Gravity And Free Fall

When gravity is the only force acting on an object,it is said to be in free fall. 1

The acceleration of an object in free fall is called the Acceleration due to gravity. Free fall acceleration is denoted by the symbol g g = 9.80 m/s² When estimating, use g ≈ 10 m/s 2 g is always directed downward toward the center of the earth Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion 2,3,4,5,6

(384 BC – March 7, 322 BC) 7 Aristotle

Galileo formulated the laws that govern the motion of objects in free fall Galileo took an interest in rates of fall when he was about 26 years old and a math teacher at the University of Pisa. It seemed to him that -- with no air resistance -- a body should fall at a speed proportional to its density. He decided to test this modified Aristotelian view by making an experiment.

Galileo was trying to prove that earth's gravity exerts the same acceleration on all masses regardless of their weight and size. His experiment consisted of dropping a large and a small canon balls from the top of the leaning tower of Pisa and observing that they reached ground at the same time. 8

Newton studied objects Falling under the influence of Gravity and explained why Galileo’s ideas had been correct. 9

A famous story says that Newton uncovered the laws of gravity after being hit on the head by a falling apple. There is no proof that this story is true. However, his assistant John Conduitt later wrote that Newton had said he was inspired to think about gravity after seeing an apple fall in his garden around 1666.

Free Fall – Object being dropped from rest A.Initial velocity is zero B.Down is negative C.Acceleration is g = m/s 2 10

Free Fall – Object thrown downward A.Initial velocity is not zero B.Down is negative C.Acceleration is g = m/s 2 11

Free Fall – Object thrown upward A.Initial velocity is upward, so positive. B.The instantaneous velocity at the maximum height is zero. C.A = g = m/s 2 12

Let’s try some sample problems! A stone is dropped off a cliff. What is its velocity 5 seconds later? A ball is tossed straight up at 30 m/s. How long will it take To land? (It returns to the same height.)

At 400 km above the earth's surface, gravitational acceleration is reduced from 9.8 m/s/s to approximately 8.7 m/s/s. This would cause an astronaut weighing 1000 N to be reduced in weight to approximately 890 N.

Suppose that an elephant and a feather are dropped off a very tall building from the same height at the same time. Suppose also that air resistance could be eliminated such that neither the elephant nor the feather would experience any air drag during the course of their fall. Which object - the elephant or the feather - will hit the ground first ?

In the animation at the right, the motion of the elephant and the feather in the absence of air resistance is shown. In the absence of air resistance, the elephant and the feather strike the ground at the same time. Why is this so?

In the absence of air resistance objects fall at the same rate regardless of their masses. 13,14 Falling objects encountering air resistance, do not fall at the same rate

where A.g is the acceleration of gravity. B.t is the time in seconds v = g * t The formula for determining how fast an object is falling from rest (the instantaneous velocity) after an elapsed time of t seconds is Free Fall – How Fast 15

Example calculations for the velocity of a free-falling object after six and eight seconds are shown below. v = g * t At t = 6 s v f = (9.8 m/s 2 ) * (6 s) = 58.8 m/s At t = 8 s v f = (9.8 m/s 2 ) * (8 s) = 78.4 m/s

Free Fall – How Far d = 0.5 * g * t 2 Or ½ gt 2 where g is the acceleration of gravity (9.8 m/s/s on Earth). t is the time d is the distance The distance which a free-falling object has fallen from a position of rest is also dependent upon the time of the fall. This distance fallen after a time of t seconds is given by the formula. 16, 17, 18

Jason hits a volleyball so that it moves with an initial velocity Of 6 m/s straight upward. If the volleyball starts from 2m Above the floor, how long will it be in the air before it strikes The floor? Choose origin to be the initial position of ball The displacement of the ball is –2m

At t = 1 s d = (0.5) * (9.8 m/s 2 ) * (1 s) 2 = 4.9 m At t = 2 s d = (0.5) * (9.8 m/s 2 ) * (2 s) 2 = 19.6 m

The End