AP Physics Chapter 6
Forces and Newton’s Laws of Motion
Kinematics: How objects move
Dynamics: Why objects move
First studied by Isaac Newton
Isaac Newton
Sir Isaac Newton at 46 in Godfrey Kneller's 1689 portrait
Born 4 January [O.S. 25 December 1642] 1643
Woolsthorpe-by-Colsterworth, Lincolnshire, England
Died 31 March [O.S. 20 March] 1727
Kensington, London
Residence England
Nationality English
Field Mathematics, physics, astronomy, alchemy, and
natural philosophy
Institution University of Cambridge
Alma Mater University of Cambridge
Doctoral Advisor Isaac Barrow
Known for Gravitation, optics, calculus, mechanics
Societies President of the Royal Society,
Master of the Royal Mint
Prizes Knighthood
Religion Prophetic Unitarianism, Church of England
Force
a push or a pull
Can be a field force: gravity,
magnetism
Does not involve physical contact.
Or it can be a contact force like
friction
4 types of forces
1. Gravitational: attractive force that exists
between all objects that have mass,
It is the weakest of all forces
But holds the universe together
2. Electromagnetic: result of electric
charge, gives materials their physical
characteristics, strength, ability to bend,
squeeze, stretch, shatter, malleability
Greater than gravity
3. Strong Nuclear: holds particles of
nucleus together
strongest force
but only over a very, very small
distance
4. Weak Force: involved in radioactive
decay of some nuclei,
may be a form of electromagnetic force
Force diagram
Sketch a free body diagram
Isolate the object
And draw the forces acting on it
Normal Force
It is the force supplied by the surface
supporting the object
It is a contact force
Usually due to weight of the object
The object pushes down
The surface pushes up
Newton’s Laws of Motion
 Newton’s 1st Law of Motion: an object
with no outside force acting on it will
move at a constant velocity in a straight
line or remain at rest
 Newton wrote the law, but Galileo
speculated about this concept in his
writings
Demo
Ballistic Car
Inertia apparatus
Called the Law of Inertia
What is inertia?
Inertia is the tendency of a body or
object to resist a change in its motion
The more mass a body has, the more
inertia it has
Newton’s 1st Law of Motion
Law of Equilibrium
(law of inertia): net
sum of the forces is
equal to zero
Uniform Motion
Constant velocity
Or no motion
F

0

Equilibrant
The equilibrant is equal to the resultant
in magnitude but opposite in direction.
When the vector sum is not zero, a
force can be applied that will produce
equilibrium. That is the equilibrant
force.
Mass
Is a measurement of inertia, a body’s
tendency to stay in equilibrium
Friction
The force that opposes motion between
two surfaces
It is parallel to the surface and opposite
the direction of motion
Static and Kinetic Friction
Static Friction: the force that opposes
the start of motion, it is the maximum
frictional force.
Kinetic friction: the force that opposes
motion between two surfaces in relative
motion.
Coefficient of Static Friction
s
Depends on the
normal force and
types of surfaces in
contact
Coefficient of Kinetic Friction
k
Less than static
friction, object is in
motion
Is also called sliding
friction
Frictional Force
Is the product of the
coefficient and the
normal
F f  N
Free body diagram
All vectors are drawn at the center of
mass
Draw a free body diagram of a box
moving at constant velocity across the
floor with friction
What does Net Force mean?
Newton’s Second Law of Motion
The acceleration of a body is directly
proportional to the Net Force on it and
inversely proportional to its mass.
Net Force causes acceleration
ΣF = ma
Unit: the newton = 1kg meter/s2
Net Force
ΣF=ma
Weight
The magnitude of the force of gravity
on an object.
When the mass and acceleration due to
gravity are known, the weight of an
object can be calculated
Weight = mg
Example 1
Find the weight of a 2.25 kg bag of
sugar. What direction is the force?
Mass
There are two kinds of mass:
1. Gravitational – found on a scale or
balance
2. Inertial mass – calculated using
Newton’s 2nd law of motion
Weight and Mass
Is your weight the same everywhere in
the universe?
What about your mass?
Example 2
Roberto and Laura are studying across
from each other at a wide table. Laura
slides a 2.2 kg book toward Roberto. If
the net external force acting on the
book is 2.6 N to the right, what is the
book’s acceleration?
Newton’s Third Law
If two object’s interact, the magnitude
of the force exerted on Object #1 by
Object #2 is equal to the magnitude of
the force simultaneously exerted on
Object #2 by Object #1, and these two
forces are equal in magnitude and
opposite in direction.
Forces always exist in pairs.
Newton’s 3rd Law of Motion
F1,2 = F2,1
Action – Reaction pairs
For every action, there is an opposite
and equal reaction
Terminal Velocity
Objects reach terminal velocity in free
fall when the drag force of air
resistance (friction) equals the force of
gravity
ΣF = 0
No acceleration, therefore, constant
velocity
Uniform Motion
Terminal Velocity
Example 3
A smooth wooden block is placed on a
smooth table top. A 14.0 N force is
exerted to keep the 40.0 N block
moving at a constant velocity.
What is the coefficient of kinetic
friction?
If a 20.0 N brick is placed on top of the
block, what force will be required to
keep the block and brick system moving
at a constant velocity?
Example 4
What net force is required to accelerate
a 1500.0 kg car at +3.00 m/s2?
Example 5
An artillery shell has a mass of 55.0 kg.
It is fired and leaves the barrel with a
velocity of 770.0 m/s. The barrel is
1.50 meters long.
What is the force of the shell inside the
barrel?
Example 6
If a 10.0 kg object is on a frictionless
surface and has a 100.0 N force acting
on it, find the resulting acceleration.
If the same object rests on a rough
surface where friction will oppose
motion and the frictional force in -20.0
N. What is the acceleration now?
A Fish in the Elevator
A spring scale hangs from the ceiling of
an elevator that is not moving.
It supports a fish that weighs 25.0 N.
What upward force does the scale
exert?
What force must the scale exert when
the elevator and fish accelerate upward
at +1.50 m/s2
Example 8
A 24.0 kg crate initially at rest on a
horizontal floor requires a 75.0 N
horizontal force to set it in motion.
Find the coefficient of static friction
between the crate and the floor.
Simple Harmonic Motion
Repetitive motion
If a spring is vibrating, it has a restoring
force
A force that wants to bring it back to
equilibrium
Hooke’s Law
At equilibrium position, velocity is
reaches a maximum
At maximum displacement, spring force
and acceleration reach a maximum
In SHM, restoring force is proportional
to displacement
A stretched or compressed spring has
elastic potential energy
Formula for Hooke’s Law
F  kx
http://www.colorado.edu/physics/phet/
simulations/massspringlab/MassSpringL
ab2.swf
Example #1
A mass of 0.55 kg is attached to a
vertical spring. It stretches 2.0 cm
from equilibrium position.
What is the spring constant?
The Pendulum
For small angles, is repetitive motion
The restoring force of a pendulum is a
component of the bob’s weight
The pendulum’s motion is SHM
Gravitational potential energy increases
as the pendulum’s displacement
increases
The Pendulum
Amplitude = maximum displacement
from equilibrium
Period = the time it takes to make one
complete cycle of motion or wave
Frequency = the number of cycles in
one unit of time (usually the second)
Period and frequency are inversely
related
Period of a Pendulum
T  2
l
g
Depends on the
length of the
pendulum and
gravity
Example #2
You need to know the height of a
tower, but darkness obscures the
ceiling.
You note that a pendulum extending
from the ceiling almost touches the
floor and that its period is 12 seconds.
How tall is the tower?
Period of a mass-spring system
Depends on the
mass and the spring
constant (k)
m
T  2
k
Example #3
You have a 1275kg car, you and your
friend have a combined mass of 153 kg.
You drive over a pothole that makes
your car vibrate with a period of 0.840
seconds.
Find the spring constant of one of your
springs (shocks).