Physics I
Class 04
Newton’s Laws of Motion
Rev. 08-Aug-03 GB
04-1
Newton’s Laws of Motion
Isaac Newton, 1642-1727
Philosophiae Naturalis Principia Mathematica
(“Mathematical Principles of Physics”) 1687
There are three laws of motion.
They explain the motion of any object resulting from
its initial state of motion and the forces acting on it.
04-2
What is a Force?
A force is an interaction between two objects.
A force always requires two objects:
1. The target (acted upon).
2. The source (due to).
Force
Target
Source
Gravity is a familiar force.
What are the target and source objects for the force of
gravity pulling you down at this moment?
04-3
Forces Are Vectors Adding Force Vectors
To add forces, first write the individual force vectors
in component form.
In one dimension, there is only one component and
the + or – sign tells you the direction.
Add components for each dimension (X,Y,Z).
Examples (1D):
+3 N
+
+3 N
+
+3 N
=
+6 N
-3 N = 0 N
04-4
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 in motion with
constant velocity, it will continue to do so.
How does this law relate to our common experiences
with real objects in motion on the earth?
In what ways do our experiences confirm this law?
In what ways do our experiences seem to contradict
this law?
04-5
“Consider a body on which no net
force acts…”
An important word here is “net” – it means the same
as “total” or “sum of all” (forces).
This does not mean that there are no forces on the
object, only that all the forces on the object sum (as
vectors) to zero.
Example:
Your professor is standing still in front of the class.
What forces are acting on him/her?
04-6
Under the condition that no net
force acts on a body...
If the body is at rest, it will remain at rest.
(This was obvious to everyone in 1687.)
If the body is in motion with a constant velocity, it
will remain in motion with a constant velocity.
(This was not obvious to most people in 1687 –
what about today?)
What happens to a body if the net force is not zero?
What about motions where the velocity changes?
Newton’s Second Law takes care of these cases.
04-7
Newton’s Second Law
“F = ma”
The correct expression for Newton’s
 Second Law:
 

 Fnet
 F  Fnet  m a or a  m
Only forces that act on a body contribute to the net
force on the body.
Forces exerted by the body (as a source) on other
bodies do not count in Newton’s Second Law.
The net force and acceleration are always in the same
direction because m is a positive number.
04-8
Using Newton’s Second Law to
Solve Problems
1.
2.
3.
4.
5.
6.
Identify all forces acting on the object.
Pushes or Pulls
Friction (if specified)
Gravity
Normal (Surface) Forces
Choose a coordinate system.
If you know the direction of acceleration, one
coordinate axis should be in that direction.
Draw a “Free-Body Diagram.”
We will show you how in the next slide.
Express the force vectors in components.
This may require trigonometry (later).
Use Newton’s Second Law to write one
equation for each direction considered.
We will do 1D today, 2D later.
Solve the equation(s).
04-9
Free-Body Diagrams
1.
2.
3.
4.
Draw the object as a box or a circle, detached
from everything else. (“free-body”)
Draw and label the force arrows acting on the
object, with all tails on the object. The arrows
should point in the correct directions relative to
your choice of coordinate system. If you have
some indication of the relative magnitudes of
the forces, you can adjust the lengths of the
arrows, but that is not critical.
It helps to put the coordinate axes in the
diagram to remember which direction is +.
It helps if you know the direction of
acceleration to align it with the + direction of
one of the axes.
a
Y
X
N
F
P
W = mg
04-10
Example Problem in 1D
An Elevator Going Down
Consider an elevator moving downward and speeding
up with an acceleration of 2 m/s2. The mass of the
elevator is 1000 kg. Ignore air resistance. What is
the tension in the elevator cable?
1.
Forces: Weight (W) down and Tension (T) up.
2.
Coordinates: +X down. (Why?)
3.
Free-body diagram:
4.
X Components: (W) and (–T). (Why – for T?)
5.
Second Law: (W) + (–T) = m a.
6.
Solve: T = W – m a = m g – m a = m (g–a)
T = 1000 (9.8–2) = 7800 N.
a
X
T
W = mg
04-11
Newton’s Third Law:
“Action and Reaction”
“For every action, there is an equal and opposite reaction.”
What does that mean?
It means that forces always occur in pairs. If object A is the
target (acted upon) of a force whose source (due to) is object
B, then there is another force vector with the same length but
opposite direction on B due to A.
F on A from B
Object A
F on B from A
Object B
04-12
Newton’s Third Law Pairs:
How to Recognize Them
A pair of forces qualifies as a Newton’s Third Law Pair if (all of)
1.
2.
3.
They act on two different objects.
They are the same type of force.
Each object is a target for one force and a source for the other.
A pair of forces is not a Newton’s Third Law Pair if (any of)
1.
2.
3.
They act on the same object.
They are two different types, like normal force and gravity.
They are only equal and opposite for a certain combination of
accelerations and/or other conditions in the problem.
04-13
Class #4
Take-Away Concepts
1.
2.
3.
Newton’s First Law: Nonet force, no change in motion.

Newton’s Second Law: Fnet  m a
Newton’s Third Law: All forces come in pairs.
4.
Solve force/acceleration problems with Newton’s
Second Law and free-body diagrams.
04-14
Class #4
Problems of the Day
_______1. You are pushing a sled on smooth ice (in one dimension),
wearing spiked shoes so that you do not slip. The friction of the
sled on the ice can be neglected. Which of the following motions,
if any, is possible during a two-second time interval in which you
are pushing the sled with a constant force?
A)
B)
C)
D)
E)
F)
G)
The sled moves at a constant speed, not zero.
The sled starts at rest (zero speed) and remains motionless.
The acceleration of the sled changes.
The sled speeds up, then slows down.
The sled slows down, then speeds up.
More than one of the above is possible.
None of the above is possible.
04-15
Answer to Problem 1 for Class #4
The answer is E.
Motions A and B violate Newton’s First Law (net force is not zero).
Motion C violates Newton’s Second Law (net force is constant).
Motion D is not possible because if the sled is speeding up, that means its
velocity and acceleration are in the same direction. It has to keep speeding
up because the velocity cannot change direction.
Motion E seems at first to be impossible. However, if the sled is slowing
down, that means its velocity is in the opposite direction as its acceleration.
Eventually, it will slow to zero speed, then reverse its direction. Once its
velocity is in the same direction as its acceleration, it will speed up. This
motion is possible depending on the force and initial velocity.
04-16
Class #4
Problems of the Day
_______2. Which of the following are Newton’s Third Law Pairs?
A) Your weight and the normal force of the seat holding you up.
B) The tension in a yo-yo string and the force of gravity pulling the
yo-yo down.
C) The force of your finger pushing on a cart on a frictionless track
and the mathematical expression: –(m a), where m is the mass of
the cart and a is the acceleration of the cart.
D) The force of your feet pushing against the ground with 3 N in the
north direction and a 3 N force of the wind pushing you south.
E) All of the above.
F) None of the above.
04-17
Answer to Problem 2 for Class #4
The answer is F.
In case A, gravity and normal force are two different types of forces and
they are not always equal. (What if you were sitting in an elevator?)
Case B also has two different forces which are not always equal (the yo-yo
can accelerate up or down). In many yo-yo tricks, the string isn’t vertical,
so tension and gravity aren’t even in opposite directions.
In case C, the mathematical expression of –(m a) is not a physical force.
In addition, if your finger is pushing at an angle, force and –(m a) are not
even numerically equal.
In case D, the forces are equal and opposite but they are different and not
on the same pair of objects. One pair is your feet and the ground, the other
is the wind (air molecules) and your body.
04-18
Activity #4
Newton’s Laws in 1D
Objectives of the Activity:
1.
2.
3.
More experience with LoggerPro and taking data.
Investigate Newton’s Second Law –
Do the force and acceleration always point in the same direction?
How does the formula work out for real objects?
Explore the relationship between the direction of velocity and the
direction of acceleration in terms of speeding up and slowing down.
04-19
Class #4 Optional Material
Are Newton’s Laws True?
It’s been over 300 years since Newton published Principia Mathematica.
How have his laws done since then?
The First Law is still doing fine. In modern times, many types of very lowfriction motion (space travel, magnetic bearings, air hockey tables, etc.) make
this notion more intuitively appealing than in the past.
The Third Law is also doing fine. All forces currently known to physics
obey this law. Any force not obeying this law would cause big problems in
physics, like getting free mechanical energy from nothing.
However, the Second Law in the form we learn it in Physics I is not exactly
correct. Where did Newton go wrong?
04-20
Where Did Newton Go Wrong?
Albert Einstein (1879–1955)
Newton defined time and space as follows:
“Absolute, true, and mathematical time, of itself and from its own
nature, flows equably without relation to anything external…”
“Absolute space, in its own nature, without relation to anything external,
remains always similar and immovable.”
At the beginning of the 20th century, Albert Einstein showed that these
definitions were inconsistent with the observed properties of
electromagnetic waves (light) and electromagnetic interactions with
moving bodies. This was the basis of his Special Theory of Relativity.
04-21
If the Second Law isn’t true,
why do we still use it?
The Second Law is true to a very good approximation when dealing with
velocities much less than the speed of light. For most calculations
involving ordinary objects, it is close enough for practical purposes.
“Disintegration of the Persistence of
Memory” by Salvador Dalí, 1931
Art inspired by the
Theory of Relativity?
04-22