EXPERIMENT

1. MECHANICAL ENGINEERING LAB
DPETT. OF MECHANICAL ENGINEERING
NAME: Mohammed Basel Noor Al-Deen Qasem
SUPERVISIOR : PROFFESSOR/ Sirag Aldeen
SUBJECT: Course Project
REG.NO.: 171583
CLASS: B4MAE
FREE FALL Experiment

2. Free Fall
1)_Objectives :-
Acceleration is the rate at which the velocity of an object changes
over time. An object’s acceleration is the result of the sum of all the
forces acting on the object, as described by Newton’s second law.
Under ideal circumstances, gravity is the only force acting on a freely
falling object.
Measure the displacement of a freely falling object, calculate the
average velocity of a falling object at set time intervals, and calculate
the object’s acceleration due to gravity.
The objectives of this experiment are as follows:
1. to measure the displacement of a freely falling object,
2. to test the hypothesis that the acceleration of a freely falling
object is uniform,
3. to calculate the uniform acceleration of a falling object due to
gravity, g. Theory

3. 2)_Theory:-
When the initial speed (𝑽𝑽𝟎𝟎) is 0, the drop height (H) is
with (g) being the acceleration of gravity and (t) is time
of flight.
𝑽𝑽𝒇𝒇 = 𝑽𝑽𝟎𝟎 ± g𝑡𝑡
𝐻𝐻 = 𝑽𝑽𝟎𝟎 ±
𝑔𝑔𝑡𝑡2
2
so
Equation (1) ;-
𝑔𝑔 =
2𝐻𝐻
𝑡𝑡2
_When (H) is plotted as a function of ( 𝑡𝑡2
= T) , the result is a
straight line. From the slope, (g) can be found.The mass of the ball
doesn’t occur in the formula at all.
Equation (2) ;-
𝐻𝐻 =
𝑔𝑔 𝑇𝑇
2
Equation (3) ;-
𝑀𝑀 =
𝛥𝛥𝛥𝛥
𝛥𝛥𝛥𝛥
=
(𝑯𝑯𝟓𝟓 − 𝑯𝑯𝟏𝟏)
(𝑻𝑻𝟓𝟓 − 𝑻𝑻𝟏𝟏)

4. Equation (4) ;-
𝑔𝑔𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺ℎ = 2𝑀𝑀
Equation (5) ;-
𝑔𝑔𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 =
𝒈𝒈𝒎𝒎𝒎𝒎𝒎𝒎 + 𝒈𝒈𝒎𝒎𝒎𝒎𝒎𝒎
2
_When (𝑽𝑽𝒇𝒇) is plotted as a function of ( t ) , the result is a linear
function. (g) can be found.
Equation (5) ;-
𝑔𝑔𝑣𝑣𝑣𝑣.𝐺𝐺𝐺𝐺𝐺𝐺. =
𝑽𝑽𝒇𝒇
t
Where ;
M : Slop line of (H) .
T : (T=𝑡𝑡2
)
𝑽𝑽𝒇𝒇 : Final velocity at imapact of ball.
𝑽𝑽𝟎𝟎: Intial velocity which equals to zero.
𝑔𝑔 : Gravitional acceleration .
t : time to impact or taken by ball to reach final position.
± : is taken +when the motion of ball is with the direction of
Gravitional acceleration.
• The Equations above expresses that heavy and light objects fall
equally fast in the gravitational field (as long as air drag can be
ignored).

5. 3)_Setup & Procuder :-
• Connect the free-fall apparatus to a timer.
Make sure you keep to the colour coding of the sockets.
• Set the release lever and adjust the height of fall.
The height of fall can be read off the scale on the rod and is
referenced to the top edge of the bore on the start fitting.
The reading on the scale corresponds to the distance covered, the
distance between the ball and the contact plate at the bottom.
• Place the steel ball between the contact pins from below so that it
is held in place by the retaining lug when the latter is pressed down.
• Allow the ball to fall by pushing lightly on the release lever.
For optimum precision and reproducibility, the release must be
operated gently and carefully.
The micro-magnet moves away from the surface of the ball.
The start contact opens at the instant the ball begins to fall.
When the ball hits the contact plate at the bottom, the stop contact
is opened briefly and the time measurement is stopped.

6. 3)_Caculation :-
Data collected from the expirement For every Hieght Drop, time
interval is measured :
As
shown in the Following table ;
Value
No.
H
(m)
t
(Sec)
T
(𝒔𝒔𝒔𝒔𝒔𝒔𝟐𝟐
)
𝑽𝑽𝒇𝒇
( m/s)
g
( m/𝒔𝒔𝟐𝟐
)
1 0 0 0 0 0
2 0.5 0.319 0.101761 3.134796238 9.826947455
3 0.6 0.35 0.1225 3.428571429 9.795918367
4 0.7 0.378 0.142884 3.703703704 9.798157946
5 0.8 0.404 0.163216 3.96039604 9.802960494
6 0.9 0.429 0.184041 4.195804196 9.780429361
7 - - - 𝑔𝑔𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 9.800882725 m/𝒔𝒔𝟐𝟐
8 - - - 𝑔𝑔𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺ℎ 9.722897423 m/𝒔𝒔𝟐𝟐
9 - - - 𝑔𝑔𝑣𝑣𝑣𝑣.𝐺𝐺𝐺𝐺𝐺𝐺. 9.645526891 m/𝒔𝒔𝟐𝟐

7. 4)_GRAHPS :-
a) Height vs Time graph ;-
b) Final VELOCTIY vs TIME taken graph ;-

8. 6)_ Discussion ;-
As
𝑔𝑔𝑎𝑎𝑎𝑎𝑎𝑎 = 9.800882725 m/𝑠𝑠2
At the equater of earth G=9.800665m/𝑠𝑠2
taken as IS
At the location of experiment but from different refence
For given coordinates
Latitude = 120
50′
50.52′′
N
Longitude =440
55′
01.81′′
E
Approximately above sea level elevation at h=16.0019 meters
G= 9.78283 m/𝑠𝑠2
it is the closest value to value 6 from the table.
Resource website :-
https://www.ngs.noaa.gov/cgi-bin/grav_pdx.prl
or
https://www.sensorsone.com/local-gravity-calculator/