST - FALL 2010
TUESDAY, October 20 2010, 2:30-4:30pm
Aids Permitted: Calculator and attached ECE105 Formula Sheet.
Name: (Print)
Signature:
Student ID:
Division:
Professor:
IMPO
1
CHAPTER 6
MOTION IN A RESISTING MEDIUM
6.1 Introduction
In studying the motion of a body in a resisting medium, we assume that the resistive force on a
body, and hence its deceleration, is some function of its speed. Such resistive forces are not
genera
1
CHAPTER 9
CONSERVATIVE FORCES
9.1 Introduction.
In Chapter 7 we dealt with forces on a particle that depend on the speed of the particle. In
Chapter 8 we dealt with forces that depend on the time. In this chapter, we deal with forces that
depend only on
5
1.3 Plane areas.
Plane areas in which the equation is given in x-y coordinates
FIGURE I.3
We have a curve y = y(x) (figure I.3) and we wish to find the position of the centroid of the
area under the curve between x = a and x = b. We consider an elementa
Formula Sheet, ECE105
1
Mathematics
Rotational motion:
Energy:
2
quadratic equation, ax + bx + c = 0 :
b b2 4ac
x=
2a
cosine law:
c2 = a2 + b2 2ab cos
vectors:
vr
at
=
=
=
=
=
ar
=
s/r
d/dt
r
d/dt
r
v2
r
Ug
= mgy
Us
= 12 k (s)2
K
=
Kr
=
Power:
(gravitati
10
x2
2 x 1 + 2
a x2
1/ 2
a
0
a
dx = 2a 0
(a
xdx
2
x2
)
1/ 2
.
From this point the student is left to his or her own devices to derive x = 2a / = 0.6366a.
Plane curves in which the equation is given in polar coordinates.
FIGURE I.8
Figure I.8 shows how
6
For y we notice that the distance of the centroid of the slice from the x axis is
therefore the first moment of the area about the x axis is 21 y.yx.
1
2
b 2
y dx
a
y =
Therefore
y, and
1.3.3
2A
Example. Consider a semicircular lamina, x 2 + y 2 = a 2 ,
7
The area of the elemental slice this time is yx (not 2yx), and the integration limits are from a
to +a. To find y , use equation 1.3.3, and you should get y = 0.4244a.
Plane areas in which the equation is given in polar coordinates.
FIGURE I.6
We consid
8
Therefore
x =
2 r 3 cos d
y =
2 r 3 sin d
3 r 2 d
.
1.3.5
.
1.3.6
Similarly
3 r 2 d
Example: Consider the semicircle r = a, = /2 to +/2.
+ / 2
2a / 2 cos d
2a + / 2
4a
x =
=
cos d =
.
+ / 2
/ 2
3
3
3
d
/ 2
1.3.7
The reader should now try to find the
4
FIGURE I.1
Thus the points C1 and C2 are identical, and the same would be true for the third median, so
Theorem I is proved.
Now consider an elemental slice as in figure I.2. The centre of mass of the slice is at its midpoint. The same is true of any si
ECE-105 Mechanics
Dr. G. Scholz
University of Waterloo, Fall 2016
Official Course Textbook :
"PHYSICS for Scientists and Engineers. (Technology Update)"
Authors: Serway and Jewett, 9th edition
.
Tutorials:
Contacting me
Dr. G. Scholz
Office: Rm. Phy 358
O
KINEMATICS: Motion in 1, 2 and 3D
- Kinematics is concerned with Describing an Object's motion
- Kinematics is Not concerned with the Cause of that motion
One-Dimensional (1D) Kinematics
One dimensional Kinematics refers (conceptually and
mathematically)
University of Waterloo
Department of Physics and Astronomy
ECE 105 - Final Exam - FALL 2010
THURSDAY, December 9 2010, 19:30-22:00
Aids Permitted: Calculator and attached ECE105 Formula Sheet.
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Professor:
IMPO
University of Waterloo
Department of Physics and Astronomy
ECE 105 - Final Exam - FALL 2009
WEDNESDAY, December 16 2009, 9:00-11:30am
Aids Permitted: Calculator and attached ECE105 Formula Sheet.
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I