Download Lecture 3

NEWTON’S LAWS OF
MOTION
Review

Equations for Motion Along One Dimension
x
vave 
t
x dx
v  lim

t  0 t
dt
v
aave 
t
v dv
a  lim

t 0 t
dt
Review
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Motion Equations for Constant Acceleration
• 1.
v  v0  at
• 2. x  x0  v0t  1 2 at 2
• 3. v  v  2ax
2
• 4. vave
2
0
v  v0

2
Dynamics vs Kinematics
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So far we’ve been studying kinematics, we’ve been
describing how things move.
We were only concerned with a particles position,
velocity or acceleration.
But why do things move?
What gives objects motion?
What is Force?
What is Force?
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Force is either a push or
a pull. It is an interaction
between two bodies.
Force is a vector. It has
both magnitude and
direction.
When force is a result of
two objects touching, we
call that a contact force.
Aside from that there
are also long-range
forces or field forces
Examples of Contact Forces
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Normal Force
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Frictional Force
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Tension Force
Examples of Field Forces
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Gravitational Force
Magnetic Force
Electric Attraction
Fundamental Forces
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Gravitational Forces –
weakest of the four forces
Electromagnetic Forces –
force between electrically
charged particles.
Weak Nuclear Forces –
responsible for some
nuclear phenomena like
beta decay
Strong Nuclear Forces –
only holds inside an atomic
nucleus.
Superposition of Forces
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Throwing a basketball into the hoop
What are the forces involved?
Superposition of Forces
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Throwing a basketball into the hoop
What are the forces involved?
 Force
of your hand on the ball
 Force of gravity (i.e. weight)
Superposition of Forces
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If we can add forces, we can also separate a force
into its components!
A  Ax  Ay
Ax  A cos 
Ay  A sin 
Examples
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Young and Freedman 4.4
A man is dragging a trunk up a loading the loading
ramp of a mover’s truck. The ramp has a slope
angle of 20.0o, and the man pulls upward with a
force F, who’s direction makes an angle of 30o with
the ramp. (a) How large a force F is necessary for
the component Fx parallel to the ramp to be 60.0
N? (b) How large will the component Fy
perpendicular to the ramp then be?
Isaac Newton
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Born January 4, 1643 (December 25,
1642 under old calendar)
He was a physicist, mathematician,
astronomer, natural philosopher,
alchemist and theologian.
Considered by many to be the “greatest
scientist who ever lived”.
He published the “Philosophiæ Naturalis
Principia Mathematica” in 1687 which
laid the foundations for classical
mechanics.
He also invented calculus
Isaac Newton – lesser known facts

Was a religious nut
 He
published more papers on
scripture than science.
 He poured over the bible looking
for secret codes.
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He also poured a lot of effort
into alchemy and the
philosophers stone
Isaac Newton – questionable facts
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Invented the cat door (pet door)
Apple hitting Newton on the head
Principia was written due to a bet
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Christopher Wren was with some astronomers when
he bet 40 shillings (around 4,000 php now) that no
one could explain elliptical orbits.
It took Newton years to find the answer so he
didn’t get any money.
But he expanded his answers and published
Principia.
Included in Principia are the Three Laws of Motion
First Law of Motion
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Lets examine an object at rest
If there are no forces acting on it the object what
will happen to the object?
If the sum of forces on an abject equal zero, what
will happen to the object?
First Law of Motion
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Lets examine an object in motion
If there are no forces acting on it the object what
will happen to the object?
If the sum of forces on an abject equal zero, what
will happen to the object?
First Law of Motion
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Every object continues in its state of rest or of
uniform velocity as long as no net force acts on it.
Inertia – the tendency of an object to maintain its
state of rest or uniform motion
Law of inertia
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A body is in equilibrium if
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F  0
But wait
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If you’re in a decelerating car, your body gets
thrown forward, but there is no net force acting on
you!!!
Inertial Frames of Reference
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Frames of reference where First Law of Motion
holds
Frames fixed on the Earth can be considered to be
inertial frames of reference
Frames of reference travelling at constant velocity
relative to another inertial frame are also inertial
frames (a=0).
Mass
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Mass is usually defined as quantity of matter an
object has.
We need to be a bit more specific here
Mass is a measure of inertia of an object.
Uses SI unit kg
Mass vs Weight
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Mass and weight are used interchangeably in
everyday language
In physics, mass and weight are different
 Mass
is the measure of inertia. It is an intrinsic property
of matter. No matter where you are, or where the
observer is, your mass will be the same.
 Weight is the force of gravity on an object. Your weight
will be different here than on the moon or in space.
Young and Freedman 4.20
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An astronauts pack weighs 17.5N on earth and
3.24N on an asteroid. (a) what is the acceleration
due to gravity on the asteroid? (b) what is the mass
of the pack on the asteroid?
What happens then if net Force is not
equal to 0
F  0

F
Newton’s Second Law of Motion
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The acceleration of an object is directly
proportional to the net force acting on it and
indirectly proportional to its mass. The direction of
the acceleration is in the direction of the net force
acting on the object.
F

a
m
 F  ma
Force
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We now define the Newton
1 Newton is the amount of force needed to
accelerate a 1kg object by 1m/s2
1N=1kg m /s2
It is the SI unit for Force
Force
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We now define the Newton
1 Newton is the amount of force needed to
accelerate a 1kg object by 1m/s2
1N=1kg m /s2
It is the SI unit for Force
Pull of the earth is a force
 Weight
has SI unit of N
Example
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What average force is required to stop an 1,100
kg car in 8.0 s if the car is travelling at 95 km/h
Example
 F  ma
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We have mass, we need acceleration
v0  95 km h  26.389 m s
v  0ms
t  8.0s
Example
v  v0  at
v  v0
a
t
0  26.389
a
8
a  3.298 m s 2
 F  ma
 F  (1100kg)(3.298
 F  3,600 N
m
s2
)
Newton’s Third Law of Motion
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Force is an interaction between two objects
It always comes in pairs
Newton’s Third Law of Motion
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Whenever one object exerts a force on a second
object, the second exerts an equal force in the
opposite direction on the first.
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FAonB  FBonA
Newton’s Third Law of Motion
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To every action there is an equal but opposite
reaction
Remember the action and reaction forces are acting
on different objects
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FAonB  FBonA
Horse and Cart Paradox
Example
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Giancoli 4-19
A box weighing 77.0N
is resting on a table. A
rope tied to the box
runs vertically upward
over a pulley and a
weight is hung from the
other end. Determine the
force the table exerts on
the box if the weight on
the other side of the
pulley weighs (a) 30.0N
(b) 60.0N (c) 90.0N
77N
Example
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Force table exerts on the box is just
normal force
Normal Force = Weight of box on
table
77N
Application of Newton’s Laws
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Serway 5-18
A bag of cement weighs
325 N and hangs from
three wires. Two of the
wires make angles 60.0o
and 25.0o with the
horizontal. If the system
is in equilibrium, find the
tensions, T1, T2, T3 in the
wires.
Young & Freedman 5.10
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A 1130 kg car is held in
place by a light cable
on a very smooth
(frictionless) ramp. The
cable makes an angle
of 31.0o above the
surface of the ramp. The
ramp itself rises 25.0o
above the horizontal. (a)
find the tension in the
cable. (c) How hard
does the surface of the
ramp push on the car?
Giancoli 4-30
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At the instant a race
began a 65kg sprinter
exerted a force of
720N on the starting
block at an angle of
22o with respect to the
ground. (a) What is the
horizontal acceleration
of the sprinter? (b) if the
force was exerted for
0.32s with what speed
did the sprinter leave
the starting block?
Serway 5-24
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A 5.00 kg object
placed on a
frictionless, horizontal
table is connected to a
string that passes over
a pulley and then is
fastened to a hanging
9.00-kg object. Find
the acceleration of the
two objects and the
tension in the string.
Giancoli 4-34
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Two masses each
initially 1.80 m above
the ground, and the
massless fricitonless
pulley is 4.8m above
the ground. What
maximum height does
the lighter mass reach
after the system is
released?
4.80 m
2.2
1.80 m
3.2
Friction
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Results from contact
between two surfaces.
Parallel to the surface
of contact.
Always opposite to the
relative motion of the
two surfaces.
Kinetic Friction
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Frictional force can be
approximated to be
proportional to normal
force
f k  k N
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Where µk is the
coefficient of kinetic
friction
Note: friction is not
dependent on surface
area
Static Friction
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Force of friction that
arises even when
objects are not in
relative motion.
f s  s N
Where µs is the
coefficient of Static
friction
k  s
Friction Graph
Young & Freedman 5.30
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A box of bananas weighs 40.0N and rests on a
horizontal surface. µs=0.40 while µk =0.20. (a) if no
horizontal force is being applied and the box is at rest,
what is the friction force exerted on the box. (b) What
is the magnitude of friction is a monkey exerts a force
of 6.0 N on the box. (c) What is the minimum horizontal
force the monkey needs to apply to start the box in
motion? (d) What is the minimum horizontal force the
monkey needs to keep the box in motion? (e) If the
monkey applies a horizontal force of 18.0N what is the
magnitude of friction force and the boxes acceleration.
Young & Freedman 5.30
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FN=40.0N
(a) = 0
(b) max fs=0.4*40=16N => fs=6N
(c) 16N
(d) fk=0.2*40=8N
(e) Fnet=ma=F-fk
ma=18-8=10N
a=10/m=10*9.8/40=2.45m/s2
Serway 5-44
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Three objects are
connected as shown.
Table has µk =0.350.
(a) determine the
acceleration of each
object in the system (b)
Determine the tensions
in the two chords.
Serway 5-49
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A block weighing 75.0N rests on a plane inclined at
25.0o to the horizontal. A force F is applied at
40.0o to the horizontal pushing it upward on the
plane. If µs =0.363 and µk =0.156 (a) What is the
minimum value of F to prevent the block from
slipping down the plane. (b) what is the minimum
value of F that will start the block up the plane. (c)
What value of F will move the block up at constant
velocity.
Apparent Weight
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Tension in an elevator cable
Elevator has a total mass of 800 kg. its moving
downwards at 10 m/s but slows to a stop at
constant acceleration for 25.0m. Find the tension T
while the elevator is being brought to rest.
Apparent Weight
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Elevator has a total mass of 800 kg. its moving
downwards at 10 m/s but slows to a stop at
constant acceleration for 25.0m. Find the tension T
while the elevator is being brought to rest.
A woman is on a scale while riding the elevator.
Mass of the woman is 50.0 kg, what is the reading
on the scale?
Common Movie Mistakes
Seat Work/Home Work (time
dependent)
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A block with mass
15.0kg is placed on a
frictionless inclined
plane with slope 20.0o
and is connected to a
second block with mass
6.00kg hanging over a
small, frictionless pulley.
(a) Will the first block
accelerate to the left or
to the right? (b) What is
the magnitude of the
acceleration?
15kg
6kg
Seat Work/Home Work (time
dependent)

A block with mass
15.0kg is placed on an
inclined plane with slope
20.0o and is connected
to a second block with
mass 6.00kg hanging
over a small, frictionless
pulley. If µs= 0.300 and
µk= 0.150 (a) Will the
system accelerate? Why
or why not? (b) If yes,
what is the magnitude of
the acceleration?
15kg
6kg