Chapter 4
Forces and Mass
Classical Mechanics
does not apply for
• 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
zero 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 a push or pull
Vector
Either contact or field force
Contact and Field Forces
Fundamental (Field) Forces
Types
• Strong nuclear force
• Electromagnetic force
• Weak nuclear force
• Gravity
Strong Nuclear Force
•
•
QCD (Quantum chromodynamics) confines quarks
by exchaning gluons
Nuclear force: binds protons and neutrons
by exchanging pions
Electromagnetic Forces
•
•
•
Opposites attract, like-signs repel
Electric forces bind electrons in atoms
Magnetic forces arise from moving charges
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
m 1 m2
r2
Inertia (Newton’s First Law)
•
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
SI units are kg
Newton’s Second Law
•
Acceleration is proportional to net force and
inversely proportional to mass.
r
 F  ma
Units of Force
•
SI unit is Newton (N)
F  ma
kg  m
1 N 1 2
s
•
US Customary unit is pound (lb)
• 1 N = 0.225 lb
Weight
Weight is magnitude of gravitational force
mass
weight
w  mg
M earth m
wG
r2
GM earth
g
2
Rearth
Weight vs. Mass
•
•
Mass is inherent property
Weight depends on location
Newton’s Third Law
r
F12   F21
Force on “1” due to “2”
•
•
Single isolated force cannot exist
For every action there is an equal and opposite
reaction
Newton’s Third Law cont.
•
•
F12 is action force F21
is reaction force
• You can switch
action <-> reaction
Action & reaction
forces act on
different objects
Action-Reaction Pairs
r
n   n
Fg  Fg'
Define the OBJECT (free body)
•
•
•
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
•
•
Objects behave as particles
• ignore rotational motion (for now)
Consider only forces acting ON object
• neglect reaction forces
Definition of Equilibrium
F  0
Example 4.1a
A Ford Pinto is parked in a parking lot
There is no net force on the Pinto
A) True
B) False
Example 4.1b
A Ford Pinto is parked in a parking lot
The contact force acting on the Pinto from the
parking lot surface ______________ .
A) Points upwards
B) Is zero
C) Points downward
Example 4.1c
A Ford Pinto drives down a highway on the moon
at constant velocity (where there is no air
resistance)
The Pinto’s acceleration is __________
A) Less than zero
B) Equal to zero
C) Greater than zero
Example 4.1d
A Ford Pinto drives down a highway on the moon
at constant velocity (where there is no air
resistance)
The force acting on the Pinto from the contact with
the highway is vertical.
A) True
B) False
Mechanical Forces
•
•
•
•
•
Strings, ropes and Pulleys
Gravity
Normal forces
Friction
Springs (later)
Some Rules for Ropes and Pulleys
•
•
•
Force from rope points AWAY from object
Magnitude of the force is tension
Tension does not change when going over
frictionless pulley
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)
b)
c)
d)
a = g/6 = 1.635 m/s2
T = 57.2 N
T3=24.5 N
Fpulley=2T = 114.5 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
cos(10o)=0.985
sin(10o)=0.173
Example 4.3b
2) Which statements are correct?
Assume the objects are static.
T2 is ______ T3
A) Less than
B) Equal to
C) Greater than
cos(10o)=0.985
sin(10o)=0.173
Example 4.3c
2) Which statements are correct?
Assume the objects are static.
T1 is _____ Mg
A) Less than
B) Equal to
C) Greater than
cos(10o)=0.985
sin(10o)=0.173
Example 4.3d
2) Which statements are correct?
Assume the objects are static.
T1+T2 is ______ Mg
A) Less than
B) Equal to
C) Greater than
cos(10o)=0.985
sin(10o)=0.173
Example 4.4
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
Find the acceleration and the tension
a = 4.43 m/s2, T= 53.7 N
Example 4.6
M
Find M such that the box slides at constant v
M=15.6 kg
Forces of Friction
•
•
RESISTIVE force between object and neighbors
or the medium
Examples:
• Sliding a box
• Air resistance
• Rolling resistance
Sliding Friction
f  s N
f  k N
s  k
•
•
•
Parallel to
surface, opposite to
other forces
~ independent of
the area of contact
Depends on the surfaces in contact
Coefficients
of Friction
f  s N
f  k N
s  k
Static Friction, ƒs
fs   s N
•
•
s is coefficient of
static friction
N is the normal force
f
F
Kinetic
Friction, ƒk
f  k n
k is coefficient of
kinetic friction
• Friction force opposes F
• n is the normal force
•
f
F
Friction Demo
Example 4.7
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 4.8
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?
a) s = 0.5
b) a=1.96 m/s2
c) 39.25 N
Example 4.9
What is the minimum s required to
prevent a sled from slipping down a
hill of slope 30 degrees?
s = 0.577
Other kinds of friction
• Air resistance, F ~ Area  v2
• Rolling resistance, F ~ v
Terminal velocity:
Fresistance  CAv 2
 mg at terminal velocity
Coffee Filter Demo
Example 4.9
An elevator falls with acceleration a = 8.0 m/s2.
If a 200-lb person stood on a bathroom scale
during the fall, what would the scale read?
36.9 lbs
Accelerating Reference Frames
•
Equivalent to “Fictitious” gravitational force
g fictitious  a frame
Fictitious Force: Derivation
1 2
x  v0 t  at
2
1F 2
 v0 t 
t
2m
Eq. of motion in fixed frame
1
x0 (t)  a f t 2
2
1 (F  ma f ) 2
x  x0 (t)  v0 t 
t
2
m
F-maf looks like force in new frame,
maf acts like fake gravitational force!
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?

 = 17 deg
T= 25.6 N
Example 4.11a
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.
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 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.
On the way back down, while descending at
constant velocity, the reading on the scale will be
________________ 20 lbs.
a) Greater than
b) Less than
c) Equal to
Example 4.11c
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.
In the instant just before the elevator comes to a
stop on the 78th floor, the mass of the fish will be
______________ 9.072 kg.
a) Greater than
b) Less than
c) Equal to