Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Chapter 4.

• Chapter 4

Goals for Chapter 4

• To understand force – either directly or as the net force of multiple components.

• To study and apply Newton’s First Law.

• To study and apply the concept of mass and acceleration as components of Newton’s Second Law.

• To differentiate between mass and weight.

• To study and apply Newton’s Third Law.

• To open a new presentation of problem data in a free body diagram.

Dynamics, a new frontier

• Stated previously, the onset of physics separates into two distinct parts:

– statics and

– dynamics.

• So, if something is going to be dynamic, what causes it to be so?

– A force is the cause, it is either

• pushing or

• pulling.

Types of Force Illustrated I – Figure 4.1

Types of Force II – Figure 4.2

• Single or net

– Contact force

– Normal force

– Frictional force

– Tension

– Weight

A force may be resolved into components – Figure 4.4

•Fx = F CosΘ

•Fy = F SinΘ

Components and Resultants II – Figure 4.6

• An example of component resolution.

R = F1 + F2 + F3 + ……..= Σ F, (resultant, and vector sum, of forces)

Rx = Σ Fx , Ry = Σ Fy

(components of vector sum of forces)

Once we have the components Rx and Ry, we can find the magnitude and direction of the vector R.

HOMEWORK

3; 5; 12; 13; 17; 18; 20; 22; 26; 28;

30; 31; 33; 35; 36; 37; 38

Newton’s First Law – Figure 4.7

•“Objects at rest tend to stay at rest and objects in motion tend to stay in motion in a straight line unless it is forced to change that state by forces acting on it”

R = F1 + F2 = 0• Zero resultant force is equal to no force at all.• When an object is acted on by no forces or by several forces whose vector sum (resultant) is zero, we say that the object is in equilibrium, R = Σ F = 0 (equilibrium under zero resultant force) Each component of R must be zero, so Σ Fx = 0, Σ Fy = 0. (object in equilibrium)

We determine effect with the net force. – Figure 4.8

Mass and Newton’s Second Law II – Figure 4.12

•Let’s examine some situations with more than one mass.

INERTIA

Newton’s Second Law of Motion (Vector Form)

The vector sum (resultant) of all the forces acting on an object equals the object’s mass times its acceleration :

ΣF = ma

The acceleration a has the same direction as the resultant force ΣF.

Newton’s Second Law of Motion (Components Form)

For an object moving in a plane, each component of the total force equals the mass times the corresponding component of acceleration:

ΣFx = max ΣFx = max

Definition of the newton

One newton is the amount of force that gives an acceleration of 1 meter per second squared to an object with a mass of 1 kilogram. That is,

1 N = (1 kg) ( 1 m/s2)

ON THE MOON

Measurement of mass – Figure 4.20

•Since gravity is constant, we can compare forces to measure unknown masses.

Forces are the origin of motion

Forces Acceleration a=F/m

Velocityv= v0 + at

Positionx = x0 + v0t + ½ at2

Forces and free body diagrams

• we account for the forces and draw a free body diagram.

•In this case, the net force is unbalanced.

•This is a good example of forces in dynamics.

Newton’s Third Law

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

•Rifle recoil is a wonderful example.

For two interacting objects A and B, the formal statement of Newton’s third law is

FA on B = -FB on A

Newton’s own statement, translated from the latin of the Principia, isTo every action there is always opposed an equal reaction; or, the mutual actions of two objects upon each other are always equal, and directed to contrary parts.

Free-Body Diagram

Use free body diagrams in any situation – Figure 4.24

•Find the object of the focus of your study and collect all forces acting upon it

Homework

• 3, 9, 14, 20, 21, 23, 30, 34, 41, 52

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