Questions: Do heavier objects fall faster than lighter ones when starting from the same position? Does air resistance matter? If the free fall motion has a constant acceleration, what is this acceleration and how was it found? How do we solve problems involving free fall?

What happens ? 1) When you drop a rock from a cliff? Ans: It falls downward. 2) When a Skydiver jumps from a plane? Ans: He/She will fall to the ground. 3) To a skydiver’s speed as he is falling? Ans: It will reach a terminal velocity due to air resistance. Terminal velocity is the highest velocity attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object. Since the net force on the object is zero, the object has zero acceleration.

Free-Fall Motion An object moving under the influence of gravity only!!

Apollo 15 -Astronaut David Scott on the Moon (1971) Hammer and Feather on the Moon http://www.archive.org/details/NIX-LV-1998-00046

Galileo (1564 – 1642) and the leaning tower of Pisa.

Does Air Resistance Matter?

Air Resistance The force of friction or drag acting on an object in a direction opposing its motion as it moves through air.

Hammer & Feather in the presence of air

Hammer & Feather in the absence of air

If the free fall motion has a constant acceleration, what is this acceleration and how was it found?

Galileo’s Ball and Channel Experiment http://www.ifa.hawaii.edu/~barnes/ast110_06/rots/pftim19_01.png

Galileo’s Ball and Channel Experiment He varied the starting position of the ball along the channel. He measured the times for the ball to travel the various lengths. He raised the channel until it was steep enough to simulate free fall.

Galileo’s Finding “ We compared the time for the whole length with that for the half, or with that for two-thirds, or three-fourths, or indeed for any fraction; in such experiments, repeated a full hundred times, we always found that the spaces traversed were to each other as the squares of the times, and this was true for all inclinations of the plane, i.e., of the channel, along which we rolled the ball.

How Far? Distance (m) Time (s) 5 1 20 2 45 3

To Find Distance from t and g:

How Fast?

Equations of Motion for Uniform Accelerated Motion (Kinematic Formulas)

Example 1: Free Fall A ball is dropped from rest from the top of a building. Find: The instantaneous velocity of the ball after 6 sec. How far the ball fell. The average velocity up to that point. Answers: -60m/s, 180m, -30m/s

Example 2: Free Fall on the Moon A hammer is dropped on the moon. It reaches the ground 1s later. If the distance it fell was 0.83m: Calculate the acceleration due to gravity on the surface of the moon. Calculate the velocity with which the hammer reached the ground and compare to the velocity it would have, if it was dropped on the earth’s surface. Answer:-1.66m/s2, -1.66m/s, -9.8m/s

The Velocity vs. Time Graph Pictorial representation of velocity vs. time graph. As time increases, the velocity increases in this graph. The Slope of this graph gives us the acceleration of this object.

Do You Understand It? Can you Describe the motion of this object? It’s Acceleration? Ans : Zero Acceleration, Constant Velocity

Experimental Error What if our values do not match g? Remember question regarding terminal velocity

Our Goal For Next Class 1) Perform an experiment to analyze a free-falling object. 2) Determine the value of g. 3) Enable you to solve problems dealing with free-falling objects.

Expermiental Error We must calculate the percent error for each of our trials: