Acceleration of Gravity, Free Fall, and Projectile Motion

Acceleration of Gravity

• The acceleration of gravity near the earth’s surface is 9.8 m/s2 for ALL objects.

• This means that objects will accelerate at a rate of 9.8 m/s every second when in free fall.

• Equation– V = g x t

Galileo dropped a cannon ball and musket shell and found they landed at the same time

Example ProblemExample Problem: If an object is dropped from a building, how fast will it be going if it falls for 4 seconds?

V = g x tV = (9.8 m/s2) x (4 seconds) = 39.2 m/s (which is about 100 mph)

Example #2• You want to know how high above the ground you are,

so you drop a rock off a tall bridge.• Distance = ½gt2

• You count and see it takes 7.3 seconds to hit the river.

Example #2• You want to know how high above the ground you are,

so you drop a rock off a tall bridge.• Distance = ½gt2

• You count and see it takes 7.3 seconds to hit the river.• Thus d = ½ * (9.8 m/sec2) * (7.3sec)2

• D = 267 meters or 876 feet tall

Free Fall• Free Fall

– When something falls through the air it is experiencing free fall

(meaning it accelerates at a rate of 9.8m/s2).

• Terminal Velocity– The velocity reached when the force

of friction (air resistance) becomes equal to the force of gravity pulling down.

– Diagram The force of air resistance going up equals the force of gravity going down

Fair

F gravity

102,000 feet

614 mph

Terminal velocity helps flying squirrels jump from tree to tree

• Two primary factors affect Terminal Velocity.

• Area (how much air is caught under it)

• Mass (how much air can be pushed out of the way).

• Heavier objects increase TV while wider objects decrease it.

Terminal Velocities Compared

134 mph

20 mph

200 mph

204 mph 74 mph

20 mph2 mph

Projectile Motion• Objects thrown through the air are called projectiles.• As an object goes up it slows at a rate of 9.8 m/s2,

and as the object comes down it speeds up at a rate of 9.8 m/s2.

• Projectiles have a vertical dimension and a horizontal dimension to their movement.

– The horizontal velocity of the object is constant due to no forces acting horizontally.

– The vertical velocity of the object is changing due to the force of gravity acting on it.

Projectile MotionAlmost all sporting events incorporate some form of projectile motion.

Football, basketball, baseball, track, swimming, hunting, etc.

These projectiles always move in symmetrical shapes called parabolas

Parabolic Paths

Definitions:

• MASS: The amount of matter in an object

• WEIGHT: Depends on the force of gravity on that object.

Formula’s• Formula

– F = m x a W = m x g

– Units• Force or Weight = Newtons (N)• Mass = kg• Acceleration or g – m/sec/sec or m/sec2

A force is present when an object is accelerating!

Weight is a force due to the acceleration of gravity!

The force and weight formula’s are very similar because they are both forces due to an acceleration!!!

Comparing the Earth v. the Moon

• Earth v. Moon– Mass on earth = mass on the moon

• This is because you have the same amount of matter on earth as you do on the moon (assuming that you do not stop to go to the bathroom or to eat while traveling to the moon)

– Weight on earth is > Weight on the moon• This is due to the earth being more massive and

having a greater gravitational pull on you than the moon.

Jumping on the moon with a 300 lb space suit. You try that at home!

With no gravity, there is no weight Heavy-g’s while the plane accelerates. G-forces can crush blood vessels and

cause blackouts