Chapter 1: Basics


The Laws of Motion

These basic laws form the centerpiece of Isaac Newton's description of motions.

The First Law:

A moving object will continue moving is a straight line at a constant speed, and a stationary object will remain at rest, unless acted or by an unbalanced force. An object is in uniform motion if it travels in a straight line at constant speed.
All other motions are called accelerated.

Acceleration can involve changes of speed, changes of direction, or both. Newton's first law tells us that where we see an acceleration, something must have acted to produce that change. We define a force as something that produces a change in the state of motion of an object.

The Second Law:

The acceleration produced or a body by a force is proportional to the magnitude of the force and in versely proportional to the mass of the object.

In words: The greater the force, the greater the acceleration; but the more massive the object being acted or by a given force, the smaller the acceleration.

In equation form:

force (in N=kg.m/s2 = mass (in kg) * acceleration (in m / s2)

In symbols:

F = m * a



Example

What is force needed to accelerate a 100 kg sprinter from rest to a speed of 10 m/s in 1/2 second?

Reasoning:
We must first find the acceleration, and then use Newton's second law to find the force.

Solution:
1) find acceleration

acceleration (in m/s2) = final velocity - initial velocity ( in m/s) / time (in s)

= [ 10 m/s - 0 m/s ] / [0.5 s]

= [ 10 m/s ] / [ 0.5 s]

= 20 m/s2

2) find force

force in (in N ) = mass ( in Kg ) * acceleration ( in m/s2)

= 100 kg * 20 m /s2

= 2000 N



The Third Law:

For every action there is an equal and oppsite reaction.

This law tells us that whenever a force is applied to an object, that object simultaneously exerts an equal and opposite force.



The Universal Force of Gravity

Gravity is the most obvious force in our daily lives. It holds us down in our chairs and keeps us from floating off into space. It guarantees that when we drop things, they fall. The force of gravity pulls objects towards the Earth and keeps the planets on their orbits around the Sun. This insight can beformulated in what is called Newton's law of universal gravitation .

In words:
Between any two objects in universe there is an attractive force (gravity) that is proportional to the masses of the objects and inversaly proportional to the distance between them.

In equation form:
force ( in N) = g x [ mass1 (in kg) * mass2 (in kg)] / [ distance (in m)] 2

In symbols:
F = g x [ m1 * m2 ] / d2

g is a number known as gravitational constant and has a value of:

g = 9.81 m/s2
at the Earth's surface.



Weight is the force of gravity on an object located at a particular point. Weight depends on where you are- on the surface of the Earth you weigh one thing, or the surface of the Moon another, and in the depth of interstellar space you would weigh next to nothing. Weight constants with mass (the amount of matter), which stays the same nomatter where you go.



Example:

A cantaloupe has a mass of 0.5 Kg. What does it weigh?
Reasoning:
To answer this question, we have to calculate the force of gravity exerted on the cantaloupe at the Earth's surface.

Solution:
The relation between mass and force is :
force (in N) = mass (in kg) * acceleration (in m/s2), or in case of the Earth's surface,

Weight = mass * g

= 0.5 kg * 9.8 m/s2

= 4.9 kg m/s2

= 4.9 N

This value is the weight of the cantaloupe. Note that "kilogram" is not a unit of weight, despite popular usage to the contrary.

Ch. Elster
Aug 26 14:27:03 EDT 2019