Free Fall

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?

Aristotle’s Theory Of Motion 1. The fall of a heavy object toward the center of the earth is a natural motion because the object is just returning to its natural place

Aristotle’s Theory Of Motion 2. Heavy objects fall faster than lighter ones. He explained that increase in the rate of motion is proportional to the weight of the object.

Aristotle’s Theory Of Motion 3. Object fall faster in air than in water. He assumed that the decrease in the rate of motion is in proportion to thr resisting force of the medium(air or water).

Aristotle’s Theory Of Motion 4. Objects sometimes move away from their natural force. He called this type of motion “ violent motion” which he explained was caused by an outside force.

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

Galileo’s Theory Of Motion 1. The two objects(light and heavy), dropped simultaneously from the tower of Pisa, fell and struck the earth at the same time.

Galileo’s Theory Of Motion 2. when a ball was rolled down an incline at a fixed angle, the ratio of the distance covered to the square of the corresponding time was always the same.

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 Theory Of Motion 2. when a ball was rolled down an incline at a fixed angle, the ratio of the distance covered to the square of the corresponding time was always the same.

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. Galileo “Two New Sciences” http://galileoandeinstein.physics.virginia.edu/lectures/gal_accn96.htm

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

To Find Distance from t and g: d=vit + ½ g t2

How Fast?

Acceleration due to Gravity, g g=-9.8m/s2 (we often use -10m/s2) g= v f –v i t When vi=0: vf=gt Note: the down direction is usually assumed negative.

Equations of Motion for Uniform Accelerated Motion vf= vi+ gt vavg = ½ (vf +vi) d= ½ (vf + vi)t d= vit + ½ gt2 vf2 = vi2 + 2gd d is the displacement (or Δd) Assume that ti=0

A ball is dropped from rest by a little boy from the window of a three-storey apartment. How far has it fallen after 1 second? What is the ball’s velocity after 1 second of fall? How far does the ball fall during the second second?

V0=0 d1 1s d2 2s

Carry threw a ball upward with an initial velocity of 2000 cm/s and was able to catch it before it reached the ground on its return. A. What was its velocity after 1 second? B. What was its displacement in the first second

C. how long did it take the ball to reach its maximum height? D. How far was the maximum height from the starting point?

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