Acceleration due to Gravity and the Mass of the Earth
Objectives:
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Calculate the acceleration due to gravity.
Use Newton’s Law of Universal Gravitation and value of acceleration due to gravity to
calculate the mass of the Earth .
Calculate the percentage error in acceleration due to gravity and the mass of the Earth.
Equipment Needed: Small and medium size objects such as marbles, a timer that can record
tenth of a second (Lap time recorder) or cell phone, a measuring tape, and a calculator.
Procedure:
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Find a place approximately 4.0 meters or higher for dropping small object (marbles.). It
is better to complete this experiment inside a building (Why?)
Mark a position from where the objects will be dropped.
Drop the light object and simultaneously record the time it takes to reach the ground.
Try dropping the object and recording the time a few times before recording the data
(Why?)
Take 20 trials and complete the table below.
Repeat the experiment with the heavier object.
Data Table: Time it takes the object to fall on the ground
Light Object
Trial
Time (t)
Seconds
Trial
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Heavy Object
Time
Trial
Time
Trial
Seconds
Seconds
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Time
Seconds
Analysis:
Distance from which the ball is dropped (y) =
Average Time (t) for the light object =
Average Time (t) for the Heavy object =
2y
;
t2
Where “y “ is the distance through which the light object is dropped; “t” is
the average time of fall of the light object.
Experimental Acceleration due to gravity of the light object (g)
g
2y
t2
Where “y “ is the distance through which the heavy object is dropped; “t” is
the average time of fall of the light object.
Experimental Acceleration due to gravity of the Heavy Object g 
Actual Value of acceleration due to gravity: 9.81 m/s2
Percentage Error in the value of acceleration due to gravity: Light Object
Actual value  Experimental Value of acceleario n due to gravity
 100
ActualValue
Percentage Error in the value of acceleration due to gravity: Heavy Object
Actual value  Experimental Value of acceleario n due to gravity
 100
ActualValue
Explanation of Error: Be generous in including all the sources of errors. Your grade
depends on how well you explain your result.
Calculation of the Mass of the Earth:
aR 2
;
G
R = Radius of the Earth = 6.378 x 106 m
G = Gravitational Constant =6.67 x 10-11 m3/ kg s2
Mass of the Earth M 
Experimental value of the Mass of the Earth using Light Object =
Experimental Value Mass of the Earth using Heavy Object =
Actual Value of the Mass of the Earth = 6. 0 x 1024 kg.
Percentage Error using the Mass of the Earth using the Light Object:
Actual  Experimental
x100
Actual
Percentage Error using the Mass of the Earth using the Heavy Object:
Actual  Experimental
x100
Actual
Explanation of your result and assumptions: