Download Physics 106P: Lecture 1 Notes

Physics 101: Lecture 8
Newton's Laws

Today’s lecture will be a review of Newton’s Laws and
the four types of forces discussed in Chapter 4.
Concepts of Mass and Force
Newton’s Three Laws
Gravitational, Normal, Frictional, Tension Forces
Physics 101: Lecture 8, Pg 1
Sir Isaac Newton, English Physicist, 1643-1727
Physics 101: Lecture 8, Pg 2
Newton’s First Law
 The motion of an object does not change
unless it is acted upon by a net force.
• If v=0, it remains 0
• If v is some value, it stays at that value
 Another way to say the same thing:
• No net force 
• velocity is constant
• acceleration is zero
• no change of direction of motion
Physics 101: Lecture 8, Pg 3
Mass or Inertia
 Inertia is the tendency of an object
to remain at rest or in motion with
constant speed along a straight line.
 Mass (m) is the quantitative measure of
inertia. Mass is the property of an
object that measures how hard it is to
change its motion.
 Units: [M] = kg
Physics 101: Lecture 8, Pg 4
Newton’s Second Law
This law tells us how motion changes
when a net force is applied.
 acceleration = (net force)/mass

F



Fnet Ftot
in symbols : a 


M
M M
alternate way to write it :


Fnet  M a
Physics 101: Lecture 8, Pg 5
Newton’s Second Law


Fnet  M a
Units:
 [F] = [M] [a]
[F] = kg m/s2
1 Newton (N)  1 kg m/s2
 A vector equation:
Fnet,x = Max
Fnet,y = May
Physics 101: Lecture 8, Pg 6
Newton’s 1. Law
An airplane is flying from Buffalo airport to O'Hare. Many forces act
on the plane, including weight (gravity), drag (air resistance), the trust
of the engine, and the lift of the wings. At some point during its trip
the velocity of the plane is measured to be constant (which means its
altitude is also constant). At this time, the total (or net) force on the
plane:
1. is pointing upward
2. is pointing downward
3. is pointing forward
4. is pointing backward
5. is zero
lift
correct
drag
thrust
weight
Physics 101: Lecture 8, Pg 7
Newton’s 1. Law
Newton's first law states that if no net force acts on an object, then the
velocity of the object remains unchanged. Since at some point during the trip,
the velocity is constant, then the total force on the plane must be zero,
according to Newton's first law.
lift
SF= ma = m0 = 0
drag
thrust
weight
Physics 101: Lecture 8, Pg 8
Example: Newton’s 2. Law
F1
M
M=10 kg F1=200 N
Find a
a = Fnet/M = 200N/10kg = 20 m/s2
F1
M
F2
M=10 kg F1=200 N F2 = 100 N
Find a
a = Fnet/M = (200N-100N)/10kg = 10 m/s2
Physics 101: Lecture 8, Pg 9
Newton’s Third Law
 For every action, there is an equal and opposite
reaction.
Ffingerbox
• Finger pushes on box
• Ffingerbox = force exerted on box by finger
Fboxfinger • Box pushes on finger
• Fboxfinger = force exerted on finger by box
• Third Law:
Fboxfinger = - Ffingerbox
Physics 101: Lecture 8, Pg 10
Newton's Third Law...

FA ,B = - FB ,A. is true for all types of forces
Fw,m
Fm,w
Fm,f
Ff,m
Physics 101: Lecture 8, Pg 11
Conceptual Question: Newton’s 3.Law

Since Fm,b = -Fb,m why isn’t Fnet = 0, and a = 0 ?
Fb,m
Fm,b
a ??
ice
Physics 101: Lecture 8, Pg 12
Conceptual Question: Answer

Consider only the box !
Fnet, box = mbox abox = Fm,b
What about forces on man?
Fnet,man = mman aman = Fb,m
Fb,m
Fm,b
abox
ice
Physics 101: Lecture 8, Pg 13
Newton’s 2. and 3. Law
Suppose you are an astronaut in outer space giving a brief push to a
spacecraft whose mass is bigger than your own (see Figure 4.7 in
textbook).
1) Compare the magnitude of the force you exert on the spacecraft, FS, to
the magnitude of the force exerted by the spacecraft on you, FA, while
you are pushing:
1. FA = FS
2. FA > FS
3. FA < FS
correct
Third Law!
2) Compare the magnitudes of the acceleration
you experience, aA, to the magnitude of the acceleration
of the spacecraft, aS, while you are pushing:
1. aA = aS
correct
2. aA > aS
a=F/m
3. aA < aS
F same  lower mass gives larger a
Physics 101: Lecture 8, Pg 14
Summary:
• Newton’s First Law:
The motion of an object does not change unless it
is acted on by a net force
• Newton’s Second Law:
Fnet = ma
• Newton’s Third Law:
Fa,b = -Fb,a
Physics 101: Lecture 8, Pg 15
Forces: 1. Gravity
m2
F2,1
F1,2
m1
r12
F1,2 = force on m1 due to m2 = G m1m 2 = F2,1 = force on m2 due to m1
r122
Direction: along line connecting the masses; attractive
G = universal gravitation constant = 6.673 x 10-11 N m2/kg2
Example: two 1 kg masses separated by 1 m
Force = 6.67 x 10-11 N
(very weak, but this holds the universe together!)
Physics 101: Lecture 8, Pg 16
Gravity and Weight
m
Re
mass on surface
of Earth
Me
Force on mass:
 GM e 
Fg   2  m  gm  mg
 Re 
 GM 
g   2e 
 Re 
using M e  5.98 x 10 24 kg and R e  6.38 x 106 m
g  9.81 m/s
2
g
Fg  W = mg
Physics 101: Lecture 8, Pg 17
Forces: 2. Normal Force
FN
book at rest on table:
What are forces on book?
W
• Weight is downward
• System is “in equilibrium” (acceleration = 0  net force = 0)
• Therefore, weight balanced by another force
• FN = “normal force” = force exerted by surface on object
• FN is always perpendicular to surface and outward
• For this example FN = W
Physics 101: Lecture 8, Pg 18
Forces: 3. Kinetic Friction
FN
direction of motion
F
fk
W
• Kinetic Friction (aka Sliding Friction):
A force, fk, between two surfaces that
opposes relative motion.
• Magnitude: fk = kFN
k = coefficient of kinetic friction
a property of the two surfaces
Physics 101: Lecture 8, Pg 19
Forces: 3. Static Friction
FN
fs
F
W
• Static Friction:
A force, fs, between two surfaces that
prevents relative motion.
• fs ≤ fsmax= sFN
force just before breakaway
s = coefficient of static friction
a property of the two surfaces
Physics 101: Lecture 8, Pg 20
Forces: 4. Tension
T
• Tension: force exerted by a rope (or string)
• Magnitude: same everywhere in rope
Not changed by pulleys
• Direction: same as direction of rope.
Physics 101: Lecture 8, Pg 21
Forces: 4. Tension
example: box hangs from a
rope attached to ceiling
y
T
SFy = may
T - W = may
T = W + may
W
In this case ay = 0
So T = W
Physics 101: Lecture 8, Pg 22
Examples: Inertia


Seat-belt mechanism (see textbook)
A man dangles his watch from a thin chain as his
plane takes off. He observes that the chain
makes an angle of 30 degrees with respect to the
vertical while the plane accelerates on the runway
for takeoff, which takes 16 s.
What is the speed of the aircraft at takeoff ?
Physics 101: Lecture 8, Pg 23
Examples: Tension

A lamp of mass 4 kg is stylishly hung from the ceiling
by two wires making angles of 30 and 40 degrees. Find
the tension in the wires.
Physics 101: Lecture 8, Pg 24
Examples:

Consider two blocks of mass m1 and m2 respectively
tied by a string (massless). Mass m1 sits on a horizontal
frictionless table, and mass m2 hangs over a pilley. If
the system is let go, compute the aceleration and the
tension in the string.
Physics 101: Lecture 8, Pg 25