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Olegario, Kevin A.

BSChE -2

Motion of Freely Falling Objects

Objectives:

  To study the motion of free falling objects

  To determine the acceleration due to gravity, g.

  To derive quantities from the slope and intercept of graphs

  To determine if the motion of a falling object changes by varying its mass

Theory:

The free fall is a known example or the most common example of a uniformly accelerated

movement, with an acceleration a = -9.8m/s2  (vertical axis pointing vertically upward). If you

choose the vertical axis pointing vertically downward, the acceleration is taken as + 9.8m/s2. The

kinematic equations for a rectilinear movement under the acceleration of gravity are the same as

any movement with constant acceleration:

(1) v = vi - gt velocity as function of time.

(2) y - yi = ½(vi + v)t displacement as function of time

(3) y - yi = vit - ½gt2

displacement as function of time

(4) v2 = vi

2 -2g(x - xi) velocity as function of displacement

The sub index i denotes initial quantities, g the gravity acceleration and t, the time.

But for this type of motion, the displacement of the object as a function of time is described

mathematically as:

(5) ot + ½gt2

  where Vo is the initial velocity of the object. If object if just drop

velocity, Equation (5) becomes

(6) ) ½gt2 

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Olegario, Kevin A.

BSChE -2

Methodology

Procedure:

  A digital balance was used to measure the masses of the small and big steel balls.

 

A set-up of the free fall sensor was followed on the book.  The color-coded cables was connected to its color-coded socket.

  Coach 6 free fall activity was clicked in the desktop of the computer.

  The small steel ball was attached to the free fall sensor.

  The steel ball was released after clicking the Start Button.

  The stop button was clicked after the steel ball reaches the sensor.

  The time of free fall was determined.

  Another trial was done for the same height. The average of the two trials was recorded.

  The steps 5 - 9 was repeated for the other heights.

  The steps 5-9 was repeated using the bigger steel ball.

  The height of fall  as a function of t2 of fall was plotted.

  The slopes and error in the slopes were determined.

  The value acceleration due to gravity and its corresponding error from the slopes of the

two graphs were also determined.

Conclusion

Free fall describes any motion involving a dropped object that is only acted on by gravity and

no other forces. Remember, with free fall we have to ignore any impacts of air resistance on the

object. We're only concerned with the acceleration due to gravity, which is a constant value

of -9.8 m/s^2 and represented by a lower-case g . The reason that two objects of different masses

hit the ground at the same time is because, when an object is in free fall, it is "weightless". This

is because there is no force pushing up on it whatsoever. Since both of these objects are

experiencing the same force, gravitational force (that being -9.8N), then they both will fall at the

same velocity and they will both hit the ground at the exact same time. The only factor that

would change this result is air resistance. For example: if one were to take a feather and a

 bowling ball and drop both at the same time, the bowling ball would hit the ground first while

the feather remains floating. This is because the feather is experiencing "air resistance" while the

 bowling ball is barely affected. If one were to take this experiment to the moon, the bowling ball

and feather would hit the surface at the exact same time. This is because there is no "airresistance" on the moon. So, just remember that the mass of an object makes no difference when

it is in free fall, because it is basically weightless.

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Olegario, Kevin A.

BSChE -2

Application 

One application would be a skydiver jumping out of an air plane. As he falls, he accelerates. It is

important, because when you are talking about acceleration, you are also dealing with air

resistance. Thus, knowing the amount of acceleration can be helpful in determining the size of

 parachute needed to decelerate to a safe speed for landing.