PHYSICS 231 INTRODUCTORY PHYSICS I

1
PHYSICS 231INTRODUCTORY PHYSICS I

• Lecture 3

2
Announcement

• HW 2 due Wednesday Jan 23
  _at_ 359 am
• (MLK Jr. Day on Jan 21)
• Note related reading for each lecture listed on
  Calendar page at PHY 231 website

3
Main points of last lecture

• Acceleration defined
• Equations with constant
• Acceleration
• (?x, v0, vf, a, t)
• Acceleration of freefall

4
Example 2.9a
B
A man throws a brick upward from the top of a
building. (Assume the coordinate system is
defined with positive defined as upward) At
what point is the acceleration zero?
A
C
C
A

• A
• B
• C
• D
• None of the above

D
D
E
5
Example 2.9b
B
A man throws a brick upward from the top of a
building. (Assume the coordinate system is
defined with positive defined as upward) At
what point is the velocity zero?
A
C
C
A

• A
• B
• C
• D
• None of the above

D
D
E
6
CHAPTER 3
Two-Dimensional Motion and Vectors
7
Scalars and Vectors

• Scalars Magnitude only
• Examples time, distance, speed,
• Vectors Magnitude and Direction
• Examples displacement, velocity,
  acceleration,

8
Vectors in 2 Dimensions
Vector distinguished by arrow overhead A
Representations
(x, y)
(r, q)
Cartesian Polar
9
Vector Addition/Subtraction

• 2nd vector begins at end of first vector
• Order doesnt matter

Vector addition

• A B can be interpreted as A(-B)
• Order does matter

10
Vector Components

• Cartesian components are projections along the x-
  and y-axes

11
Example 3.1a
The magnitude of (A-B) is
a) lt0 b) 0 c) gt0
12
Example 3.1b
The x-component of (A-B) is
a) lt0 b) 0 c) gt0
13
Example 3.1c
The y-component of (A-B) gt 0
a) lt0 b) 0 c) gt0
14
Example 3.2
Some hikers walk due east from the trail head for
5 miles. Then the trail turns sharply to the
southwest, and they continue for 2 more miles
until they reach a waterfalls. What is the
magnitude and direction of the displacement from
the start of the trail to the waterfalls?
5 mi
2 mi
3.85 miles, at -21.5 degrees
15
2-dim Motion Velocity
v Dr / Dt It is a vector(rate of change of
position)
Graphically,
16
Multiplying/Dividing Vectors by Scalars

• Example v Dr / Dt
• Vector multiplied by scalar is a vector B 2A
• Magnitude changes proportionately B 2A
• Direction is unchanged ?B ?A

B
A
17
2-d Motion with constant acceleration

• X- and Y-motion are independent
• Two separate 1-d problems
• ?x, vx, ax
• ?y, vy, ay
• Connected by time t
• Important special case Projectile motion
• ax0
• ay-g

18
Projectile Motion

• X-direction (ax0)
• Y-direction (ay-g)

• Note we ignore
• air resistance
• rotation of earth

19
Projectile Motion
Acceleration is constant
20
Pop and Drop Demo
The Ballistic Cart Demo
21
Finding Trajectory, y(x)
1. Write down x(t)
2. Write down y(t)
3. Invert x(t) to find t(x)
4. Insert t(x) into y(t) to get y(x)
Trajectory is parabolic
22
Example 3.3
v0
An airplane drops food to two starving hunters.
The plane is flying at an altitude of 100 m and
with a velocity of 40.0 m/s. How far ahead of
the hunters should the plane release the food?
h
X
181 m
23
Example 3.4a
The Y-component of v at A is
a) lt0 b) 0 c) gt0
24
Example 3.4b
The Y-component of v at B is
a) lt0 b) 0 c) gt0
25
Example 3.4c
The Y-component of v at C is
a) lt0 b) 0 c) gt0
26
Example 3.4d
The speed is greatest at
a) A b) B c) C d) Equal at all points
27
Example 3.4e
The X-component of v is greatest at
a) A b) B c) C d) Equal at all points
28
Example 3.4f
The magnitude of the acceleration is greatest at
a) A b) B c) C d) Equal at all points
29
Range Formula

• Good for when yf yi

30
Range Formula

• Maximum for q45?

31
Example 3.5a
A softball leaves a bat with an initial velocity
of 31.33 m/s. What is the maximum distance one
could expect the ball to travel?
100 m
32
Example 3.6
A cannon hurls a projectile which hits a target
located on a cliff D500 m away in the horizontal
direction. The cannon is pointed 50 degrees above
the horizontal and the muzzle velocity is 75 m/s.
Find the height h of the cliff?
68 m