Transcript A body acted on by no net force moves with constant velocity

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lecture 10
Dynamics
Connection between force and motion
The concept of force gives us a quantitative
description of the interaction between two
bodies or between a body and its environment
Newton’s Laws
1st Law: A body acted on by no net force moves with
constant velocity (which may be zero) and zero acceleration
2nd Law: The acceleration of an object is directly
proportional to the net force acting on it and is inversely
proportional to its mass. The direction of the acceleration
is in the direction of the net force acting on the object.
3rd Law: For every action there is an equal, but
opposite reaction
Newton’s law of gravitation
Falling with air resistance
dv
2
a=
= g - kv
dt
Terminal Velocity with Coffee Filters
mg - Fr = ma
where Fr is the resistance force.
Fr
a=gm
1. A penny and a quarter dropped from a ladder land at the
same time (air resistance is negligible).
2. A coin dropped in a coffee filter from a ladder lands later
than a coin without coffee filter (the terminal velocity is
smaller for larger cross-section area).
3. A quarter dropped in a coffee filter will land faster than a
penny in a coffee filter (the terminal velocity is larger for
larger mass)
4. Two identical coins dropped in coffee filters of different
diameters land at different times (the terminal velocity is
smaller for larger cross-section area).
Resistance force: Fr = gAv
2
A – area of the projectile
For a spherical projectile in air at g = 0.25 N ´ s /m
STP:
2
4
Terminal velocity:
Fr
a=g=0
m
Fr = mg
gAv = mg
mg
vT =
gA
2
A 70-kg man with a parachute: vT ~ 5 m/s
A 70-kg man without a parachute: vT ~ 70
m/s
Newton’s
st
1
Law
A body acted on by no net force moves
with constant velocity (which may be zero)
and zero acceleration
Aristotle: a natural state of
an object is at rest; a force
is necessary to keep an
object in motion. It follows
from common sense.
384-322 B.C.
Galileo: was able to
identify a hidden force of
friction behind commonsense experiments
1564-1642
Galileo: If no force is applied to
a moving object, it will continue
to move with constant speed in
a straight line
Inertial reference frames
Galilean principle of relativity: Laws of
physics (and everything in the Universe)
look the same for all observers who move
with a constant velocity with respect to
each other.
Newton’s second law


F  ma
The vector acceleration of an object is in the same
direction as the vector force applied to the object
and the magnitudes are related by a constant called
the mass of the object.
A faulty model rocket moves in the xy-plane (the positive ydirection is vertically upward). The rocket’s acceleration has
components ax(t)=t2 and ay(t)=-t, where =2.50 m/s4, =9.00
m/s2, and =1.40 m/s3. At
 t=0 the rocket is at the origin and has

velocity v0  v0 x i  v0 y j with v0 x  1.00 m / s and v0 y  7.00 m / s.
a) Calculate the velocity and position vectors as functions of time.
b) What is the maximum height reached by the rocket?
c) What is the horizontal displacement of the rocket when it
returns to y=0?
First exam Tuesday, September 23,
7 – 8 pm
Sections 549, 550 105 HELD
Sections 551, 552 107 HELD
Section 570 109 HELD
BRING YOUR STUDENT ID!
No calculators and cell phones
All liquids, gels and aerosols must be in
three-ounce or smaller containers.
What is included?
Chapters 1-4
Kinematics, vectors
Kinematics

 dV
a
dt

 dr
V
dt
In components:
dVy
dVx
ax 
; ay 
dt
dt
dx
dy
Vx  ; V y 
dt
dt
If

a

is given, you can find V and
Vx   a x dt ; Vy   a y d yt
x   Vx dt ;
y   V y dt

r
Vectors






A  Ax i  Ay j B  Bx i  By j
  
C  A B ?



C  Cx i  C y j
Cx  Ax  Bx
C y  Ay  By
Friendly advice
DO NOT…
DO NOT use Const acceleration case
formulas when acceleration is a function
of time. You have to integrate or
differentiate! What are the Const
acceleration case formulas?
1 2
x(t )  ac t  v(0)t  x(0)
2
v(t )  act  v(0)
v (t 2 )  v (t1 )  2ac ( x(t 2 )  x(t1 ))
2
2
DO NOT write the vector sign over a
projection!
If



F  Fx i  Fy j ,
Fx , Fy are scalars!
Do Not Forget to
•Write down what is given and
express the answer in terms of what is
given
•Box the answer
•Indicate the origin and positive x and y
Have a great day!
Reading: Chapter 5