Ch. 9 Motion Describing Motion Motion Speed & Velocity Acceleration.
Ch. 4, Motion & Force: DYNAMICS
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Transcript of Ch. 4, Motion & Force: DYNAMICS
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Ch. 4, Motion & Force: DYNAMICS
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Force
Obviously, vector addition is needed to add forces!
A Force is “A push or a pull” on an object. Usually, for a force, we use the symbol F. F is a VECTOR!
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Classes of Forces “Pulling” forces“Contact” Forces:
“Pushing” forces
“Field” Forces:
Physics I: Gravity Physics II: Electricity & Magnetism
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• Contact Forces involve physical contact between two objects– Examples (in the pictures): spring forces,
pulling force, pushing force
• Field Forces act through empty space.– No physical contact is required.– Examples (in the pictures): gravitation,
electrostatic, magnetic
Classes of Forces
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• Gravitational Forces– Between objects
• Electromagnetic Forces– Between electric charges
• Nuclear Weak Forces– Arise in certain radioactive decay processes
• Nuclear Strong Forces– Between subatomic particles
Note: These are all field forces!
The 4 Fundamental Forces of Nature
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The 4 Fundamental Forces of NatureSources of the forces: In the order of decreasing strength
This table shows details of the 4 Fundamental Forces of Nature, & their relative strength for 2 protons in a nucleus.
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Sir Isaac Newton1642 – 1727
• Formulated the basic laws of mechanics.
• Discovered the Law of Universal Gravitation.
• Invented form of Calculus• Made many observations
dealing with light & optics.
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Newton’s Laws of Motion • The ancient (& wrong!) view (of Aristotle):
– A force is needed to keep an object in motion.– The “natural” state of an object is at rest.
• THE CORRECT VIEW (of Galileo & Newton):– It’s just as natural for an object to be in motion at constant speed in a
straight line as to be at rest.– At first, imagine the case of NO FRICTION– Experiment: If NO NET FORCE is applied to an object moving at a
constant speed in straight line,it will continue moving at the same speed in a straight line!
– If I succeed in having you overcome the wrong, ancient misconception & understand the correct view, one of the main goals of the course will have been achieved!
In the 21st Century, this is still a common
MISCONCEPTION!!!
Proven by Galileo in the 1620’s!
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Newton’s Laws• Galileo laid the ground work for Newton’s Laws.
• Newton: Built on Galileo’s workNow, Newton’s 3 Laws, one at a time.
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Newton’s First Law
• Newton’s First Law (The “Law of Inertia” ):“Every object continues in a state of rest or uniform
motion (constant velocity) in a straight line unless acted on by a net force.”
Newton wasborn the sameyear Galileo
died!
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Newton’s First Law of MotionInertial Reference Frames
Newton’s 1st Law: •Doesn’t hold in every reference frame. In particular, it doesn’t work in such a reference frame that is accelerating or rotating.
An Inertial Reference frame is one in which Newton’s first law is valid.
•This excludes rotating & accelerating frames.•How can we tell if we are in an inertial reference frame?
By checking to see if Newton’s First Law holds!
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Newton’s 1st Law• Was actually stated first stated by Galileo!
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Newton’s First Law(Calvin & Hobbs)
A Mathematical Statement of Newton’s 1st LawIf v = constant, ∑F = 0
ORif v ≠ constant, ∑F ≠ 0
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Conceptual Example 4-1:
Newton’s First Law.
A school bus comes to a sudden stop, and all of the backpacks on the floor start to slide forward.
What force causes them to do this?
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• In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest & an object in motion continues in motion with a constant velocity– Newton’s 1st Law describes what happens in
the absence of a net force.– It also tells us that when no force acts on an
object, the acceleration of the object is zero.
Newton’s First LawAlternative Statement
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Inertia & Mass• Inertia The tendency of a body to maintain its state
of rest or motion.• MASS A measure of the inertia of a body.
– The quantity of matter in a body.– The SI System quantifies mass by having a standard mass
= Standard Kilogram (kg)(Similar to the standards for length & time).
– The SI Unit of Mass = The Kilogram (kg)• The cgs unit of mass = the gram (g) = 10-3 kg
• Weight is NOT the same as mass!– Weight is the force of gravity on an object.
• Discussed later in the chapter.
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Newton’s Second Law (Lab)• Newton’s 1st Law: If no net force acts, an object
remains at rest or in uniform motion in straight line.• What if a net force acts? That question is answered by doing
Experiments.• It is found that, if the net force ∑F 0
The velocity v changes (in magnitude, in direction or both).
• A change in the velocity v (Δv). There is an acceleration a = (Δv/Δt) OR
A net force acting on a body produces an acceleration! ∑F a
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Newton’s 2nd LawExperiments Show That:
The net force ∑F on a body & the acceleration a of that body are related.
• How are they related? Answer this by doing more
EXPERIMENTS! – Thousands of experiments over hundreds of years find
(for an object of mass m): a ∑F/m (proportionality)
• The SI system chooses the units of force so that this is not just a proportionality but an
Equation: a ∑(F/m) OR (total force!)
Fnet ∑F = ma
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Newton’s 2nd Law: Fnet = maFnet = the net (TOTAL!) force acting on mass m
m = mass (inertia) of the object. a = acceleration of the object.
OR, a = a description of the effect of F. OR, F is the cause of a.
• To emphasize that F in Newton’s 2nd Law is the TOTAL (net) force on the mass m, your text writes:
∑F = ma
∑ = a math symbol meaning sum (capital sigma)
The Vector Sumof all Forces on mass m!
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• Newton’s 2nd Law: ∑F = ma
A VECTOR Equation!! It holds component by component.
∑Fx = max, ∑Fy = may, ∑Fz = mazll
THIS IS ONE OF THE MOST FUNDAMENTAL & IMPORTANTLAWS OF CLASSICAL PHYSICS!!!
Based on experiment! Not derivable mathematically!!
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Summary
• Newton’s 2nd Law is the relation between acceleration & force.
• Acceleration is proportional to force and inversely proportional to mass.• It takes a force to change either the direction of
motion or the speed of an object. • More force means more acceleration; the same force exerted
on a more massive object will yield less acceleration.
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Now, a more precise definition of Force: Force An action capable of accelerating an object. Force is a vector & is true along each coordinate axis.
The SI unit of force is The
Newton (N) ∑F = ma, unit = kg m/s2
1N = 1 kg m/s2
NoteThe pound is a unit of force, not of mass, & can therefore be equated to Newtons but not to kilograms.
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Laws or Definitions?
These are NOT Laws!
This is based onexperiment!
Not on math!!
• When is an equation a “Law” & when is it just an equation?Compare
• The one dimensional constant acceleration equations: v = v0 + at, x = x0 + v0t + (½)at2, v2 = (v0)2 + 2a (x - x0)
These are nothing general or profound. They are valid for constant a only. They were obtained from the definitions of a & v!
With ∑F = ma. • This is based on EXPERIMENT. It is NOT derived
mathematically from any other expression! It has profound physical content & is very general.
It is A LAW!!Also it is a definition of force!
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ExamplesExample 4-2:
Estimate the net force needed to accelerate (a) a 1000-kg car at a = (½)g
(b) a 200-g apple at the same rate.Example 4-3:
Force to stop a car. What average net force is required to bring a 1500-kg car to rest from a speed of 100 km/h (27.8 m/s) within a distance of 55 m?