PHYSICS 1A
Physics for Scientists and Engineers: Mechanics
Winter 2013 Lecture 4
Instructor:
Dr. Mostafa El Alaoui
Office: 3854 Slichter Hall
E-mail: [email protected]
Discussion T.A.: Li, Yi
e-mail: [email protected]
Textbook : Young and Freedm
Chapter 7
Potential Energy and Energy
Conservation
Chp-07
1
Gravitational Potential energy for motion along curved path
To find the work done by the gravitational force during
an arbitrarydisplacement , we divide the path into small
segment s .
s = x + y
Chapter 7
Potential Energy and Energy
Conservation
Chp-07
1
2
Lec 17 Chap 7
3
7.3 Conservative and Non-conservative Forces
A conservative force allows conversion between kinetic and
potential energy. Gravity and the spring force are conservative.
The wo
Chapter 8
Momentum, Impulse,
and Collisions
Chp-08
1
Momentum, Impulse, and Collisions
Let us consider the following situation
and see if we can solve it with the
models we have developed so far:
A 60-kg archer stands at rest on
frictionless ice and fires
Chapter 8
Momentum, Impulse,
and Collisions
Chp-08
1
2
8.3 Collisions
The term collision represents an event during which two particles
come close to each other and interact by means of forces. The interaction
forces are assumed to be much greater than an
Chapter 8
Momentum, Impulse,
and Collisions
Chp-08
1
Example
Two particles with masses m and 3m are moving toward each other along
the x-axis with the same initial speeds vi. The particle with mass m is
traveling to the left, and particle 3m is traveling
Chapter 8
Momentum, Impulse,
and Collisions
Chp-08
1
The Center of Mass (system of many particles)
We can extend the concept of center of mass to a system of many
particles in three dimensions.
xCM =
M = mi
i
m x
i
i
M
i
yCM
;
yCM =
m y
i
i
M
i
; zCM =
m
Chapter 9
Rotation of Rigid
Bodies
Chapter 9
1
Introduction
A wind turbine, a CD, a ceiling fan, and a Ferris wheel all
involve rotating rigid objects. All points in a rigid body
rotate with the same angular velocity and same angular
acceleration.
Real-
Chapter 9
Rotation of Rigid
Bodies
Midterm-2:
Chapters: 5, 6, 7, and 8
Chapter 9
1
2
9.4 Rotational Kinetic Energy
A rotating rigid body consists of mass in motion so it has a kinetic energy.
For a rigid bodies, systems of particles in which particles com
Chapter 9
Rotation of Rigid
Bodies
For Midterm-2:
Chapters: 5, 6, 7, and 8
Chapter 9
1
2
9.35.
Identify and Set Up:
I = mi ri2
I
implies = I rim + Ispokes
Execute: I rim = = kg)(0.300 m)2 = kg m 2
MR 2 (1.40
0.126
Each spoke can be treated as a slender ro
Chapter 10
Dynamics of Rotational
Motion
In chapter 9, we have studied rotational motion analogs to
translational motion in the areas of kinematics and energy. Let us
now consider the analog to force by investigating the cause of
changes in rotational mot
Chapter 10
Dynamics of Rotational
Motion
In chapter 9, we have studied rotational motion analogs to
translational motion in the areas of kinematics and energy. Let us
now consider the analog to force by investigating the cause of
changes in rotational mot
Chapter 10
Dynamics of Rotational
Motion
Chapter 10
1
10.4 Work and Power in Rotational Motion
A rigid body rotates about an axis through O under the
action of an external force F applied at P.
The object rotates through an infinitesimal angle d about a
f
Chapter 10
Dynamics of Rotational
Motion
Chapter 10
1
We know use conservation of angular momentum
Li = L f
I i = 9.0kg.m 2
I f = 3.54kg.m 2
I ii = I f f
i = 0.75rad / s
f = 1.91rad / s
2
3
4
5
6
7
8
9
Example:
Two blocks (m1 = 10.0 kg, m2 = 3.00 kg) are
Chapter 11
Equilibrium and Elasticity
You have until 8:00 AM Saturday, March 16 to log into MyUCLA to complete
your evaluations for this course : PHYSICS 1A section 4.\
Chapter 11
1
Goals for Chapter 11
To study the conditions for equilibrium of a body
Chapter 6
Work and Kinetic Energy
Midterm-2 will be
Tuesday, February 26, 2013 4-4:50 p.m.
Room: WGYOUNG CS50
Chp-06
1
6.5 Power
The definition of work makes no reference to the passage of time. If you
lift a box weighing 100N through a vertical distance
Chapter 6
Work and Kinetic Energy
Midterm-2 will be
Tuesday, February 26, 2013 4-4:50 p.m.
Room: WGYOUNG CS50
Chp-06
1
Work Done by a Spring
Forces exerted by springs represent a prime example of forces varying with
position. If the block is moved, thereb
Chapter 1
Units, Physical Quantities,
and Vectors
Chp-01
1
Goals for Chapter 1
To learn three fundamental quantities of physics and
the units to measure them
To keep track of significant figures in calculations
To understand vectors and scalars and how
Chapter 1
Units, Physical Quantities,
and Vectors
Lecture 2
Chp-01
1
1.5
Coordinate Systems
Describing the position of an object, or the motion of an object
in space requires specifying its location. In general, a
coordinate system consists of 3 things:
1
Chapter 2
Motion Along a Straight Line
Chp-02
1
Motion Along A Straight Line (1-dimensional motion)
Classical Mechanics deals with the relation of:
Force
Matter
Motion
Kinematics is the aspect of mechanics that describes motion
while ignoring forces and m
Chapter 2
Motion Along a Straight Line
Chp-02
1
2.4 Motion with Constant Acceleration
For constant acceleration vx increases uniformally with time as time
varies from 0 to t.
Use eqt (2.4) and replace: v2 by vx, t2 by
t, t1 by to, and aav-x by ax
Use eqt
Chapter 2
Motion Along a Straight Line
Chp-02
1
Problem 2.9 from Serway & Jewett (Chap. 2, Problem 55, page 67)
2
Solution:
total time = rock time down + sound up so t=tr+ts
Equation for rock
12
12
yr = yi + vi t r gt r yr yi = gt r = h 0 = h
2
2
assume g
Chapter 3
Motion in Two or Three Dimensions
Chp-03
1
Projectile Motion cont.
Plugging eqts (3.15), (3.16), (3.18), and (3.19) into the above equations
and assume for simplicity that xo=yo=0 at t=0
x = v o cos o t
y = v sin t 1 gt 2
o
o
2
(3.20)
(3.21)
Ve
Chapter 3
Motion in Two or Three Dimensions
Chp-03
1
v1
v2
3.4 Uniform Circular Motion in the Horizontal Plane
ac
r2
r1
Although the particle moves with
constant speed, v1 = v2 , it still
has an acceleration, called the
centripetal acceleration ac
Uniform
Chapter 4
Newtons Laws of Motion
Chp-04
1
Chapter 4 Newtons Laws of Motion
Introduction:
Up until now our study of mechanics has been limited to the
mathematical description of motion. We now introduce the
concepts of force and mass.
Mechanics is the bran
Chapter 4
Newtons Laws of Motion
Chp-04
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Problem 4.11 from University Physics, p. 129
Use Newtons second law in component form (Eq. 4.8) to calculate the acceleration produced by
the force. Use constant acceleration equations to calculate the effect of t
Chapter 5
Applying Newtons Law
In this chapter we will first extend the applications of Newtons law to
other situations and then we will introduce frictional forces and examine
how they in conjunction with the constant forces already examined
affect moti
Chapter 5
Applying Newtons Law
In this chapter we will first extend the applications of Newtons law to
other situations and then we will introduce frictional forces and examine
how they in conjunction with the constant forces already examined
affect moti
Review for Midterm 1 Physics 1A
Winter 2013 Mostafa El Alaoui
Covers Chapters 1 through 5 in Principles of Physics Young and
Freedman: University Physics, Volume 1
Chapter 1 Units
Use SI system of units, also known as the MKS system:
Length [L] meters (m)
Chapter 5
Applying Newtons Law
Chp-05
1
Example 5.2 (from Serway and Jewett)
a) How is the coefficient of static friction related to the
critical angle c at which the block begins to move?
b) How could we find the coefficient of kinetic friction?
A block