Free Fall

FREE FALL

According to Aristotle, objects in the terrestrial realm move according to the material they contain. Terrestrial objects rise or fall, to a greater or lesser extent, according to the ratio of the four elements of which they are composed.

furthermore, heavier objects fall faster than lighter ones.

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​Types of Motion

​Heavier objects fall faster than lighter ones.

Galileo questioned Aristotle's idea of falling bodies. In one of his experiments.he rolled steel balls of different weights down an inclined plane and measured with reasonable accuracy the time it took the balls to reach the different markings on the plane as well as the bottom of the plane. He found out that the balls reached the bottom of the plane at almost the same time and that the distance traveled was proportional to the square of the elapsed time, Thus Galileo inferred that without air resistance, all objects would fall to the ground at the same rate.

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In the absence of air resistance, all bodies at the same location above Earth's surface fall vertically with the same acceleration, regardless of their size and weight. this very idealized motion in which air resistance is neglected and the acceleration is constant is called free fall.

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​Free Fall

Let d_y be the maximum height. Recall that v=0 at the maximum height and a =-g. since v₀,v and a are known, the most appropriate equation to

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​Sample Problem 1.1

is (Eq.). Manipulating the equation and substituting values give.

2ad_y= v² -v₀²

d_y =v²-v₀²/2d

= 0-(4.9m/s)² /2(-9.8m/s)

=1.225 m

=1.2 m

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​Cont.

b. The time of flight (T) is the total time the ball is in the air.

T=time to rise +time to fall =2 (time to rise)

Using (Eq.2 ) and substituting values,

a=v-v₀ /t

-g=v-v₀ /t

t-v-v₀ /-g

= 0-4.9m/s/-9.8m/s²

=0.5s

Therefore, T=2t=1.0s.

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Cont.

c. Starting from the maximum height, the velocity when the ball returns to its starting point can be computed using (Eq.2) . With v₀ =0 and a=-g,

-g = v-v₀ /t

v=-gt+v₀

= (-9.8m/s² ) (0.5s) +0

=-4.9 m/s

The negative sign means the ball is moving down.

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Cont.

Practice Exercises