Gravity and Free Fall

Gravity• Sir Isaac Newton (1642-1727) developed a law

of gravitation which said all objects in the universe attract each other through gravitational force

• Universal Gravitation Equation• F = G m1m2

d2

• Equation shows grav. Force ↑ as both masses ↑

• Equation shows grav. Force ↓ as the distance b/w masses ↑

Free FallFree fall- when gravity is the only force acting on an object (free fall acceleration is directed toward center of earth)

The acceleration of gravity (g) for objects in free fall at the earth's surface is 9.8 m/s2.

Galileo found that all things fall at the same rate in the absence of air resistance, regardless of their mass

Free Fall

The rate of falling increases by 9.8 m/s every second.

Height = ½ gt2

For example:

½ (9.8 )12 = 4.9 m

½(9.8)22 = 19.6 m

½ (9.8)32 = 44.1 m

½ (9.8)42 = 78.4 m

Air Resistance

• In air…– A stone falls faster

than a feather• Air resistance

affects stone less

• In a vacuum– A stone and a

feather will fall at the same speed.

Mass and Weight different!

► Mass is an intrinsic propertyintrinsic property of an object. It is completely determined by the number and type of atoms that make up the object. It does not depend on the environmentenvironment in which the object is located. ► But weight is different. Weight depends on both the object itself, and on some other object that exerts the gravitational force.So, for example, the mass of an object

would be the same on the moon or the Earth; but the weight would be different.

What does weight depend on?

• The weight of an object depends on the object’s mass.– In fact, an object’s weight is directly

proportional to the object’s mass.

• The weight of an object also depends on the object’s location.– In fact, an object’s weight is directly

proportional to its free fall acceleration, g at its current location.

Weight = the force of gravity

The weight of an object is, by definition, the strength of the force of gravity pulling the object downward.

force of gravity

W = m g

newtons

kg

Weight of a 1 kg object

• Since W = mg, the weight of a 1 kg object is:– W = (9.8 m/s2)(1 kg) = 9.8 N on Earth– W = (1.6 m/s2)(1 kg) = 1.6 N on the Moon

Mass vs. Weight

• Mass is not Weight

• Weight is a force - an interaction between 2 objects involving a push or a pull. One of these objects is typically VERY big - the Earth or the Moon, for instance.

• Weight is NOT a property of an object

Weight

• In symbols:

W = mg Wm g

Gravity

What is the force acting on the mass m due to the Earth’s gravity?

downward gaIf released, the acceleration of m would be … By Newton’s second law the force on m must be …

downward mgF

By the way, what is the reaction force?

Solution

That is, the magnitude, or strength, is mg and the direction is downward.

g = 9.81 m/s2

F

2-5. Free Fall

A ball thrown horizontally

will fall at the same rate as a ball dropped

directly.

2-5. Free Fall

A ball thrown into the air will slow down, stop,

and then begin to fall with the acceleration

due to gravity. When it passes the thrower, it will be traveling at the same rate at which it

was thrown.

Example. Playing catch with a softball

The trajectory has 3 parts.

the throw the catch

free fall

What is the force acting on the ball, during each part of the trajectory?

Projectile Motion

•An object thrown upward at an angle to the ground follows a curved path called a parabola.• combines vertical and horizontal motioncombines vertical and horizontal motion•Orbiting objects- forward motion combines with free fall and object follows a curved path

2-6. Air Resistance• Free Fall

– A person in free fall reaches a terminal velocity of around 54 m/s which means the person stops acceleratingstops accelerating b/c:

– Force of air resistance = gravitational force

– Called terminal velocity (balanced forces)

– With a parachute, terminal velocity is only 6.3 m/s

• Allows a safe landing

Free Fall Review

• Dropping something from a resting position (gains speed as it falls so it accelerates)

• Gravity pulls objects down (air resistance can affect how fast) (no air resistance- in a vacuum)

• When gravity is the only thing that affects falling object → FREE FALL

• Acceleration due to gravity is 9.8 m/s2

Free Fall equations

• V = g x t

• D = 1 gt2

2