Newton’s Laws of Motion 4.pdfNewton’s 2nd Law Describes motion when the net force is not zero. When the sum of the forces is not zero, the resultant force has a magnitude equal

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

PowerPoint® Lectures forUniversity Physics, Twelfth Edition

– Hugh D. Young and Roger A. Freedman

Lectures by James Pazun

Chapter 4

Newton’s Laws of Motion


Goals for Chapter 4

• To visualize force as a vector

• To find the net force acting on a body and apply Newton’s First Law

• To study mass, acceleration, and their application to Newton’s Second Law

• To calculate weight and compare/contrast it with mass

• To see action–reaction pairs and study Newton’s Third Law


Homework

4.17, 4.21, 4.24, 4.33, 4.39, 4.57 (Bonus)


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.

• You have only to go to a playground and watch children playing on slides, swings, and with each other to see all of Newton’s laws in action. It does seem a more relaxed approach than reading The Principia.


Force and InteractionsForces that involve direct contact between two or more bodies

• Contact Force

Forces that do not involve direct contact

• Long-Range Forces

Memorize Table 4.1 on pg 121

Just Kidding!!


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 II

• 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—Figure 4.1

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


Use the net (overall) force—Figure 4.2

• Several 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.


Superposition of Forces

The effect of any number of forces on a single point is the same as a resultant force equal to the vector sum of the forces.

1 2 3+ + =∑R = F F F F


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 ForcesThree professional wrestlers are fighting over the same championship belt. The magnitudes of the three forces are F1= 250 N, F2= 50 N and F3= 120 N. Find the magnitude and direction of the net force on the belt.


Newton’s First LawA body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration.

“Law of inertia”

Which of the following situations have no net force?

Car moving with at a constant 55 mph due east.

Car accelerating passed another car.

Car driving with a constant 55 mph on a circular track.


Newton’s First Law—Figure 4.6

• 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.”


Balanced vs. Unbalanced ForcesBalanced (Equilibrium) Unbalanced

0=∑F 0≠∑F


Newton’s First Law II—Figure 4.7

• Figure 4.7 shows an unbalanced force causing an acceleration and balanced forces resulting in no motion.


Zero net force means constant velocity

In the classic 1950 science fiction film RocketshipX-M, a spaceship is moving in the vacuum of outer space, far from any planet, when its engindies. As a result, the spaceship slows down and stops.

What does Newton’s first law say about this event?


Constant velocity means no net force.You are driving a Porsche 911 Carrera on a straight testing track at a constant speed of 150 km/h. You pass a 1971 Volkswagen Beetle doing a constant 75 km/h.

For which car is the net force greater?


Inertial Reference Frame

A frame of reference that can be considered at rest:

• Where Newton’s 1st Law is obeyed.

• No acceleration.

Is the earth an inertial reference frame?


Inertial frames of reference—Figure 4.11

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


Newton’s 2nd Law

Describes motion when the net force is not zero.

When the sum of the forces is not zero, the resultant force has a magnitude equal to the object’s mass multiplied by the object’s acceleration.

ma is not a force. It equals the magnitude of a force.

Newton’s 2nd Law also states that fig newtons are yummy.

ma=∑F


An unbalanced force (or sum of forces) will cause a mass to accelerate.


An object undergoing uniform circular motion

• Refer to Figure 4.11. 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.


The relationship of F, m, and a• Because a depends

linearly on m and F, an acceleration will be directly proportional to the applied force.

• Solution of the units gives a new combination of (kg*m)/s2 for the force. The neat thing about being a scientist then was that you got to leave your name on the unit. We give you… the Newton.


2nd as Vectors!!

If a net external force acts on a body, the body accelerates. The direction of acceleration is the same as the direction of the net force. The net force vector is equal to the mass of the body times the acceleration of the body.

Components:

m=∑F a


The relationship of F, m, and a

• Because a depends linearly on m and F, an acceleration will be inversely proportional to the object’s mass.


Concepts of the 2nd Law

Mr. Burr golfing:

• Ball vs. Cart

If: F=ma

• Let F1=F2

• m1a1=m2a2

• Or: m1/m2 = a2/a1

Ratio of the masses equals the inverse ratio of the acceleration.


A worker applies a constant horizontal force with magnitude 20 Nto a box with mass 40 kg resting on a level floor with negligible friction. What is the acceleration of the box?


Using the Second Law II—Example 4.5A waitress shoves a ketchup bottle with mass 0.45 kg toward the right along a smooth, level counter. As the bottle leaves her hand, it has an initial velocity of 2.8 m/s. As it slides, it slows down because of the constant horizontal friction force exerted on it by the counter top. It slides a distance of 1.0 m before coming to rest.

What are the magnitude and direction of the friction force acting on it?


Homework

Read 119 to 134

4.3, 4.5, 4.7, 4.11

Read 135 to 146

4.17, 4.19, 4.23, 4.27, 4.33, 4.35, 4.57


Mass vs. WeightMass is how much matter an object has, a quantitative measure ofinertia, how much an object will resist a change in its motion

Weight is a force

Mass is measured in kilograms

Weight is measured in Newtons, as are all forces.

One newton is the amount of net force that gives an acceleration of one meter per second squared to a body with a mass of one kilogram.

21 1 mN kg s= im = ∑F

a

w mg=


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.

• Conceptual Question 4.6 ponders this enigma with a euro.

• Cable TV has allowed those two science guys who test such “myths” to debunk this one.


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

• On Earth, g depends on your altitude.

• On other planets, gravity will likely have an entirely new value.


Mass and Weight

A 1.96 x 104 N Lincoln Town Car traveling in the +x-direction makes a fast stop; the x-component of the net force acting on it is -1.50 x 104 N.

What is its acceleration?

How many g’s is that?


on’s 3rd LawWall Push

Paper Punch

If body A exerts a force on body B (an “action”), then body B exerts a force on body A (a “reaction”). These two forces have the same magnitude but are opposite in direction. These two forces act on different bodies.

AonB BonA= −


Which force is greater?

While driving your Porsche 911 you hit a bumblebee.

Which force is greater: the force the car exerts on the bee compare to the force the bee exerts on the car?

Why is the result of these forces so different?


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—Page 144


Homework

4.17, 4.21, 4.24, 4.33, 4.39, 4.57 (Bonus)

Documents

Newton’s Laws of Motion 4.pdfNewton’s 2nd Law Describes motion when the net force is not zero. When the sum of the forces is not zero, the resultant force has a magnitude equal