Download Physics for the Sciences 07:150:193 Fall 2003

Newtonian DYNMICS
(NewtoN’s Laws)
Corresponding Activities:
Discuss Forces
Complete Worksheet
Isaac Newton’s work represents one of the greatest contributions to
science ever made by an individual. Most notably, Newton derived the
law of universal gravitation, invented the branch of mathematics
called calculus, and performed experiments investigating the nature
of light and color.
Lecture Outline and Outcomes
Lecture outline:
Lecture outcomes:
• You will learn how to:
• Comparison between
kinematics and dynamics as
– Identify and denote forces acting on an
object
the branches of physics
(mechanics)
– Draw a Free Body Diagram (FBD)
– Use a FBD to write an equation of
• The Language of Dynamics
motion
• Description of interaction
• You will understand the meaning of
between the objects
Newton’s 1st and 2nd laws:
st
• Newton’s 1 law: the Law of
– via making everyday life connections
Inertia
– Via doing testing experiments (making
• Newton’s 2nd law: cause and
predictions)
effect law
• You will practice problem solving applied
• Application of Newton’s laws
to:
to problem solving
st
nd
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– Applications of Newton’s 1 and 2
laws of motion.
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I. Observations: Newtonian Dynamics
• Goal: Description of motion
• Questions answered by Kinematics:
– How far? How fast? How long does it take? When (i.e. meeting time and
place)? Where is an object going to be at a certain time?
• Questions answered by Dynamics:
– Why is the object moving in a certain way? What causes the object to
change its velocity? How the interaction between objects influence their
motion?
• Dynamics studies motion at a deeper level than kinematics: it
studies the causes of changes in objects’ motion!
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The Language of Dynamics
• Force: The measure of interaction between two objects
(pull or push). It is a vector quantity – it has a
magnitude and direction, the unit of force is Newton, N
• Mass: The measure of how difficult it is to change
object’s velocity (sluggishness or inertia of the object). It
is a scalar. SI unit of mass is a kilogram, kg
• Weight: The force the Earth is pulling the object with.
Weight is a vector quantity, it has a magnitude and
direction, the unit of weight is Newton, N
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A Force as an Interaction Between Two Objects
The Meaning of a Net Force:
One object can interact with many. So many
forces can be exerted on it. Right now, at
least 2 forces are acting on you: the Earth is
pulling you downwards and a chair pushing
you upwards.
A spring scale shows the strength of
the interaction between the Earth and A NET FORCE (Fnet) is a resultant force
the object. The stronger the
acting on an object. To find the resultant
interaction is, the more it stretches!
The force of attraction between the force (Fnet) you have to add up all the
Earth and the object is called
forces acting on an object. (Remember,
WEIGHT of the object. We can
forces are vector, so take into account their
measure weight in lbs or in Newtons:
Created by Dr. Marina
Milner-Bolotin
Lecture #7
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directions
& magnitudes)
1 lbs5/22/2017
= 4.45 N
PRS 7-1: Figuring out the Net Force
Find magnitude and direction of the net force acting on
an object of mass m. Explain your answer.
1. 1 N North-East
3N
2. 3 N North
3. 4 N East
4N
4. 5 N East
N
m
5. 5 N North-East
W
E
6. 7 N North-East
S
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Newton’s 1st Law: The Law of Inertia
1. An object at rest remains at rest as long as no Fnet acts on it
2. An object moving with constant velocity continues to
move with the same speed and in the same direction (the
same velocity) as long as no net force acts on it
3. Every object continues in its state of rest, or uniform
motion in a straight line, unless it is compelled to change
that state by unbalanced forces impressed upon it
4. Inertia is a property of objects to resist changes is motion!
An additional force is NOT
required to keep a cart moving
with a constant speed on a
frictionless track!
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Why Is the 1st Law So Important?
1. The 1st law holds true only in the non-accelerating
reference frames which will be called INERTIAL
REFERENCE FRAMES (IRF)
2. Newton’s laws work only in IRF, for other frames of
reference modifications must be made!
3. For instance, an accelerating car or train or elevator are not
an IRF (think why you need seat belts in your car!)
4. Our Earth is not an exactly IRF due to its rotation and
annual motion. However, we will treat the Earth as an IRF!
For the experimental accuracy we need, this approximation
is good enough!
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PRS 7-2: Newton’s 1st Law
In which of the following cases a net force acting on an
object (Fnet) is zero? Explain.
1. You are speeding up from 50 km/h to 65 km/h
2. You are slowing down from 65 km/h to 55 km/h
3. You are turning left at constant speed of 25 km/h
4. You are making a U-turn at constant speed of 15 km/h
5. You are turning right while slowing down from 50 km/h to
30 km/h
6. None of the above
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Newton’s 2nd Law: Cause & Effect Law
1. Only unbalanced forces cause object to accelerate.
2. An object of mass m has an acceleration a, equal to
the net force SF, divided by the mass of the object, m.

F


Fnet
a


m
m


Fnet  ma
 m
1N   1kg 1 2 
 s 
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Drawing Free Body Diagram - FBD
F table on book
Denoting forces:
A force has to have:
 a magnitude and
direction (an arrow);
 two indices:
F Earth on book
F Earth on Dr. M
F Dr. M on the floor
F chair on your …
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Physics Problem Solving Tips
Problem solving
tips:
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1.
Sketch the forces
(indices!)
2.
Choose a system
(object) of interest
3.
Choose and draw
a coordinate
system
4.
Resolve the
forces into
components
5.
Write the
equations
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Bridging Kinematics and Dynamics
Kinematics
Question - Quantity
Where? - Position
When? - Clock reading
For how
long?
- Time interval
How
fast?
- Velocity, speed,
Acceleration
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Dynamics
Question - Quantity
How much matter? - Mass
How strong is the
interaction?
- Force
What is the
effect of the
interaction?
- Acceleration
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Example 1: Braking Force (1-D case)
A twenty-ton-train cart is moving at 60 mi/h (27 m/s). What
braking force is needed to stop the cart in 50 meters?
Given:
v0= 60 mi/h
vf = 0 mi/h
v = 60 mi/h = 27 m/s
Dx = 50 m
Force - ?
50 m
x
Notice, during the exam you will need to know how to convert
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by Dr.
Marina Milner-Bolotin
Lecture conversions!
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km/h or mi/h into
m/s.
Please
practice your
Detailed Solution


Fnet  ma
F  ma
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We know the mass of the cart but how can we
find its acceleration? To find acceleration we
have to use our knowledge of kinematics. If we
know the stopping distance and the initial
velocity, we can find acceleration!
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References and HW Resources:
•
Chapter 4, textbook: Physics by D. Giancoli
•
Related activities: Tutorial 3, HW Problems posted on the
website: Set 3.
•
Use ActivPhysics software (www.aw.com/young11) and sign
up for Mastering Physics (www.masteringphysics.com) if you
want to practice more and get instantaneous feedback.
•
Voltaire’s (1694-1778) letters on Newton:
http://www.fordham.edu/halsall/mod/1778voltairenewton.html
•
Isaac Newton: http://www.newton.cam.ac.uk/newtlife.html
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