Newton’s Laws and Gravity

Mass, Weight, Force, Friction.

Application of Newton’s Laws

o Introduce Newton’s three laws of motion At the heart of classical mechanics Describe a vast range of physical phenomena Example: Newton’s laws explain the motion of stars and planets.

o Frictional force between objects. Static and kinetic friction, Coefficients for static and kinetic friction.

o Aim of the lecture Concepts in Mechanics

mass weight and force Frictional Forces Newton’s Laws

o  Main learning outcomes familiarity with

mass, weight static and moving friction, coefficients Newton’s First Law Newton’s Second Law Newton’s Third Law

ability to use Newton’s Laws in linear problems use coefficients of friction

Lecture 4

Newton’s First Law

o It appears that: A force is needed to keep an object moving at constant speed. An object is in its “natural state” when at rest.

o These are wrong friction creates this illusion.

o Example: An object sliding with an initial speed vo will stop:

Quickly on a rubber sheet Slowly on ice Never if there is no friction.

o Newton was first to recognize this. Checked using the motion of the moon and the planets. In space there is no friction, he was able to derive

“Newton’s first law”

If there is no force acting on a body, its velocity cannot change; that is the body cannot accelerate

Note: If several forces act on a body (say , , and ) the net force

is defined as: i.e. is the vector sum of , , and

A B C net

nenet A B CC t A B

F F F F

F F F FF F F F

Newton’s First Law

o The meaning of force is defined by Newton.o Before Newton the word force was not even used:

o bodies had ‘influence’ on themo A body in a state of constant motion has no force on it.

x

y

o What is mass?o characteristic that relates a force F applied on the body and the resulting acceleration a.

o Then what is the relation between a force applied on the body and the resulting acceleration ?

o The answer is the Newton’s Second Law!

Newton’s Second Law

Fnet

am

The net force on a body is equal to the product of the body’s mass and its acceleration

netF ma

The above equation is a compact way of summarizing three separate equations, one for each coordinate axis:

,net x xF ma ,net y yF ma ,net z zF ma

o What is the difference between the mass and the weight ?o In order to answer this question we need to know the concept of gravitational force.

The Gravitational Force: It is the force that the earth exerts on any object (in the picture a cantaloupe) It is directed towards the center of the earth. Its magnitude

is given by Newton’s second law.

ˆ g gF ma mgj F mg

o Now we are in a position to answer the above question.

Weight: The weight of a body is defined as the magnitude of the force required to prevent the body from falling freely.

yg W

mg

, 0net y yF ma W mg W mg

So the weight of an object is not its mass. If the object is moved to a location where the acceleration of gravity is different (e.g. the moon where gm = 1.7 m/s2) , the mass does not change but the weight does.

o Except the mass and the weight what else do we know before applying Newton’s Laws to a system ?

o The answer is: Friction, normal force, and the tension.

Normal Force: When a body presses against a surface, the surface deforms and pushes on the body with a normal force perpendicular to the contact surface. An example is shown in the picture to the left. A block of mass m rests on a table.

Note: In this case FN = mg. This is not always the case.Fg

FN

Friction: If we slide or attempt to slide an object over a surface, the motion is resisted by a bonding between the object and the surface. This force is known as “friction”.

Direction of attempted slide

Direction of friction force: f

Tension: This is the force exerted by a rope or a cable attached to an object Tension has the following characteristics:

1. It is always directed along the rope

2. It is always pulling the object

3. It has the same value along the rope.

The following assumptions are made:

a.The rope has negligible mass compared to the mass of the object it pulls

b.The rope does not stretch.

If a pulley is used we assume that the pulley is massless and frictionless.

The rope is pulling by a force FTT

T

T

The rope is pulling by a force F

Newton’s Third Law:

When two bodies interact by exerting forces on each other, the forces are equal in magnitude and opposite in direction

For example consider a book leaning against a bookcase. We label FBC the force exerted on the book by the case. Using the same convention we label FCB the force exerted on the case by the book. Newton’s third law can be written as : FBC = -FCB .

Crate CBook B

FCBFBC

A second example is shown in the picture. The third-law pair consists of the earth and a cantaloupe. Using the same convention as above we can express Newton’s third las as: FCE = - FEC .

Applying Newton’s Laws / Free body Diagrams

Part of the procedure of solving a mechanics problem using Newton’s laws is drawing a free body diagram. This means that among the many parts of a given problem we choose one which we call the “system”. Then we choose axes and enter all the forces that are acting on the system and omitting those acting on objects that were not included in the system.

Recipe for the application of Newton’s law’s of motion

1. Choose the system to be studied 2. Make a simple sketch of the system 3. Choose a convenient coordinate system 4. Identify all the forces that act on the system. Label them on the diagram 5. Apply Newton’s laws of motion to the system