Transcript chapter4

Chapter 4
Forces and Mass
Classical Mechanics
Conditions when Classical Mechanics
does not apply
very tiny objects (< atomic sizes)
 objects moving near the speed of light

Newton’s First Law

If the net force SF exerted on an
object is zerok the object continues
in its original state of motion. That is,
if SF = 0, an object at rest remains at
rest and an object moving with some
velocity continues with the same
velocity.

Contrast with Aristotle!
Forces
Usually think of a force as a push or
pull
 Vector quantity
 May be contact or field force

Contact and Field Forces
Fundamental Forces
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Types
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Strong nuclear force
Electromagnetic force
Weak nuclear force
Gravity
Characteristics
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All field forces
Listed in order of decreasing strength
Only gravity and electromagnetic in mechanics
Fundamental Forces

Types

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Strong nuclear force
Electromagnetic force
Weak nuclear force
Gravity
Characteristics



All field forces
Listed in order of decreasing strength
Only gravity and electromagnetic in mechanics
Strong Nuclear Force
QCD (Quantum chromodynamics)
confines quarks to interior of protons
and neutrons
 Force between protons and neutrons
responsible for formation of nuclei
 QCD: Exchange of gluons
 Nuclear Force: Exchange of pions

Electromagnetic Force
Opposites attract, like-signs repel
 Electric force responsible for binding
of electrons to atoms and atoms to
each other
 Magnetic forces arise from moving
charges and currents
 Electric motors exploit magnetic
forces

Electromagnetic Force
Opposites attract, like-signs repel
 Electric force responsible for binding
of electrons to atoms and atoms to
each other
 Magnetic forces arise from moving
charges and currents
 Electric motors exploit magnetic
forces

Weak Nuclear Force
Involves exchange of heavy W or Z
particle
 Responsible for decay of neutrons

Gravity
Attractive force between any two
bodies
 Proportional to both masses
 Inversely proportional to square of
distance

F G
m1 m2
r
2
Inertia

Tendency of an object to continue in
its original motion
Mass
A measure of the resistance of an
object to changes in its motion due to
a force
 Scalar quantity
 SI units are kg

Newton’s Second Law

The acceleration of an object is
directly proportional to the net force
acting on it and inversely proportional
to its mass.

F and a are both vectors
Units of Force

SI unit of force is a Newton (N)
kg m
1N  1 2
s

US Customary unit of force is a pound
(lb)
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1 N = 0.225 lb
See table 4.1
Weight

The magnitude of the gravitational
force acting on an object of mass m
near the Earth’s surface is called the
weight w of the object
Weight and Mass
Mass is an inherent property
 Weight is not an inherent property of
an object
 Weight depends on location

Newton’s Third Law

If two objects interact, the force F12
exerted by object 1 on object 2 is
equal in magnitude but opposite in
direction to the force F21 exerted by
object 2 on object 1.
Equivalent to saying a single isolated
force cannot exist
 For every action there is an equal and
opposite reaction

Newton’s Third Law cont.

F12 may be called
the action force
and F21 the
reaction force
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Either force can be
the action or the
reaction force
The action and
reaction forces act
on different
objects
Some Action-Reaction Pairs
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n and n’
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n is the normal
force, the force
the table exerts on
the TV
n is always
perpendicular to
the surface
n’ is the reaction –
the TV on the table
n = - n’
More Action-Reaction pairs
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Fg and Fg’
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Fg is the force the
Earth exerts on the
object
Fg’ is the force the
object exerts on
the earth
Fg = -Fg’
Forces Acting on an Object
Newton’s Law uses
the forces acting
on an object
 n and Fg are acting
on the object
 n’ and Fg’ are acting
on other objects

Applying Newton’s Laws

Assumptions
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Objects behave as particles

ignore rotational motion (for now)
Masses of strings or ropes are negligible
 Interested only in the forces acting on
the object

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neglect reaction forces
Problem Solving Strategy
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Make a free-body diagram
Identify object (free body)
Label all forces acting on object
Resolve forces into x- and y-components,
using convenient coordinate system
Apply equations, keep track of signs!
Examples of Mechanical
Forces
Strings, ropes and Pulleys
 Gravity
 Normal forces
 Friction
 Springs (later in the book)

Some Rules for Ropes and
Pulleys
When a rope is attached to an object,
the force of the rope on that object
is away from that object
 The magnitude of the force is called
the tension
 The tension does not change when
going over a pulley (if frictionless)

Equilibrium
An object either at rest or moving
with a constant velocity is said to be
in equilibrium
 The net force acting on the object is
zero

F  0
Do Cable Pull Demo
Example
Given that Mlight = 25 kg, find all three tensions
T3 = 245.3, T1 = 147.6 kg, T2 = 195.9 kg
Example
a) Find acceleration
b) Find T
c) Find T3
d) Find force ceiling
must exert on pulley
a) a=g/6, b) T = 57.2 N
c) T3=24.5 N, d) Fpulley=2T = 114.5 N
Inclined Planes
Choose x along the
incline and y
perpendicular to
incline
 Replace force of
gravity with its
components

Fx  mg sin 
Fy  mg cos
Example
Find the acceleration and the tension
a = 4.43 m/s2, T= 53.7 N
Forces of Friction
Resistive force between object and
neighbors or the medium
 Examples:

Sliding a box
 Air resistance
 Rolling resistance

Sliding Friction
Proportional to the
normal force
 Direction is
parallel to surface
and opposite other
forces
 Force of friction is nearly independent of the
area of contact
 The coefficient of friction (µ) depends on the
surfaces in contact

Coefficients of
Friction
f  n
s  k
Static Friction, ƒs


If F   s n, f s   F
s is coefficient of
static friction
 n is the normal force

f
F
Kinetic
Friction, ƒk
If F   s n,
f  k n
k is coefficient of
kinetic friction
 Friction force
opposes F
 n is the normal
force

f
F
Example
The man pushes/pulls with a force of 200 N. The
child and sled combo has a mass of 30 kg and the
coefficient of kinetic friction is 0.15. For each case:
What is the frictional force opposing his efforts?
What is the acceleration of the child?
f=59 N, a=4.7 m/s2
/
f=29.1 N, a=5.7 m/s2
Example
Given m1 = 10 kg and m2 = 5 kg:
a) What value of s would stop the block from
sliding?
b) If the box is sliding and k = 0.2, what is the
acceleration?
c) What is the tension of the rope?
s = 0.5, a=1.96 m/s2
Example
What is the minimum s required
to prevent the sled from slipping
down a hill of slope 30 degrees?
s = 0.577
Example
You are calibrating an accelerometer so that you
can measure the steady horizontal acceleration of a
car by measuring the angle a ball swings backwards.
If M = 2.5 kg and the acceleration, a = 3.0 m/s2:
a) At what angle does the ball swing backwards?
b) What is the tension in the string?

 = 17 deg
T= 25.6 N
Quiz, All Sections
1) What is your section number?
Quiz, Section 1
2) Which statements are correct?
Assume the objects are static.
A)
B)
C)
D)
T1 must = T2
T2 must = T3
T1 must be < Mg
T1+T2 must be > Mg
a)
A only
A and B only
A, B and C only
All statements
None of the statements
b)
c)
d)
e)
cos(10o)=0.985
sin(10o)=0.173
Quiz, Section 2
2) Which statements are correct?
Assume the objects are static.
A)
B)
C)
D)
T1 must = T2
T2 must = T3
T1 must be < Mg
T1+T2 must be > Mg
a)
A only
A and B only
A, B and C only
All statements
None of the statements
b)
c)
d)
e)
cos(10o)=0.985
sin(10o)=0.173
Quiz, Section 3
2) Which statements are correct?
Assume the objects are static.
A)
B)
C)
D)
T1 must = T2
T2 must = T3
T1 must be < Mg
T1+T2 must be > Mg
a)
A only
A and B only
A, B and C only
All statements
None of the statements
b)
c)
d)
e)
cos(10o)=0.985
sin(10o)=0.173