ISNS 4371 - Phenomena of Nature

ARISTOTLE - 350 B. C.Developed laws of motion based on force producing a velocity in a body. No force, no velocity.

GALILEO - 1564-1642

Developed laws of motion discordant with those of Aristotle. Force produces an acceleration.

ISNS 4371 - Phenomena of Nature

A New View of Nature

Sir Isaac Newton (1642 - 1727)

- followed Galileo’s lead - developed fundamental laws of motion - revolutionized mathematics and science

- experienced moment of inspiration at 24 years old - saw apple fall from tree and suddenly understood gravity

- published most famous book in science in 1687 - Philosophiae Naturalis Principia Mathematica - Principia for short

- built first reflecting telescope

- invented calculus

ISNS 4371 - Phenomena of Nature

DEFINITIONS (CONTINUED)

INERTIA: Resistance a body offers to a change in its state of motion.

MASS: A measure of a body's inertia

MOMENTUM: Mass x velocity

ISNS 4371 - Phenomena of Nature

Newton’s First Law

A body remains at rest or moves along a straight line with constant velocity so long as no external force acts upon it.

I.e., things tend to keep on what they are already doing.

Also called the law of inertia.

ISNS 4371 - Phenomena of Nature

Examples:

Pulling a table cloth out from under a table setting

The reaction of coffee in a cup when accelerating or decelerating in a car

Tightening of a hammerhead by banging hammer on the ground

Getting ketchup out of a bottle

Not wearing a seatbelt during a head-on car crash

Headrests in a car to prevent whiplash during a read-end collision

ISNS 4371 - Phenomena of Nature

Gravity and Acceleration Animation

Galileo demonstrated that all objects accelerated at same rate regardless of mass - supposedly dropped balls of different mass from Leaning Tower of Pisa

ISNS 4371 - Phenomena of Nature

Acceleration of Gravity

All objects in a gravitational field fall at a constant acceleration - g -regardless of mass

On Earth - g = 9.8 m/s2 or 32 ft/s2

On the Moon - g = 1.63 m/s2 or 1/6th that of Earth

Remember: distance = 1/2at2

So,

to calculate height of building -drop a rock and timeits fall - h = 1/2gt2

ISNS 4371 - Phenomena of Nature

Hammer and Feather on the Moon

ISNS 4371 - Phenomena of Nature

The Pendulum

The Pendulum can be used to calculate g

P = 2(L/g)1/2

P is the period and L is the length of the pendulum

g = 42L/P2

This formula will be derived later when we discuss conservation of energy

ISNS 4371 - Phenomena of Nature

Newton’s Second law

A body (m) acted upon by a force (f) will accelerate (a) in the direction of the applied force. The greater the force or the smaller the mass, the greater will be the acceleration .

F = ma

ISNS 4371 - Phenomena of Nature

Pushing Cart Animation

Newton’s 2nd Law

F = ma

or

a = F/m

ISNS 4371 - Phenomena of NatureMass and Weight

•INERTIA: Resistance a body offers to a change in its state of motion.

•MASS: A measure of a body's inertia - mass resists

acceleration

A = F/m

Acceleration is inversely proportional to mass

•WEIGHT: Gravitational force on a body— Proportional to its mass.

Mass is not weight!

Weight is as force - the force of gravity.

W = F = ma = mg1 lb = 4.44 N

ISNS 4371 - Phenomena of Nature

Newton’s 2nd Law Explains the Feather and the Ball

1 kg on the Earth weighs 9.8 N or 2.2 lbs

F = W = mg

W = 1kg X 9.8 m/s = 9.8 kg m/s = 9.8 N

Take a 1 kg rock and a 10 kg rock and drop them from the same height

a1 = F1/m1 = W1/m1 = 9.8 N/1 kg = 9.8 m/s = g

a2 = F2/m2 = W2/m2 = 98 N/10 kg = 9.8 m/s = g

ISNS 4371 - Phenomena of Nature

apparent weight - weight force that we actually sense not the downward force of gravity, but the normal (upward) force exerted by the surface we stand on

- opposes gravity and prevents us falling to the center of the Earth - what is measured by a weighing scale.

For a body supported in a stationary position, normal force exactly balances earth's gravitational force

- apparent weight has the same magnitude as actual weight.

If no contact with any surface to provide such an opposing force - no sensation of weight (no apparent weight).

- free-fall - experienced by sky-divers and astronauts in orbit who feel "weightless" even though their bodies are still subject to the force of gravity - also known as microgravity.

A degree of reduction of apparent weight occurs, for example, in elevators. In an elevator, a spring scale will register a decrease in a person's (apparent) weight as the elevator starts to accelerate downwards. This is because the opposing force of the elevator's floor decreases as it accelerates away underneath one's feet.

Apparent Weight

ISNS 4371 - Phenomena of Nature

Apparent Weight Animation

ISNS 4371 - Phenomena of Nature

Friction is a Force That Affects Motion

WFN

Fg

Ff

The force due to friction, Ff, is equal to the normal force, FN.The block will slide when the friction force is equal to the component of the gravitational force in the direction along the plane, Fg.From simple trigonometry:

Ff = Wcos() Where is the coefficient of friction

Fg = Wsin()So the block will slide when Wcos() = Wsin()

So = sin()/cos() = tan()

The larger is the larger must be for the block to slide