What causes acceleration?
straight line
(line of site)
the monkey begins to fall ad the
precise moment when the ball
leaves the barrel of the gun
The ball and the
monkey arrive at
the point marked
by the red
dot at the
same
time
path of
bullet
path of monkey
What causes acceleration?
Analysis
Object
monkey
ball
First, imagine what would happen in the absence of gravity
External Influence
none
none
Motion
“floats” in place
straight line with constant speed
Result: ball hits monkey
Object
monkey
ball
External Influence
gravity
gravity
Motion
uniform acceleration toward ground
sideways at constant speed + downward
with uniform acceleration
Result: ball hits monkey
It’s very useful to consider motion without the effects of gravity!
What causes acceleration?
Aristotle: forces cause velocities
Galileo: “external influences”
Newton: “unbalanced force”
For now we define force according to its effect on the motions of things
-the operational definition we find is concisely expressed by three (3) simple
rules
First we examine how forces act – then we look at a restatement of the rules
Preliminary Issue: mass, weight and what they mean to freely falling monkeys
Mass
1. a measure of how much matter is in an object.. literally
proportional to the number and size of atoms in the object
2. a measure of the internal resistance of an object to a change in
its motion…perhaps you could think of it as a measure of the
objects “desire” to remain in motion at a constant speed in a
straight line.
What causes acceleration?
Mass
* mass is an intrinsic property of an object – to change the mass of an
one must make a change (physical, chemical, or nuclear) in the object
* in order to make two objects accelerate at the same rate one must
pull or push harder on the more massive object
In the monkey demonstration (and in Galileo’s law of falling) we observe that
objects under the influence of gravity alone fall with equivalent rates of
acceleration
object
monkey
ball
grain of sand
dump truck
External Influence
force of gravity (weight of monkey)
force of gravity (weight of ball)
weight of grain of sand
weight of dump truck
Acceleration
10 m/s2
10 m/s2
10 m/s2
10 m/s2
let’s look at this…………….
What causes acceleration?
object
resistance to acceleration
External Influence
Acceleration
monkey
mass of monkey
weight of monkey
10 m/s2
ball
mass of ball
weight of ball
10 m/s2
grain of sand
mass of grain of sand
weight of grain of sand
10 m/s2
dump truck
mass of dump truck
weight of dump truck
10 m/s2
external influence
on the stuff
acceleration of
the stuff
(the motional
reaction)
amount of stuff
• Conclusion: There must be a direct proportionality between weight and mass
more mass
greater influence
of weight force
but, same
acceleration!!
What causes acceleration?
By analyzing free-fall we conclude that:
Force
 acceleration
mass
AND that the weight force is proportional to the mass:
weight  mass
twice as much
mass
mass
weight
twice as much
weight
m weight 2  weight
10 2 

s
mass
2  mass
same
ratio
What causes acceleration?
The genius of Newton and the power of explanation
Newton: gravity is only one type of force (what about friction, pushing
pulling, electric attraction or repulsion…)
gravity is “special” in the sense that gravitational force (a.k.a. weight) is
proportional to mass
Nevertheless, whenever any net force acts upon any mass to cause any
acceleration, the rule is:
NET FORCE = MASS X ACCELERATION
F
=
m
the meaning of “net” force:
IF:
(F3 = F4) F2 > F1
(F3 = F4) F1 > F2
(F3 = F4) F1 = F2
NOW YOU TRY!!
a
F3
F2
another
force
exerted on the
object
an object
acceleration
4
to the right
to the left
none (i.e. straight line at constant speed)
F1
a force
exerted
on the
object
Net Force
When forces balance, there is equilibrium.
F1
F2
Bo
Diddley
F1 = Force felt by Bo because of Diddley.
F2 = Force felt by Diddley because of Bo.
F1 = F2
What causes acceleration?
Force is a vector quantity!
TOTAL
NET FORCE
ON AN
OBJECT
MASS
OF THE
OBJECT
=
expressed in
“Newton's”
[N]
mass
F1
expressed in
“kilograms”
[kg]
X
ACCELERATION
OF OBJECT CAUSED
BY NET FORCE
expressed in
“meters per second, per
second”
m/s2
say F1 > F2 then
F2
(F1 – F2) = mass x acceleration = ma
acceleration for F1 > F2
What causes acceleration?
The “Newton” is the standard measure of force in the system we use.
Push on a 1 kilogram MASS with a FORCE of 1 Newton then the object will
ACELLERATE at a rate of 1 m/s2 in the direction of the force….provided that
the force is not “balanced” by another force on the object.
mass acceleration
If your body contains 75 kg of mass
then…
on earth you weigh (force) about 75kg X 10 m/s2 = 750 Newtons
Some examples
1.
Mass and weight
(a) in free-fall on Earth
net force = mass X acceleration
m
W  10 kg    10 2 
 s 
W  100 Newtons
acceleration = 10 m/s2
10 kg
weight
a 10 kilogram block has a weight on
Earth of 100 N!
acceleration = 10 m/s2
1 kg
weight
m
W  1 kg    10 2 
 s 
W  10 Newtons
1 kg weighs 10 Newtons on Earth
Convert to lbs= 1 kg weighs about 2.2 lbs
F = contact force exerted
by table on the block
2. sitting on a table on Earth
What forces are acting on the apple?
1 kg
Net force
= mass X acceleration
upward
F–W
=
1 kg X 0 m/s2
F–W
=
0 Newtons
W = weight force exerted by the
Earth on the apple
for the acceleration to be equal
to zero the forces must be
balanced
If two forces act in opposite directions, the net force is in
the direction of the larger force and is equal to the
F = W = 1 Newton
difference between the larger and smaller force
Fair = force of air resistance
exerted BY air on block
3. skydiving
10 kg
acceleration
W = weight force exerted by
Earth ON block
If Fair = 60 Newtons at what rate does the block accelerate?
1.
First find the “NET FORCE” : W-Fair
What’s the weight? W = mass X g = 10 kg X 10 m/s2 = 100 N
NET FORCE = 100 N – 60 N = 40 N
2.
NET FORCE = MASS X ACCELERATION
40 N
= 10 kg X ACCELERATION
3.
Solve for acceleration:
Acceleration 
Net Force 40N

 4m 2
s
Mass
10kg
Terminal velocity – The speed at which air resistance (aka drag) matches the
pull of gravity,resulting in a constant fall rate.
What is the net force on a skydiver as she falls at terminal speed?
NET FORCE = MASS x ACCELERATION
Fait – W = M x A
Fait – W = M x 0 = 0
Fait – W = 0
Fair = force of air resistance
exerted BY air on block
40 kg
acceleration = 0
W = weight force exerted by
Earth ON block
What is the force of air resistance on a skydiver whose mass is 40 kilograms when
she falls at terminal speed?
NET FORCE = ZERO
Fait – W = 0
Fair = W = 40kg X 10 m/s2
Laws of Motion
1. Newton’s 1st Law: An object at rest, remains at rest, OR if in motion,
travels in a straight line at constant velocity, UNLESS acted on by a net
force.
Laws of Motion
2. Newton’s 2nd Law: For a body having constant mass, M, the NET FORCE
APPLIED to the body, the Mass of the body, and the observed
Acceleration of the body are related by:
FORCE = MASS X ACCELERATION
F = MA
A 2 kg mass is acted on by a 2 N force. What is its acceleration?
a = 2 N / 2 kg
F = 2N
= 1 m/s2
2 kg
What if a 0.5 N frictional force was also in place?
a = (2 - 0.5 N)/2 kg
= 0.75 m/s2
F = 2N
2 kg
f = 0.5 N
Laws of Motion
3.
Newton’s 3rd Law: For every action there is an equal and opposite
reaction. – rule of force pairs
•
•
Objects can not act on one another without being acted upon.
When you strike a wall, does it hurt your hand? You might say the wall
struck you. Newton would say the force you applied to the wall was the
same as that which the wall applied to you. The wall is bigger and more
massive, therefore has more inertia and was not harmed as much as you.
If you push on a wall, the wall pushes
back on you. It does so with a force
equal in strength to the one you
exert on it!
frictional force
from wall
Reaction
force
from
wall
Applied
Force
“Pushing”
Weight
The “rule of force pears”
For every force exerted ON an object, the object exerts an equal and
oppositely directed force ON its environment
Force on Rock from Earth = Force on Earth from Ball
a = F/m = g
a = F/m
Rock acceleration
Earth’s acceleration
Gravity
Gravity
contact force exerted
by table on the apple
contact force
exerted by the
apple on the table
force of Earth on
the apple
force of apple
on the Earth