Problem Set 1 - Solutions
Challenge Problems
CP1.
The Law of Cosines states that for any triangle with sides of length A, B, and C, the
angle subtended by sides A and B satises
C 2 = A2 + B 2 2AB cos .
Prove this law using vector methods (e.g. perhaps thi
Problem Set 1
Due Friday, January 15
Mastering Physics
See the web interface.
Challenge Problems (Due in class - bring paper copy)
CP1.
The Law of Cosines states that for any triangle with sides of length A, B, and C, the
angle subtended by sides A and B
Lecture 31 The Simple Pendulum
Consider a simple pendulum of length L which has a mass m at the end of the pendulum.
For this case, we assume that the mass of the chord is negligible compared to m. Assume
that the pendulums motion is in the X Y plane with
Physics 1a Problem Set #5 Solutions
Due November 7, 2012
of momentum tell us that
Please point out typos and other errors to river@physics.ucla.edu.
1
1
1
2
m1 u2 = m1 u2 + m2 v1
0
1
2
2
2
1. Consider a series of elastic 1-D collisions. Initially ball 1 o
SYLLABUS - 3/30/09
PHYSICS 1A, Physics for Scientists and Engineers: Mechanics, SPRING 2009
GOALS: In this course you will learn the basic concepts of Classical Mechanics, namely
the description (kinematics) and the causes of motion (dynamics), and conser
Physics 1A -Spring 2009
Practice 1st MIDTERM TEST - Thursday, April 16, 2009
This exam is closed book. One 3 inches 5 inches card with formulas (two sides) is allowed.
Write all units for all numerical results. For full credit on a claculation, always sho
Physics 1A - Discussion 1
Basic Kinematics
1. Rank the following graphs in order of decreasing average velocity. Each grid line on the vertical axis
represents one unit of position, and each grid line on the horizontal axis represents one unit of time.
Th
Problem Set 2 - Solutions
IMPORTANT NOTES.
This assignment is due at the beginning of class. Please turn in a paper copy
showing all of your work and answers.
Make sure to staple your homework before coming to class.
Make sure to box all final answers
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 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 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
1 2
1 2
yr = yi + vi t r gt r yr yi = gt r = h 0 = h
2
2
assume
Physics 1A - Discussion 2
Circular motion, relative motion, and identifying forces
1. Sieon (pronounced see-ohn) is whirling a ball on the end of a string in a nearly horizontal circle. He
is currently keeping the length of the string and speed of the bal
Physics 1A - Discussion 3
Forces, constraints, and Newtons Laws
Usain Bolt is running up a wedge whose slanted surface has length ` and makes an angle /4 radians
with the horizontal which we take to be the x-direction. Usain is running up the wedge in the
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
Physics 1A - Discussion 5
Energy Methods
Problem 1.
A block of mass m slides down a frictionless ramp that makes an angle relative to the horizontal. The
block starts a height h above the ground.
(a) Use energy methods to determine the speed of the block
Physics 1A - Fall 2016
Midterm Exam #1
READ THIS BEFORE YOU BEGIN
You are allowed to use only yourself and a writing instrument to the exam.
If you finish more than 5 minutes before the end of the exam period, then please raise
your hand and a proctor w
Physics 1A - Discussion 7
Energy, momentum, and their conservation
Sharona, a circus acrobat of mass M , leaps straight up with initial speed v from a
trampoline. As she rises up, Sharona quickly snatches a trained monkey, Omid (pronounced
Oh-meed) of mas
Physics 1A - Discussion 6
Work, energy, and conservation revisited
1
A box moving in a circle along a table
A small box of mass m tied to a string moves in a circle of radius R on the surface of a table.
At time t = 0, the tension in the string is twice t
Physics 1A - Discussion 4
Midterm Recap
Problem 1.
In the following system, all ropes are of constant length, and the circles are pulleys. The horizontal
surface at the top of the diagram is the ceiling of a room. Masses A and B start at rest at the posit
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 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 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 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
Review Chapter 11
Equilibrium and Elasticity
Monday, March 18, 2013
8:00 AM - 11:00 AM
KNSY PV 1200B
KNSY PV 1220B
KNSY PV 1240B
If you have not done so please fill out the online evaluations for your
course. You should have received MyUCLA notice for thi
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
Problem Set 1
Due Friday, September 30
IMPORTANT NOTES.
This assignment is due at the beginning of class. Please turn in a paper copy
showing all of your work and answers.
Make sure to staple your homework before coming to class.
Make sure to box all f
Problem Set 3
Due Friday, October 28
IMPORTANT NOTES.
This assignment is due at the beginning of class. Please turn in a paper copy
showing all of your work and answers.
Make sure to staple your homework before coming to class.
Make sure to box all fin
Physics 1A: Physics for Scientists and Engineers: Mechanics
Winter 2015
Discussion Week 2: Week 2
Exercise 1: (a) If the displacement of a particle as a function of time is given by x(t) = t3 t , where
and are constants, find the velocity and acceleratio
Physics 1A: Physics for Scientists and Engineers: Mechanics
Winter 2015
Discussion 3: Week 4
Exercise 1 A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be M .
Even though there is an upward lisft force on the ball