Transcript Weeks 1-4 Review

Physics 111: Week 1–4
Review
Bin Chen
NJIT Physics Department
Announcements
 Common
Exam #1 on Oct 10 (Next
Monday) from 4:15 pm to 5:45 pm
 KUPFRIAN HALL 108
 Must bring your NJIT ID
 Cell phone and electronic devices need to
be turned off
 Calculators allowed (but no sharing)
 More info this link
Announcements
 Physics
Department will offer the following
review sessions (very helpful!)
 Friday, October 7


11:30am – 1:00pm, TLH 1, Prof. Thomas
Saturday, October 8

10:00am – Noon; 1:00pm – 3:00pm, TLH1,
with Aldona Puchalski
Announcements
 General
tutoring schedule updated:
http://physics.njit.edu/students/
 (New!) Exam day tutoring available for
Phys111 on Monday, October
10th from 10:00am – 4:00pm in TIER 401B
and FMH 309.
Common Exam #1 Information
All are multiple choice questions (most, if not all,
only have one choice).
 20 questions in total. Difficulty varies.
 Budget your time (~4 min each). If you get
stuck on one question, move on.
 We will use Scantron Card. Bring your pencils.
 Physical constants and key equations are
provided (e.g., 1-D kinetic equations).
 Derived equations are NOT provided (e.g., time
for a free-fall object to hit the floor from a
height h).

Feburary 18, 2015
Sample Problem I
for Week 1’s topic
This figure shows the
position-time graph of a
moving object. At which
point the magnitude of
the velocity is the
largest?
B
C
D
A
t
A
B
C
D
E. more than one
Sample problem II
for Week #1’s topic

The rocket-driven sled Sonic Wind No. 2, used for
investigating the physiological effects of large
accelerations, runs on a straight, level track of length
1100 m. Starting from rest, it can reach a speed of 223
m/s in a time 0.880 s with approximately constant
acceleration. What is the distance covered in a time of
0.880 s (in meters)?
a. 98.1;
b. Some crazy number
c. Other crazy number
d. You know the idea…
Week 1: Units (Chap. 1)
 Three
fundamental physical quantities:
meter (m), kilogram (kg), and second (s)
 Derived units: area, volume, velocity, etc.
 Unit conversion
 Sample problems:


How to convert miles per hour (mph) to m/s?
Derived units: How many square centimeters
(cm2) are there in one square meter (m2)?
Week 1: 1D Kinetic Motions (Chap. 2)

Kinematic variables in one dimension







Position
x(t)
m
Velocity
v(t)
m/s
Acceleration
a(t)
m/s2
All depend on time
All are vectors: magnitude and direction vector
L
L/T
L/T2
Properly interpret position-time and velocity-time diagrams
Equations for motion with constant acceleration:

𝑣 = 𝑣0 + 𝑎𝑡

1
𝑥 = 𝑥0 + (𝑣0 + 𝑣)𝑡
2
missing quantities
x, x0
a

1 2
𝑥 = 𝑥0 + 𝑣0 𝑡 + 𝑎𝑡
2
v

𝑣 2 = 𝑣0 2 + 2𝑎(𝑥 − 𝑥0 )
t
See also Table 2.4 of your textbook (page 49)
Week 2: Vectors (Chap. 1)
Vector Addition
Vector Subtraction
Week2: Vector Math

Consider two vectors
𝑨 = 𝐴 𝑥 𝒊 + 𝐴𝑦 𝒋
𝑩 = 𝐵𝑥 𝒊 + 𝐵𝑦 𝒋

Then
𝑨 + 𝑩 = (𝐴𝑥 𝒊 + 𝐴𝑦 𝒋) + (𝐵𝑥 𝒊 + 𝐵𝑦 𝒋)
=(𝐴𝑥 +𝐵𝑥 )𝒊 + (𝐴𝑦 +𝐵𝑦 )𝒋

𝑹 = 𝑨 + 𝑩 = (𝐴𝑥 + 𝐵𝑥 )𝒊 + (𝐴𝑦 +𝐵𝑦 )𝒋
𝑹 = 𝐶𝑥 𝒊 + 𝐶𝑦 𝒋

So we have reproduced
𝑅𝑥 = 𝐴𝑥 + 𝐵𝑥 , 𝑅𝑦 = 𝐴𝑦 + 𝐵𝑦
Week 2: Sample Problem on Vectors

A man walking firstly takes one walk which can be
described algebraically as 𝑨 = −3𝒊 + 5𝒋, followed by
another 𝑩 = 4𝒊 − 2𝒋. Find the final displacement and
direction of the sum of these motions
𝑪 = 𝑨 + 𝑩 = (𝐴𝑥 + 𝐵𝑥 )𝒊 + (𝐴𝑦 +𝐵𝑦 )𝒋
= −3 + 4 𝒊 + 5 − 2 𝒋 = 1𝒊 + 3𝒋
𝐶𝑦 = 3
𝐶𝑥 = 1
C  (Cx  C y )1/ 2  (12  32 )1/ 2  3.16
2
2
𝐶𝑦
3
𝜃 = arctan
= arctan = 71.5°
𝐶𝑥
1
Chapter 3 Key Equations
r2 r1
t2 t1
av
r
t
(average velocity vector)
Week 2: (Vector) ˆPosition, Velocity,
r x ˆ y jˆ zk (position vector)
r dr
lim
(instantaneous
velocity3)
vector)
Acceleration
(Chap.
t dt
t

Position
0
r2 r1
t2 t1
dy
av
dx
x
y
dt
 Average velocity
r
dzt
z
(average velocity vector)
(components of instantaneous velocity)
dt
dt
r dr
lim
(instantaneous velocity vector)
t 0
t 2 dt1
 Instantaneous velocity
aav
(average acceleration vector)
t2 t1
t
dx
dt
x
dy
y
dt
a lim
t

Acceleration
d x
dt
ax

aav
0
2
dz
dtd
z
t
(instantaneous acceleration vector)
dt
1
dt2 y t1
ay
(components of instantaneous velocity)
az
dt z
dt
(average acceleration vector)
(components of instantaneous acceleration)


 dt
r (t), v (t ), and a (t ) are
d not necessarily along the same direction.
a
d
x
lim
t
0
(instantaneous acceleration vector)
t x dt ( 0 cos 0 )t (projectile motion)
d
y
z
y ( dsin
)t
1
gt 2 (projectile motion)
(3
(3.1
(3
(3.2
(3
(3.3
(3
(3.4
(3
(3.8
(3
(3.9
(3
(3
Week 2: Projectile Motion (Chap. 3)


Projectile motion is one type of 2-D motion under constant
acceleration, where ax = 0, ay = -g.
The key to analyzing projectile motion is to treat the x- and ycomponents separately and apply 1-D constant acceleration
kinematics equations to each direction:
horizontal direction
𝑣𝑥 = 𝑣0𝑥 + 𝑎𝑥 𝑡
1
𝑥 − 𝑥0 = 𝑣0𝑥 𝑡 + 𝑎𝑥 𝑡 2
2
𝑣𝑥2 = 𝑣0𝑥 2 + 2𝑎𝑥 (𝑥 − 𝑥0 )
𝑎𝑥 = 0
Vertical direction
𝑣𝑦 = 𝑣0𝑦 + 𝑎𝑦 𝑡
1
𝑦 − 𝑦0 = 𝑣0𝑦 𝑡 + 𝑎𝑦 𝑡 2
2
𝑣𝑦2 = 𝑣0𝑦 2 + 2𝑎𝑦 (𝑦 − 𝑦0 )
𝑎𝑦 = −𝑔 (projectile motion, no air resistance)
Week 2: Projectile Motion Sample Problem I

You throw a ball from your window 8 m above the
ground. When the ball leaves your hand, it is moving at
10 m/s at an angle of 20 below the horizontal. Find the
horizontal distance after 0.5 s.
A) 4.7 m
B) 5.0 m
C) 1.7 m
D) 9.4 m
E) 2.3 m
Week 2: Projectile Motion Sample
Problem II

•
•
•
•
A 5300-kg cart carrying a vertical rocket
Horizontal
launcher moves to the right at a constant
speed of 26.0 m/s along a horizontal track. It
𝑣𝑥 = 𝑣0𝑥 + 𝑎𝑥 𝑡
launches a 55.0-kg rocket vertically upward
1
with an initial speed of 42.3 m/s relative to the
𝑥 − 𝑥0 = 𝑣0𝑥 𝑡 + 𝑎𝑥 𝑡 2
2
cart.
𝑣𝑥2 = 𝑣0𝑥 2 + 2𝑎𝑥 (𝑥 − 𝑥0 )
How high will the rocket go?
Where, relative to the cart, will the rocket land?
Vertical
How far does the cart move while the rocket is
𝑣𝑦 = 𝑣0𝑦 + 𝑎𝑦 𝑡
in the air?
1
At what angle relative to the horizontal is the
𝑦 − 𝑦0 = 𝑣0𝑦 𝑡 + 𝑎𝑦 𝑡 2
2
rocket traveling just as it leaves the cart, as
2
2
measured by an observer at rest on the ground 𝑣𝑦 = 𝑣0𝑦 + 2𝑎𝑦 (𝑦 − 𝑦0 )
Week 3: Newton’s Laws (Chap. 4)
 Forces
as vectors
Fx = max å Fy = may å
 Fz = maz (Newton’
å
 Net Force: Fnet   F  F1  F2  F3  ......
 Newton’s 1st law:
An object at rest tends to stay at rest and an
object in motion tends to stay in motion with
(magnitude
of
the
weight
o
w
=
mg
the same speed and in the same direction
unless acted upon by an unbalanced force
 Newton’s
2nd law: 𝑭net = 𝛴𝑭 = 𝑚𝒂
 Newton’s 3rd law: FA on B = -FB on A (Newton’s third
Free Body Diagram



Be sure to include only the
forces acting on the
object of interest
Include any field forces
acting on the object
Do not assume the normal
force or tension force equals
to the weight
F table on book
F Earth on book
Week 3: Sample Problem
 If
the magnitude of
the pulling force is
100 N, what is the
component of the
tension force along
the ramp?
Week 4: Application of Newton’s Law
(Chap. 5)
 Equilibrium
problems: object at rest or
moving at constant velocity
𝐹net,𝒙 =
 Accelerating
𝐹𝑥 = 0
𝐹net,𝑦 =
𝐹𝑦 = 0
objects: net force is not zero,
use Newton’s 2nd Law.
Week4: Sample Problem I

A traffic light weighing 100 N hangs from a vertical cable
tied to two other cables that are fastened to a support.
The upper cables make angles of 37 °and 53°with the
horizontal beam. Find the tension in each of the three
cables.
Week 4: Sample Problem II

The glider on the air track (m1 = 1 kg) and the falling
weight (m2 = 2 kg) move in different directions, but their
accelerations have the same magnitude. What is the
magnitude of the acceleration? How long does it take for
m2 to drop by 1 m in height?
Week 4: Sample Problem III
A toboggan of weight 2000
N (including the passengers)
slides down a hill of angle
20° with no friction. What is
the toboggan’s speed after it
slides 100 m down the hill?