Download Lecture 5 PHYSICS 201 PHYSICS 201 (sections 521-525) ( )

Lecture 5
PHYSICS 201
((sections 521-525))
Instructor: Hans Schuessler
e po a y Alexandre
e a d e Kolomenski
oo e s
Temporary:
http://sibor.physics.tamu.edu/teaching/phys201/
Projectile
j
Motion
The horizontal and vertical
parts of the motion behave
p
independently
This iis why
Thi
h vectors
t
with
ith th
their
i x and
dy
components is a convenient way of
description! We will
ill use
se the same
approach for dynamic problems as well!
Ball Dropping
• Analyze Vertical
and Horizontal
separately!!!
• ay = g (downwards)
(d
d )
• ax = 0
– Constant for Both
directions!!!
Vx = 0
Vx>0
A weird consequence
Prove that an
object projected
horizontally will
reach the
ground at the
same time as
an object
dropped
vertically!
Main laws of dynamics:
Newton’s laws
•Discovered and formulated several
fundamental laws of physics.
•Created related fields of mathematics.
Isaac Newton
(1642-1727)
Chapter 4: Newton’s
Newton s Laws
Force
• First of all what is force?
• How many forces can act on a body?
• Is it a scalar or a vector?
Mass
• What is mass?
Resistance to the force?
• “Resistance”
• Vector or scalar?
Before we start
What is a Force?
Vector quantity, that can initiate a motion.
• Examples:
E
l
– Push
– Pull
– Slap
– Gravity
– Others?
Examples
• Example of non-zero net forces?
– Friction: Causing a moving block to
come to rest
– ((Net force causes acceleration in the
negative direction)
– Gravity: making a ball fall
• Example off zero net force
f
– Car just sitting on the pavement
• No
N acceleration,
l ti
mustt be
b no nett force
f
– Spaceship in outer space
• Nothing to slow it down
down… constant
velocity
Newton’ss First Law
Newton
“A body acted on by a zero net
force moves with constant
velocity (which may be zero)
zero),
i.e. it moves with zero
acceleration”
In other words…
Without a Force there is no change in the
state of the motion => an acceleration is
zero and the velocity is constant
But this holds only in special reference
frames (systems of coordinates) :
inertial systems
(to a good approximation the one related to
Earth IS such a system)
For instance,, in rotating
g reference systems
y
this statement is not valid
Force is a Vector! When several forces,
need
d to
t add
dd up allll th
the fforces ((vectors)
t ) to
t find
fi d
the Net (or total) force.
Example: inertial and non
inertial frames of reference
Newton’ss Second Law
Newton
“If
If a net external force acts on a body, the body
accelerates. The direction of acceleration is the
same as the direction of the net force. The
acceleration is directly proportional to the net force
and inversely proportional to the mass of the body.”
a
F
m
In other words...
To cause an acceleration
( h
(change
velocity)
l it ) requires
i
a
Force
An alternative formulation of the
2nd Newton
Newton’ss law:
The net force vector is equal to
th mass off the
the
th object
bj t times
ti
the
th
acceleration of the object.
j
Mass
Mass characterizes inertial
properties of an object and for
a given object this quantity is
a constant.
Newton’ss Second Law
Newton
• Now need to translate English into Math:
– Net forces cause the velocity to change
This
Thi iis a VECTOR equation
ti
Vector Equation


F  m a
:
 F x  ma x ,  F y  ma
y
Same equation presented
in components
Reminder: Pulling a tanker
Given: T1=T
Gi
T2, D,
D R
R, m
a-?
2T1cos 30o +D- R =ma
m
The Law of Gravity
Units
1 kg
Force: F=ma, 1 Newton,
1N=1kg·1m/s
1N=1kg
1m/s2
Mass:
1 N is the amount of force that gives the acceleration of
one
o
e meter
ete pe
per seco
second
d squa
squared
ed to a body
with a mass of 1 kilogram.
Example: Force to stop a car
What constant net force is required to bring
a car of mass m to rest from a speed of V
within a distance of D?
V0 = V
V=0
X0 = 0
XF = D
Getting to Newton’s Third Law
How does one apply a force?
• Applying a force requires
another object!
–A hammer exerts a force on a
nail
–However,
H
th
the nailil acts
t on th
the
hammer with a reaction force
(this is what stops the hammer)!
Newton’s Third Law
“Whenever one object exerts a
force on a second object, the
second object exerts an equal
and opposite force (reaction).”
OR
“To
To every action there is an equal
and opposite reaction.
(counter action)”
Example
Skater pushes
on the wall. The
wall pushes
back that’s why
back,
she moves off
with some nonzero speed!
d!
Weight and normal force (the force component
perpendicular to the surface that the surface
exerts on an object)
Weight: mg
Without reaction from supporting
surface the object
j
will fall with
Acceleration of gravity.
Difference: weight and mass
weight is a vector, directed toward
the center of the Earth
Earth, measured in N
N.
Mass is a scalar quantity
measured in kg of mass.
(weight)
Examples


FGround on the Person  - FPerson on the Ground
Force exerted by the person
on the ground is equal and
opposite
it tto th
the fforce exerted
t d
by the ground on the
person. She pushes on the
ground
d and
d the
th ground
d
PUSHES her forward
(especially when the motion
starts!!!).
t t !!!)
Also vertical forces: weight
reaction from the ground
upward.
FN
W=mg
Newton’s 3d law is very general:
action and reaction via field
(gravitational, electric, etc.) also is valid,
not only contact forces!
The Law of Gravity
Analysis of forces: free body diagram
Problem: pulling a box
Forces
mg=100 N
Note: FN is less than mg
The Law of Gravity
Free body diagram:
Action of surrounding
objects is replaced
with the forces they
exert.
Problem: weight, normal force and a box
mg=98.0
mg=98
0N
a-? FN-?
The Law of Gravity
Free body diagram
Free body diagram is the main approach to solve
dynamics problems, when different objects interact
with each other.
Action of surrounding objects is replaced with the
forces they exert.
If there are several interacting objects such a
diagram should be drawn for each of them
them.
Free body
di
diagram
ffor a
block on a
surface
f
with
ith
friction
F.B.D.
Dynamic equations:
The Law of Gravity
Motion of 2 blocks
No friction, force F
F
F.B.D.-?
F.B.D.
?
F
The Law of Gravity
Problem: Apparent Weight (FN)
F.B.D. ?
y
Fnet = FN – mg = m a
The Law of Gravity
Weightlessness
F.B.D. ?
The Law of Gravity
•Thanks for your
attention!