Lecture 4Force and Motion

GravitationChapter 2.7 2.15

Outline

• Laws of Motion• Mass and Weight• Gravitation

The law of gravity – 1666, 3 laws of motion – 1686

First Law of Motion

• If no net force acts on it, then

an object in motion remains in motion

A force is needed to start motion or change its velocity

A force is any influence that can change the speed or direction of motion of an object

an object remains at rest

An object continues to be accelerated as long as a net force acts upon it

Mass

The reluctance of an object to change its state of rest or of uniform motion in a straight line is inertia

Mass is a property of matter that shows itself as inertia

The SI unit of mass is kilogram (kg)1 liter (0.26 gallon) has a mass of 1 kg1 liter = 10cm x 10cm x 10cm

More about mass and inertia

Second Law of Motion

The more mass an object has, the less its acceleration for a given force.

F = net force m = mass a = acceleration

Fa = --- m

F=ma

The net force on an object equals to the product of the mass and the acceleration of the object.The direction of the force is the same as that of the acceleration.

The Newton

The second law of motion defines the unit of force.

F=ma, [m]=kg, [a]=m/s2 [F]=kg m/s2 = newton (N)

1 lb = 0.453 kg x 9.8 m/s2 = 4.45 N 1 N = 0.225 lb

Mass and WeightThe weight of an object is the force it is attracted by the earth’s gravitational pull.

Mass is a measure of the amount of matter included in an object.

F=ma w=mg

Third Law of Motion

When an object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object.

Action force is equal to reaction force

Gravitation

Centripetal force is an inward force on an object moving in a curved path

mv2

Fc = ---- r is the radius of a circle r

The centripetal force always points toward the center of curvature of the object’s path.

Centripetal and Centrifugal Force

Centrifugal force

Mass of the Earth

The Earth’s mass can be found from the law of gravity.

Weight of an object F = mg

Gravitational force on an object G m MF = ---------- R2

G = 6.67 10-11 N m2/kg2

R = 6378 km = 6.38 106 m

g = 9.8 m/s2

gR2

M = ------ = 6 1024 kg G

Orbiting the EarthIn order to launch a satellite, the gravitational force has to be overcome.

Centripetal force = gravitational force

mv2

------ = mg v2 = rg v = rg r

Escape speed (ve): the speed required to leave the gravitational influence of a body.

Minimal orbital speed

For the Earth: v = 28,400 km/h, ve=40,000 km/h

Summary• The three Newton’s laws of motion and the law of gravity

represent the foundation of the classic or Newtonian mechanics.

• Mass is a measure of an object’s inertia, while weight is the gravitational force on an object.

• They hold everywhere in the Universe, when an object’s speed is much less than the speed of light.