Physics 1A Spring 2015: Quiz 2
Version A
1
Closed book. No work needs to be shown for multiplechoice questions.
1. Two balls, identical except for color, are thrown horizontally from the roof of a tall building
at the same instant. The initial speed of t
Vector Functions and Curves
Applications
Question
What are the tangential and normal components of the Coriolis force on an
object moving with (horizontal) velocity v in the following situations
(a) At the north pole.
(b) At the south pole.
(c) At the equ
Vector Functions and Curves
Applications
Question
If an object moves with position vector r(t) satisfying
dr
= a (r(t) b)
dt
and with r(0) = r 0 .
a, b and r0 are constant vectors with a 6= 0.
Describe the path along which this object moves.
Answer
dr
d

Vector Functions and Curves
Applications
Question
If run at full power, a selfpropelled tank car can accelerate itself, when full
(mass = M kg) along a straight track at a m/sec2 .
At time t = 0 the tank is full. The contents leave the tank at a rate k k
Vector Functions and Curves
Applications
Question
Solve the initial value problem
dr
= kr
dt
r(0) = i + k
Describe the curve r = r(t).
Answer
dr
= kr
dt
r(0) = i + k
If r(t) = x(t)i + y(t)j + z(t)k
Then
x(0) = z(0) = 1
y(0) = 0
As k(dr/dt) = k(kr) = 0, ve
Vector Functions and Curves
Applications
Question
A satellite in a low (radius of orbit is approximately the radius of the Earth)
circular orbit passes over both poles. It takes the satellite two hours to make
one revolution.
If an observer stands on the
Vector Functions and Curves
One variable functions
Question
A particle is moving around a circle at constant speed. Given that the equation of the circle is x2 + y 2 = 25 and that the particle makes one revolution
every two seconds, find its acceleration
Vector Functions and Curves
One variable functions
Question
If the position and velocity of a particle satisfy r v > 0, what does this tell
you about the motion of the particle. What if r v < 0?
Answer
If r v > 0 then r is increasing.
So r is moving awa
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = t2 i t2 j + k
Answer
Position: r = t2 i t2 j + k
Velocity:
Spring 15 1A Help Times
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Physics 1A
Spring 2015: Course Policy
1
DEPARTMENT OF PHYSICS
Physics 1A
General Physics Mechanics
Spring 2015
Mar. 30, 2015
Web page: https:/ted.ucsd.edu/
Instructor:
Dr. Michael G. Anderson
[email protected]
Office: 2611 Mayer Hall Addition
Of
Homework #1: Math Skills Worksheet
This worksheet is designed to help you to practice the math skills you will need this quarter.
Quiz #1 on Friday, April 10th may have questions similar to these.
1.
On the diagram to the right, solve (to three significan
Physics 1A Quiz 2 Answers
Version A
Q1
D
Q2
A
Q3
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Q4
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Q5
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Q6
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Q7
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Q8
C
Q9
D
Q10
B
Q11
A
Version B Version C
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E
D
D
C
B
A
C
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B
A
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D
A
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Version D
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Physics 1A
Class Review!
"All good things must come to an end.
Proverb
Things We Have Learned
1) Pick an appropriate coordinate system:!
Sometimes a little thought in choosing a clever
coordinate system will save heartache with the
resulting mathematics.
Physics 1A
Lecture 1C
"Student talk is far more
important than teacher talk."
MacIsaac and Falconer
Learning Goals
From a given motion graph, be able to
determine the shape of the other motion
graphs.
From a given motion graph, be able to
interpret motio
Physics 1A
Lecture 1D
"You may hate gravity,
but gravity doesn't care."
Clayton Christensen
Quiz #1 Info
It will be a Scantron test covering
forces and motion (WS 1A through 1D).
A list of equations, constants, and
conversions will be provided.
You will
Physics 1A Lecture 1C PhET Simulation Practice
Visit the website:
http:/phet.colorado.edu/en/simulation/movingman
and run the applet (You will need to have Adobe Flash Player installed; if you cannot get
it to work, use the c
Physics 1A
Lecture 1B!
"Your education is ultimately the flavor left
over after the facts, formulas, and diagrams
have been forgotten."
Paul G. Hewitt
Learning Goals
Be able to graph given situations and ultimately
solve for motion values.!
Use force dia
Physics 1A
Lecture 1A!
"If one way be better than another, that you
may be sure is Nature's way.
Aristotle
Learning Goals
Work with the motion variables x, v, and a to
describe various types of motion.!
Draw force diagrams for various simple
situations.!
Physics 1A
Math Review Lecture
Mathematics is the door and the
key to the sciences.
 Roger Bacon
Standards/Units
Physicists study objects that range from
enormous (black holes) to microscopic (quarks).
In order to measure objects you need to have a
stand
Vector Functions and Curves
One variable functions
Question
A particle moves along the curve y = 3/x, travelling to the right. At the
point (2, 23 ) its speed is 10, what is its velocity?
Answer
When its xcoordinate is x, the object is at position
r = xi
Vector Functions and Curves
One variable functions
Question
An object travels on the curve of intersection of the cylinders y = x2 and
z = x2 with increasing x. When the particle is at (1, 1, 1), it has a speed of
9cm/s which is increasing at a rate of 3c
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = t2 j + tk
Answer
Position: r = t2 j + tk
Velocity: v =
2tj
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = a cos ti + a sin tj + ctk
Answer
Position: r = a cos ti + a
Vector Functions and Curves
One variable functions
Question
Show that r = r 0 cos(t) + (v 0 /) sin(t) satisfies the initialvalue problem.
d2 r
= 2 r
2
dt
r0 (0) = v 0
r(0) = r 0
In this case, describe the path r(t) and determine what happens to the paths
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = 3 cos ti + 4 sin tj + tk
Answer
Position: r = 3 cos ti + 4
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = t2 i + k
Answer
Position: r = t2 i + k
Velocity: v = 2ti
Sp
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = i + tj
Answer
Position: r = i + tj
Velocity: v = j
Speed: v
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = ti + t2 j + t2 k
Answer
Position: r = ti + t2 j + t2 k
Velo
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = i + tj + tk
Answer
Position: r = i + tj + tk
Velocity: v =
Vector Functions and Curves
One variable functions
Question
A particle travels along the curve of intersection of the plane x + y = 2 and
the cylinder z = x2 in the direction of increasing y. The particle has constant
speed v = 3, what is its velocity at
Vector Functions and Curves
One variable functions
Question
Find the velocity, speed and acceleration of the particle with position given
by r(t) at time t. Also determine the particles path.
r = aet i + bet j + cet k
Answer
Position: r = aet i + bet j +
Vector Functions and Curves
One variable functions
Question
Show that if the scalar product of the velocity and acceleration of an object
in motion is negative (or positive) then the speed of the object is decreasing
(or increasing).
Answer
d
d 2
v = v
Vector Functions and Curves
One variable functions
Question
It is given that the position and velocity vectors of a moving object satisfy
v(t) = 2r(t) for all times t. If r(0) = r 0 , find r(t) and a(t), the acceleration.
Also determine the path of motion