1. Gravitational Acceleration (Bodies in Free Fall)

2. Free Fall Refers to any body under the influence of gravity alone!!
e.g. a stone dropped on the surface of the moon
→no air resistance, no other forces acting on it, just gravity…
Does the stone fall with
▪ uniform motion?
▪ uniform acceleration?
If the stone was heavier, would it fall
slower or faster?

3. Background… Aristotle  3rd century B.C.
Aristotle believed that objects would fall at a constant speed and that speed would depend on the mass of that object → a 2kg stone would fall twice as fast as a 1kg stone
This theory seemed reasonable, and so it was not tested experimentally
This theory went unchallenged for nearly 2000 years!!!

4. Galileo’s Challenge… ( 17th century A.D.)
the great Italian scientist
He devised an experiment that used a ball rolling down an incline plane.
Timing devices hadn’t been invented yet, not even pendulums were perfected well enough, so he had to just observe the ball rolling down – this experiment resembled a free falling body, but would occur more slowly

6. In this re-creation, the plane is equipped with bells arranged so they would ring as the balls passed. By adjusting the positions of the bells, he could compare with time standards
He used a container with a hole in it, as a timer and measured the mass of water that ran through the hole during the time interval it took the ball to roll down the slope.
He concluded that objects fall with uniform acceleration, NOT uniform motion!!

7. BUT…did mass affect this??
He did another experiment where he dropped two objects of different masses (but of the same size and shape) from the Leaning Tower of Pisa, and found that they hit the ground at the same time!!

8. Try this experiment yourself, by dropping two different masses of similar size and shape…
Now try to drop a textbook and a piece of paper, together…
The textbook falls much faster  WHY?
Try the experiment once more, but this time put the paper on top of the textbook to eliminate the air resistance, and they will fall at the same speed.

9. For objects with a large surface area compared to their mass, the air resistance they experience causes them to accelerate less.
In fact, if air resistance is great enough, an object will stop accelerating altogether and begin to fall at a constant speed. This is call the “Terminal Velocity”.
(e.g. A skydiver will accelerate for about 10 seconds before he reaches his terminal velocity)

10. Acceleration due to Gravity:
g = 9.81 m/s2 [ ]

11. Example 1: The CN tower is 533 m high.
The CN tower is 533 m high.
a) How long would it take a rock dropped from the top to reach ground?
b) How fast would the rock be moving as it hit the ground?

12. Example 2:
A diver jumps from a 3.0 m board with an initial upward velocity of 5.5 m/s. Determine …
a) The maximum height to which she ascended
b) The time it took her to hit the water
c) The velocity at impact with water