Chapter 4 Forces and Mass Classical Mechanics Newton’s First Law

Chapter 4
Forces and Mass
Newton’s First Law
•
•
If the net force !F exerted on an object is
zero the object continues in its original state of
motion. That is, if !F = 0, an object at rest
remains at rest and an object moving with some
velocity continues with the same velocity.
Classical Mechanics
does not apply for
•
very tiny objects (< atomic sizes)
•
objects moving near the speed of light
Forces
•
Usually a push or pull
•
Vector
•
Either contact or field force
Contrast with Aristotle!
Contact and Field Forces
Fundamental (Field) Forces
Types
•
Strong nuclear force
•
Electromagnetic force
•
Weak nuclear force
•
Gravity
Electromagnetic Forces
Strong Nuclear Force
•
•
QCD (Quantum chromodynamics) confines quarks
by exchaning gluons
Nuclear force: binds protons and neutrons
by exchanging pions
•
Opposites attract, like-signs repel
•
Electric forces bind electrons in atoms
•
Magnetic forces arise from moving charges
Weak Nuclear Force
Gravity
•
Involves exchange of heavy W or Z particle
•
Attractive force between any two bodies
•
Responsible for decay of neutrons
•
Proportional to both masses
•
Inversely proportional to square of distance
F=G
Inertia (Newton’s First Law)
•
Tendency of an object to continue in its original
motion
m 1 m2
r2
Mass
•
A measure of the resistance of an object to
changes in its motion due to a force
•
Scalar
•
SI units are kg
Newton’s Second Law
•
Units of Force
Acceleration is proportional to net force and
inversely proportional to mass.
•
!
!
! F = ma
SI unit is Newton (N)
F = ma
1 N =1
•
US Customary unit is pound (lb)
•
Weight
kg ! m
s2
1 N = 0.225 lb
Weight vs. Mass
Weight is magnitude of gravitational force
mass
w = mg
weight
M earth m
r2
GM earth
g=
2
Rearth
w=G
Newton’s Third Law
!
!
F12 = ! F21
Single isolated force cannot exist
•
For every action there is an equal and opposite
reaction
Mass is inherent property
•
Weight depends on location
Newton’s Third Law cont.
•
Force on “1” due to “2”
•
•
•
F12 is action force F21
is reaction force
• You can switch
action <-> reaction
Action & reaction
forces act on
different objects
Action-Reaction Pairs
Define the OBJECT (free body)
•
!
!
n = ! n"
Fg = !Fg'
Newton’s Law uses the
forces acting ON object
•
n and Fg act on object
•
n’ and Fg’ act on other
objects
Assumptions for F=ma
Definition of Equilibrium
!
!F = 0
•
Objects behave as particles
•
•
ignore rotational motion (for now)
Consider only forces acting ON object
•
neglect reaction forces
Example 4.1a
Example 4.1b
A Ford Pinto is parked in a parking lot
A Ford Pinto is parked in a parking lot
There is no net force on the Pinto
A) True
B) False
The contact force acting on the Pinto from the
parking lot surface ______________ .
A) Points upwards
B) Is zero
C) Points downward
Example 4.1c
Example 4.1d
A Ford Pinto drives down a highway on the moon
at constant velocity (where there is no air
resistance)
A Ford Pinto drives down a highway on the moon
at constant velocity (where there is no air
resistance)
The Pinto’s acceleration is __________
The force acting on the Pinto from the contact with
the highway is vertical.
A) Less than zero
B) Equal to zero
C) Greater than zero
Mechanical Forces
A) True
B) False
Some Rules for Ropes and Pulleys
•
Strings, ropes and Pulleys
•
Force from rope points AWAY from object
•
Gravity
•
Normal forces
Magnitude of the force is tension
•
•
•
Friction
Tension does not change when going over
frictionless pulley
•
Springs (later)
Example 4.2
a) Find acceleration
b) Find T, the tension above
the bowling ball
c) Find T3, the tension in the
rope between the pails
d) Find force ceiling must exert
on pulley
a) a = g/6 = 1.635 m/s2
b) T = 57.2 N
Example 4.3a
2) Which statements are correct?
Assume the objects are static.
T1 is _____ T2
A) Less than
B) Equal to
C) Greater than
c) T3=24.5 N
d) Fpulley=2T = 114.5 N
cos(10o)=0.985
sin(10o)=0.173
Example 4.3b
Example 4.3c
2) Which statements are correct?
Assume the objects are static.
2) Which statements are correct?
Assume the objects are static.
T2 is ______ T3
T1 is _____ Mg
A) Less than
B) Equal to
C) Greater than
A) Less than
B) Equal to
C) Greater than
cos(10o)=0.985
sin(10o)=0.173
cos(10o)=0.985
sin(10o)=0.173
Example 4.3d
Example 4.4
2) Which statements are correct?
Assume the objects are static.
T1+T2 is ______ Mg
A) Less than
B) Equal to
C) Greater than
cos(10 )=0.985
sin(10o)=0.173
o
Given that Mlight = 25 kg, find all three tensions
T3 = 245.3 N, T1 = 147.4 N, T2 = 195.7 N
Cable Pull Demo
Inclined Planes
•
Choose x along the
incline and y
perpendicular to incline
•
Replace force of gravity
with its components
Fg,x = mgsin !
Fg,y = mg cos!
Example 4.5
Example 4.6 (Skip)
M
Find the acceleration and the tension
Find M such that the box slides at constant v
a = 4.43 m/s2, T= 53.7 N
M=15.6 kg
Forces of Friction
Sliding Friction
•
RESISTIVE force between object and neighbors
or the medium
•
Examples:
•
Sliding a box
•
Air resistance
•
Rolling resistance
Coefficients
of Friction
f ! µs N
f = µk N
µs > µk
•
Parallel to
surface, opposite to
other forces
•
~ independent of
the area of contact
•
Depends on the surfaces in contact
Static Friction, ƒs
fs ! µ s N
f ! µs N
f = µk N
µs > µk
•
µs is coefficient of
static friction
•
f
N is the normal force
F
Friction Demo
Kinetic
Friction, ƒk
f = µk n
•
f
µk is coefficient of
kinetic friction
•
Friction force opposes F
•
n is the normal force
F
Example 4.7
Example 4.8
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=3.80 m/s2
/
f=29.1 N, a=4.8 m/s2
Example 4.9
Given m1 = 10 kg and m2 = 5 kg:
a) What value of µs would stop the block from sliding?
b) If the box is sliding and µk = 0.2, what is the
acceleration?
c) What is the tension of the rope?
a) µs = 0.5
b) a=1.96 m/s2
Other kinds of friction
• Air resistance, F ~ Area " v2
• Rolling resistance, F ~ v
Terminal velocity:
What is the minimum µs required to
prevent a sled from slipping down a
hill of slope 30 degrees?
µs = 0.577
Fresistance = CAv 2
= mg at terminal velocity
c) 39.25 N
Coffee Filter Demo
Example 4.9
An elevator falls with acceleration a = 8.0 m/s2.
If a 100-kg person stood on a bathroom scale
during the fall, what would the scale read?
18.45 kg
Accelerating Reference Frames
•
Fictitious Force: Derivation
Equivalent to “Fictitious” gravitational force
g fictitious = !a frame
1
x = v0 t + at 2
2
1F 2
= v0 t +
t
2m
Eq. of motion in fixed frame
1
af t2
2
1 (F ! ma f ) 2
x ! x0 (t) = v0 t +
t
2
m
x0 (t) =
F-maf looks like force in new frame,
maf acts like fake gravitational force!
Example 4.11a
Example 4.10
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?
A fisherman catches a 20 lb trout (mass=9.072
kg), and takes the trout in an elevator to the
78th floor to impress his girl friend, who is the
CEO of a large accounting firm. The fish is
hanging on a scale, which reads 20 lb.s while the
fisherman is stationary. Later, he returns via the
elevator to the ground floor with the fish still
hanging from the scale.
#
# = 17 deg
T= 25.6 N
In the instant just after the elevator begins to
move upward, the reading on the scale will be
______________ 20 lbs.
a) Greater than
b) Less than
c) Equal to
Example 4.11b
A fisherman catches a 20 lb trout (mass=9.072 kg), and
Example 4.11c
A fisherman catches a 20 lb trout (mass=9.072 kg),
takes the trout in an elevator to the 78th floor to impress
and takes the trout in an elevator to the 78th floor
his girl friend, who is the CEO of a large accounting firm.
to impress his girl friend, who is the CEO of a large
The fish is hanging on a scale, which reads 20 lb.s while
accounting firm. The fish is hanging on a scale, which
the fisherman is stationary. Later, he returns via the
reads 20 lb.s while the fisherman is stationary. Later,
elevator to the ground floor with the fish still hanging
he returns via the elevator to the ground floor with
from the scale.
the fish still hanging from the scale.
On the way back down, while descending at
In the instant just before the elevator comes to
constant velocity, the reading on the scale will
be ________________ 20 lbs. a) Greater than
b) Less than
c) Equal to
a stop on the 78th floor, the mass of the fish
a) Greater than
will be ______________ 9.072 kg.
b) Less than
c) Equal to