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Home , Force, Mass

Chapter 4

Newton’s Laws The Concepts of and A force is a push or a pull.

Contact arise from physical contact .

Action-at-a- forces do not require contact and include and electrical forces. The Concepts of Force and Mass Is force a Vector or ? Vector Arrows are used to represent forces. The of the arrow is proportional to the magnitude of the force.

15 N

5 N The Concepts of Force and Mass

Mass is a of the amount of “stuff” contained in an object. 4.2 ’s First Law of

Newton’s First Law

An object continues in a state of rest or in a state of motion at a constant along a straight line, unless compelled to change that state by a . Law of

Net Force? The net force is the vector sum of all of the forces acting on an object. Newton’s First Law of Motion

The net force on an object is the vector sum of all forces acting on that object.

The SI unit of force is the Newton (N).

Individual Forces Net Force

4 N 10 N 6 N Newton’s First Law of Motion

Individual Forces Net Force 5 N 3 N 53

4 N

Mathematically, the net force is written as ∑F

where the Greek letter sigma denotes the vector sum. Newton’s Law of Motion Newton’s Second Law

When a net external force acts on an object of mass m, the that results is directly proportional to the net force and has a magnitude that is inversely proportional to the mass. The direction of the acceleration is the same as the direction of the net force.

Mathematically   F   a = ∑ ∑F = ma m Newton’s Second Law of Motion SI Unit for Force   ∑F = ma

 m  kg ⋅m (kg)  =  s2  s2 This combination of units is called a newton (N). Newton’s Second Law of Motion A free-body-diagram is a diagram that represents the object and the forces that act on it.

The net force in this case? 275 N + 395 N – 560 N = +110 N and is directed along the + x axis of the coordinate system. Newton’s Second Law of Motion

If the mass of the car is 1850 kg then, by Newton’s second law, the acceleration is

F +110 N a = ∑ = = +0.059m s2 m 1850 kg The Vector Nature of Newton’s Second Law

The direction of force and acceleration vectors can be taken into account by using x and y components.   ∑F = ma

is equivalent to

= = ∑ Fy may ∑ Fx max Newton’s Third Law of Motion Newton’s Third Law of Motion

Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body. The Gravitational Force Newton’s Law of Universal Gravitation

Every in the exerts an attractive force on every other particle.

A particle is a piece of , small enough in to be regarded as a mathematical point.

The force that each exerts on the other is directed along the line joining the . 4.7 The Gravitational Force

For two particles that have m1 and m2 and are separated by a distance r, the force has a magnitude given by m m F = G 1 2 r 2 G = 6.673×10−11 N ⋅m2 kg2 The Gravitational Force

m m F = G 1 2 r 2 (12 kg)(25 kg) = (6.67×10−11 N ⋅m2 kg2 ) (1.2 m)2 =1.4×10−8 N The Gravitational Force

This image cannot currently be displayed. The Gravitational Force Definition of

The weight of an object on or above the is the gravitational force that the earth exerts on the object. The weight always acts downwards, toward the center of the earth.

SI Unit of Weight: newton (N)

On or above another astronomical body, the weight is the gravitational force exerted on the object by that body. The Gravitational Force

Relation Between Mass and Weight

M m W = G E r 2

W = mg

Both must be equal

M g = G E r 2 4.7 The Gravitational Force

On the earth’s surface: M = E g G 2 RE 24 −11 2 2 (5.98×10 kg) = (6.67×10 N ⋅m kg ) 2 (6.38×106 m) = 9.80 m s2 Forces

Fundamental Non-Fundamental Result of fundamental Forces

1. Gravitational • Frictional force 2. Strong Nuclear • force 3. Electro-weak • • , etc • Electromagnetic • Nuclear Weak The Normal Force

The normal force is one component of the force that a surface exerts on an object with which it is in contact – namely, the component that is perpendicular to the surface. The Normal Force

FN −11 N −15 N = 0

FN = 26 N

FN +11 N −15 N = 0

FN = 4 N In an elevator • accelerated upward with acceleration of a

Apparent weight is more than real weight • accelerated downward with acceleration of a

Apparent weight is less than real weight Static and Kinetic Frictional Forces Frictional Force

When an object is in contact with a surface there is a force acting on that object. The component of this force that is parallel to the surface is called the frictional force. Static and Kinetic Frictional Forces

When the two surfaces are not across one another the is called static friction.

When the two surfaces are sliding across one another the friction is called Kinetic friction. 4.9 Static and Kinetic Frictional Forces

The magnitude of the static frictional force can have any value from zero up to a maximum value. MAX fs ≤ fs

MAX fs = µs FN

is called the coefficient of static friction. 0 ≤ µs Note that the magnitude of the frictional force does not depend on the contact of the surfaces. Static and Kinetic Frictional Forces

Static friction opposes the impending relative motion between two objects.

Kinetic friction opposes the relative sliding motion that actually does occur.

fk = µk FN

0 ≤ µk is called the coefficient of kinetic friction. Static and Kinetic Frictional Forces

This image cannot currently be displayed. The Tension Force Tension

Cables and ropes transmit forces through tension. Application of Newton’s Laws of Motion Strategy • Select an object(s) to which the equations of equilibrium are to be applied. • Draw a free-body diagram for each object chosen above. Include only forces acting on the object, not forces the object exerts on its . • Choose a set of x, y axes for each object and resolve all forces in the free-body diagram into components that point along these axes.

• Apply the equations and solve for the unknown . For Practice

FOC Questions: 1, 3, 12, and 16 Problems: 1, 11, 35, 46, 55, 91 and 115