newton’s laws of motion - university of texas at...

Newton’s Laws of Motion

Monday, September 26, 11

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

Introduction• We’ve studied motion in one, two, and

three dimensions… but what causes motion?

• This causality was first studied in the late 1600s by Sir Isaac Newton.

• The laws are easy to state but intricate in their application.

• All around us we see Newton’s laws in action. Easier than reading The Principia!



Introduction• We’ve studied motion in one, two, and

three dimensions… but what causes motion?

• This causality was first studied in the late 1600s by Sir Isaac Newton.

• The laws are easy to state but intricate in their application.

• All around us we see Newton’s laws in action. Easier than reading The Principia!

“If I have seen further, it is by standing on the shoulders of giants.”


Copyright © 2010 Pearson Education, Inc.

Force and Mass

Force: push or pull

Force is a vector – it has magnitude and direction



Force and Mass

Mass is the measure of how hard it is to change an object’s velocity.Mass can also be thought of as a measure of the quantity of matter in an object.



What are the properties of force(s)?

• Combinations of “push” and “pull”



There are four common types of forces

• The normal force—When an object rests or pushes on a surface, the surface pushes back.

• Frictional forces—In addition to the normal force, surfaces can resist motion along the surface.



There are four common types of forces

• Tension forces—When a force is exerted through a rope or cable, the force is transmitted through that rope or cable as a tension.

• Weight—Gravity’s pull on an object. This force can act from large distances.



How to denote a force

• Use a vector arrow to indicate magnitude and direction of the force.



Use the net (overall) forceSeveral forces acting on a point have the same effect as their vector sum acting on the same point.



Decomposing a force into components• Fx and Fy are the parallel and perpendicular components of a

force to a sloping surface.

• Use F*Cosθ and F*Sinθ operations to find force components.



Notation and method for the vector sum

• We refer to the vector sum or resultant as the “sum of forces” R = F1 + F2 + F3 … Fn = ΣF.

• Use Tanθ = Ry/Rx and R = (Rx2 + Ry

2)1/2.



Superposition of forces

• Adding all x components and all y components allows you to add many vectors. This example has three.



Newton’s First Law of Motion




If you stop pushing an object, does it stop moving?





Only if there is friction!






In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest.






In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest.This is also known as the law of inertia.



Newton’s First Law




• Simply stated—“objects at rest tend to stay at rest, objects in motion stay in motion.”

• More properly, “A body acted on by no net force moves with constant velocity and zero acceleration.”


First law: Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force.

This means that in the absence of a non-zero net force, the center of mass of a body either remains at rest, or moves at a constant speed in a straight line.


http://en.wikipedia.org/wiki/Velocity

http://en.wikipedia.org/wiki/Velocity

http://en.wikipedia.org/wiki/Net_force


http://en.wikipedia.org/wiki/Center_of_mass

http://en.wikipedia.org/wiki/Center_of_mass

http://en.wikipedia.org/wiki/Physical_body

http://en.wikipedia.org/wiki/Physical_body

http://en.wikipedia.org/wiki/Speed

http://en.wikipedia.org/wiki/Speed



The figure shows an unbalanced force causing an acceleration and balanced forces resulting in no motion.



Inertial frames of reference

When a car turns and a rider continues to move, the rider perceives a force.



Newton’s Second Law of MotionExample of a free-body diagram:



Newton’s Second Law of MotionTwo equal weights exert twice the force of one; this can be used for calibration of a spring:



Newton’s Second Law of Motion

Now that we have a calibrated spring, we can do more experiments.

Acceleration is proportional to force:




Acceleration is inversely proportional to mass:




Combining these two observations gives

Or, more familiarly,




An object may have several forces acting on it; the acceleration is due to the net force:



5-3 Newton’s Second Law of Motion


Second law: A body of mass m subject to a net force F undergoes an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e., F = ma.

Alternatively, the total force applied on a body is equal to the time derivative of linear momentum of the body.


http://en.wikipedia.org/wiki/Mass

http://en.wikipedia.org/wiki/Mass





http://en.wikipedia.org/wiki/Acceleration

http://en.wikipedia.org/wiki/Acceleration

http://en.wikipedia.org/wiki/Time_derivative

http://en.wikipedia.org/wiki/Time_derivative

http://en.wikipedia.org/wiki/Momentum

http://en.wikipedia.org/wiki/Momentum


An object undergoing uniform circular

We have already seen the centripetal acceleration. But, if we measure the mass in motion, Newton’s Second Law allows us to calculate the centripetal force.



Using the Second Law



g, and hence weight, is only constant on earth, at sea level

• On Earth, g depends on your altitude.

• On other planets, gravity will have a different value.

• An object will have a different “apparent weight” in a rapidly stopping car.



Newton’s Third Law of Motion

Forces always come in pairs, acting on different objects:

If object 1 exerts a force on object 2, then object 2 exerts a force – on object 1.

These forces are called action-reaction pairs.



Newton’s Third Law of Motion

Some action-reaction pairs:



The Vector Nature of Forces: Forces in Two Dimensions

The easiest way to handle forces in two dimensions is to treat each dimension separately, as we did for kinematics.



Weight

The weight of an object on the Earth’s surface is the gravitational force exerted on it by the Earth.



WeightApparent weight:Your perception of your weight is based on the contact forces between your body and your surroundings.

If your surroundings are accelerating, your apparent weight may be more or less than your actual weight.



Normal Forces

The normal force is the force exerted by a surface on an object.



Normal Forces

The normal force may be equal to, greater than, or less than the weight.



Normal Forces

The normal force is always perpendicular to the surface.



Newton’s Third Law

• Exerting a force on a body results in a force back upon you.

• For every action there is an equal and opposite reaction.



Newton’s Third Law—Objects at rest

An apple on a table or a person in a chair—there will be the weight (mass pulled downward by gravity) and the normal force (the table or chair’s response).



Newton’s Third Law—Objects in motion

An apple falling or a refrigerator that needs to be moved—the first law allows a net force and mass to lead us to the object’s acceleration.



Free-body diagrams

A sketch accounting of forces



Many have asked “how lethal is a coin dropped from atop a tall building”?

Urban legends have said that a penny dropped from the top of the Empire State Building can kill.


newton’s laws of motion - university of texas at...

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