Isaac Newton (1642 – 1727): born the year Galileo died. Raised by mother and grandmother. Left school at 14 ½
to family farm. Uncle sent to Cambridge University for 5 years. London plague in 1665 so returned to mom’s farm.
Math professor at Cambridge, 1st reflector telescope, Parliament at age 46, invented calculus, Universal Law
of Gravitation, prism & light theory, master of mint, Knight by Queen Anne at 63, died at 85, buried at Westminster
Abbey.
Laws of motion overthrew Aristotle’s work, extended Galileo’s work
Ushered in the Age of Reason by showing that the universe runs according to natural, predictable laws.
NEWTON’S 1ST LAW (law of inertia)
A body at rest stays at rest and a body in motion stays in motion unless acted on by an outside force.
Inertia - an object’s resistance to change in position or motion.
Mass - a measure of the inertia of an object; indicates the actual material in a body.
Weight - a measure of the gravitational force that acts on a body.
Mass is more fundamental than weight and does not depend on location.
Weight can change. Mass stays constant
FORCES
A force is a push or a pull; there are 4 types (all are vectors)
+ forces to the right /forward
- forces to the left /reverse
1. Gravitational force – attractive force between all objects (weakest)
2. Electromagnetic force – results from electric charges; gives materials their
properties.
3. Strong nuclear force – holds particles in nucleus together (strongest)
4. Weak force – involved in radioactive decay; a form of EM force
NEWTON’S 2nd LAW
1st law deals with objects at rest or moving at a constant velocity (no net force acting on the objects)
2nd law covers more common cases in which there is a change in motion (accelerated motion)
Force causes acceleration (gravitational, or other)
F = ma m=F/a a=F/m
Acceleration – rate at which velocity is changing and/or a change in the direction of motion.
Uniform acceleration – acceleration that doesn’t change.
Average acceleration – acceleration measured over a finite time interval.
a = v = v2 – v1
unit: m / s2
slope of velocity-time graph
t
t2 – t1
Deceleration = - acceleration
Acceleration applies to changes in direction as well as changes in speed.
Acceleration is a vector and can be positive or negative.
Negative acceleration can mean either:
1) the velocity is getting lower (decelerating)
2) the object is moving in a negative direction
Initial velocity – velocity when t = 0 Acceleration – rate at which velocity is changing
and/or a change in the direction of motion.
Uniform acceleration – acceleration that doesn’t change.
Average acceleration – acceleration measured over a finite time interval.
Deceleration - negative acceleration.
Acceleration applies to changes in direction as well as changes in speed.
Acceleration is a vector and can be either positive or negative.
Negative acceleration can mean either:
1) the velocity is getting lower (decelerating)
2)
the object is moving in a negative direction
a = v
t
= v2 – v1
t2 – t1
unit: m / s2
Ex.
The velocity of a car increases from 5.0 m/s to
20.0 m/s in the time period from 2.0 s to 6.0 s. What is the average acceleration?
v1 = 5.0 m/s
t1 = 2.0 s
v2 = 20.0 m/s
t2 = 6.0 s
a=?
a = v2 – v1 = 20.0 m/s – 5.0 m/s = 15 m/s
t2 – t1
6.0 s – 2.0 s
4.0 s
a = 3.75 m/s2
Ex.
A car is moving in a negative direction and its velocity changes from – 3.5 m/s to – 11.5 m/s in
3.0 s. Find the average acceleration.
v1 = – 3.5 m/s
v2 = – 11.5 m/s
a = v = (– 11.5 m/s) – (– 3.5 m/s) = - 8.0 m/s
t
3.0 s
3.0 s
a = - 2.7 m/
t = 3.0 s
NEWTON’S 3rd LAW (action-reaction)
For every action there is an equal and opposite reaction-examples? Friction!
Weight depends on gravitational acceleration and can vary from place to place
Forces are measured in Newtons
1 N = 1 kg m/s2
Weight is a type of force; it’s also measured in Newtons; acts in a direction toward the center of Earth
W=mg
g = 9.80 m/s2
Free Fall
Galileo was the first scientist to use experiments to test hypotheses and was the first
to show that all objects fall to earth with a constant acceleration (University of Pisa).
Galileo was forced to resign from the University of Pisa and spent the last years of his life under house arrest
because his findings opposed those of Aristotle (heavier things fall faster).
Ignoring air resistance, all objects (regardless of mass) fall at the same rate, g, the acceleration due to gravity.
g = 9.80 m / s2
ON EARTH will vary with location in universe
g is an acceleration unit
vf = vi + gt
v= gt
g=v/t
Objects gain more speed during the time to drop from a great height than from a shorter height.
Non Free Fall
Non-free fall problems take place in air not in a vacuum and they deal with the difference between an object’s
weight and air resistance.
Air Resistance – force which opposes gravity
Air Resistance depends on:
1. surface area of the object
2. velocity of the object
Terminal Velocity – velocity of falling object reached when force of air resistance equals weight; Speed at
which the acceleration of a falling body is zero because friction balances the weight.
Air Resistance – friction acting on something moving through air
Friction – force that opposes motion between two surfaces that are in contact; its direction is
parallel to the surface and opposite to slipping
Static Friction – force that opposes the start of motion
Sliding Friction – force between surfaces in relative motion
Ff – frictional force
Fw - weight
Ff = FN
FN – normal force
Fa – applied force
 = coefficient of friction (MU) “meu”
FN = Fw
Fnet = Fa + Ff
Friction – force that opposes motion between two surfaces that are in contact; its direction is parallel to
the surface and opposite to motion.
Friction does not depend on area of contact.
Static Friction –force that opposes the start of motion.
Sliding Friction – force between surfaces in relative motion.
Ff – frictional force
Fa – applied force
Fa = Ff if and only if the motion is uniform and the object is horizontal
Fw - weight
FN – normal force
FN = Fw (same as above)
 = coefficient of friction ( NO UNIT)
Fnet = Fa + Ff
 = Ff / FN
Ex.
or
 = Fa / Fw
A box weighing 43.2 N is pulled horizontally until it slides uniformly over a level floor. If the
applied force is 6.30 N, what is the coefficient of friction between the box and the floor?
Fw = 43.2 N
 =?
Fa = 6.30N
FN
F
fN
Ff = Fa = 6.30
(because box slides uniformly)
 = Ff / FN
 = (6.30 N) / (43.2 N)
 = .146
Fw
Fa
Ex.
friction of
A mover pushes a 85 kg dresser across a wooden floor. The floor resists with a force of
320 N. What is the coefficient of friction between the dresser and the floor?
m = 85 kg
Ff = 320 N
=?
FN
 = Ff / FN
FN = Fw
Ff
Fw = mg
Fw = (85 kg)(9.8 m/s2)
Fw = 833 N
Fa
g = 9.8 m/s2
Fw
FN = Fw = 833 N
 = Ff / FN
 = (320 N) / (833 N)
 = .38
Ex.
Sally tries to make her 70 kg dog go into the vet’s office but it refuses to move. If the
coefficient of friction between the dog and the floor is .50, how hard must Sally push to make the dog move
with a constant speed?
m = 70 kg
 = .50
Fa = ?
FN
Fa = Ff
Ff
Fw = mg
Fw = (70 kg) (9.8 m/s2)
Fw = 686 N
Ff =  FN
Ff = (.50) (686 N)
Ff = 343 N
Fa = Ff = 343 N
Ff =  FN
FN = Fw
g = 9.8 m/s2
Fw
Fa
Newton’s Law of Universal Gravitation
Every particle in the universe attracts every other particle with a force that is directly
proportional to the product of their masses and inversely proportional to the square of the distance
between them.
F = G m1 m2
r2
F = force
m1 = mass of first object
m2 = mass of second object
r = distance between masses
G = gravitational constant
N
kg
kg
m
G = 6.67 x 10-11 N m2/kg2
Ex. Two objects are located 25 m apart. One has a mass of 18 kg and the other has a mass of 37 kg.
What is the force between the two objects?
r = 25 m
m1 = 18 kg
m2 = 37 kg
G = 6.67 x 10-11 N m2/kg2
F = G m1 m2
r2
F = (6.67 x 10-11 N m2/kg2)(18 kg)(37 kg)
(25 m)2
F = 7.12 x 10-11 N
Ex. A 45 kg object is 117 m from a second object of unknown mass. If the force between the two
objects is 8.5 x 10-11 N what is the mass of the second object?
m1 = 45 kg
r = 117 m
F = 8.5 x 10-11 N
G = 6.67 x 10-11 N m2/kg2
F = G m1 m2
r2
m2 = F r2
G m1
m2 =
=
(8.5 x 10-11 N)(117 m)2
(6.67 x 10-11 N m2/kg2)(45 kg)
1.16 x 10-6 N m2
3.00 x 10-9 N m2/kg
m2 = 387.86 kg