Download NEWTON'S LAWS OF MOTION

NEWTON’S LAWS
of
MOTION
NEWTON'S LAWS OF MOTION
There are three of them.
They explain the motion of an object as
resulting from the forces acting on the object.
What is a force?
An interaction between TWO objects.
For example, pushes and pulls are forces.
We must be careful to think about a force as
acting on one object
from (or due to ) another object.
Adding Forces
 Forces are vectors (They have both magnitude and
direction) and so add as follows:
 In one dimension, note direction using a + or – sign
then add like scalar quantities (regular numbers with
no direction associated with them)
 Examples:
+3 N
+
+3 N
+
+3 N
=
-3 N
0N
=
+6 N
Newton’s First Law
Consider a body on which no net force acts. If
the body is at rest, it will remain at rest. If the
body is moving with constant velocity, it will
continue to do so.
“Consider a body on which no net
force acts…”
 An important word here is NET. It means “total”
or “sum of all” (forces).
 It is not that no force at all can act on the body. It
is just that all the forces must add to zero (cancel
each other out).
Under this condition
(no net force is acting on the body):
•If the body is at rest, it will remain at rest.
•If the body is moving with constant
velocity, it will continue to do so.
What if the body is moving with a velocity which is
not constant? Why isn’t this discussed?
Newton’s Second Law
in One Dimension
Commonly shortened to “F=ma”.
Correctly, it is :



 F  ma,
 F
a
m
Only forces which act on that object affect the
acceleration of the object.
Forces exert by the object on another object do not.
Using Newton’s 2nd Law to
Solve Problems
1. Identify all forces acting on the object
-Pushes or Pulls
-Frictional forces -Tension in a string
-Gravitational Force (or weight = mg where g is 9.8 m/s2)
- “Normal forces” (one object touching another).
2. Draw a “Freebody Diagram”
-draw the object, show all forces acting on that object as vectors
pointing in the correct direction. Show the direction of the
acceleration.
3. Chose a coordinate system.
4. Translate the freebody diagram into an algebraic expression based on
Newton’s second law.
Consider an elevator moving downward and speeding
up with an acceleration of 2 m/s2. The mass of the
elevator is 100 kg. Ignore air resistance.
What is the tension in the cable?
1. Identify Forces: Tension in cable, weight of the
elevator
v 2. Draw freebody diagram
T
a
W=Fg earthelevator.
Note: No
negative
sign
3. Chose coordinate system: Let up be the +y
direction and down –y. Then :
4. Translate the FBD into an algebraic expression. TW = m(-a) so
T-(100 kg)(9.8 m/s2) = (100 kg)(-2 m/s2)
Newton’s Third Law
Whenever one object (object A) exerts a force on
another object (object B), the second object exerts a
force back on the first object.
These forces are ALWAYS equal in magnitude (but
they point in opposite directions).
Such forces are called “Newton’s third law force
pairs”.
Not all forces that are equal and opposite are third
law force pairs.
The forces are on different bodies, so do not add to
zero.
First Example of 3rd Law
A horse harnessed to a cart
exerts an equal and
opposite force to the cart
as it exerts a force against
the ground.
Second Example of 3rd Law
Space shuttle’s rocket
boosters propel the
orbiter into space by
exerting an equal and
opposite force to
exhaust gasses.
Concept Question 1
Why are we able to
walk?
Concept Question Answer
Force exerted
by the person’s
foot on the
ground. Fpg
Fgp=-Fpg
We walk forward
because when one foot
pushes backward
against the ground, the
ground pushes forward
on that foot.
Force exerted by the ground
On the person’s foot. Fgp
Concept Question 2
What makes a car go
forward?
Concept Question answer
By Newton’s third law,
the ground pushes on
the tires in the
opposite direction,
accelerating the car
forward.
Concept Question
Which is stronger, the
Earth’s pull on an
orbiting space shuttle
or the space shuttle’s
pull on the earth?
Concept Question Answer
According to Newton’s Third
Law, the two forces are equal
and opposite. Because of the
huge difference in masses,
however the space shuttle
accelerates much more towards
the Earth than the Earth
accelerates toward the space
shuttle.
a = F/m
Problem 1
What force is needed to
accelerate the 60 kg
cart at 2m/s^2?
How to solve Problem 1
What force is needed to accelerate the
60kg cart at 2 m/s^2?
Force = mass times
acceleration
F=m*a
F = 60kg * 2m/s^2
F = 120kgm/s^2
Kgm/s^2 = Newton
Newton = N
F =120 N
Problem 2
A force of 200 N
accelerates a bike and
rider at 2 m/s^2. What
is the mass of the bike
and rider?
How to solve Problem 2
 A force of 200 N accelerate a bike
and rider at 2m/s^2. What is the
mass of the bike and rider?
F = ma therefore:m =F/a
m = 200N/2m/s^2
N= kgm/s^2 so when divide
your answer will be kg
left.
m = 100kg