Honors Physics
Universal Gravitational Constant (Cavendish Experiment)
Lab
Name __________________
Date __________
Per ______
Objective:
Experimentally determine the magnitude of the Universal Gravitational Constant (G).
Background:
Isaac Newton gets credit for working out the Universal Law of Gravity sometime around 1687. However,
since the mass of the Earth was unknown in his time he was unable to write
the complete Law of Gravity. He could not determine the proportionality
constant G, also known as the Universal Gravitational Constant. To determine
G the force of gravity between 2 objects of known mass must be measured.
Since this force is extremely small, this is a very difficult experiment to do
accurately. Henry Cavendish was the first to do so in 1798 utilizing what is
known as a ‘torsion balance’. Cavendish was trying to determine the average
density of the entire Earth. He was dubbed “The man who weighed the Earth”
after his experimental results were published. Other physicists then used his
data to determine G and thus completed Newton’s work.
Pre-Lab:
In the Universal Law of Gravity lab the fundamental characteristics of mass and separation distance
affecting the force due to gravity were summarized as:
𝐹𝑔 ∝
𝑀1 𝑀2
𝑟2
(1)
In order to determine the exact magnitude of the force due to gravity a ‘constant of proportionality’ is
required. This constant is officially referred to as the Universal Gravitational Constant (G):
𝐹𝑔 = 𝐺
𝑀1 𝑀2
𝑟2
(2)
ANY constant of proportionality is determined by the slope of the line modeled by graphing the IV and DV.
In this case expression (2) is modeled by graphing the following quantities:
𝑦 = 𝑚𝑥 + 𝑏
𝑀1 𝑀2
𝐹𝑔 = 𝐺 ( 2 ) + 0
𝑟
Where G:
𝐺=
Directions:
𝐹𝑔
𝑀1 𝑀2
( 2 )
𝑟
(3)
Go to the PhET site and open Gravity Force Lab simulation. Access by the following website
(http://phet.colorado.edu/en/simulation/gravity-force-lab) or go to PhETPhysicsMotionGravity
Force LabRun Now!. This experiment will be conducted in 3 parts after which each will be graphed in
Logger Pro and analyzed.
1
Procedure:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Play around with the site for a moment to
get familiar with the simulation.
Click ‘Reset All’ to return all settings to
original values.
Drag M1 to the far left so CM1 is just inside
the left margin.
Drag the ruler up placing the 0m mark
under CM1; the 10m end of ruler should
now be visible to the right.
Begin by placing CM2 at the 3m mark.
Pick any mass you like for M1. Place value in box on PhET and fill in all rows in table below.
Pick any mass you like for M2. Place value in box on PhET and fill in all rows in table below.
Record the gravitational force between the two masses in the table below with the CM 2 at 3 m.
Vary the separation distance (r) between 3m and 10m and record the Force on M1 by M2 (F). Note
that the force must be recorded in scientific notation. (Ex: 2.53𝑥10−9 𝑁)
M1
(kg)
Analysis:
M2
(kg)
r
(m)
F
(N)
The following analysis will be conducted in Logger Pro.
1.
2.
Open Logger Pro.
Properly head and input all of your recorded data for M 1 (kg), M2 (kg), r (m) and F (N).
[Recall that to enter the data for F (N) in scientific notation you
must do the following: double-click the F column heading and select
the Options tab at the top; in the Displayed Precision box choose ‘2’
and check the Use Scientific Notation box at the bottom, Done. You
must type it in like this … (example) 2.53E-9. Once you hit enter it
will ‘snap’ into the proper mode communicating 2.53x10-9.]
3.
4.
5.
6.
7.
Construct 3 Calculated Columns of the following: M1M2 (kg2), r2 (m2)
and (M1M2)/r2 (kg2/m2).
Add a Page and insert a Table presenting all of your data.
Insert a Page and insert a Graph presenting your graphed data.
Plot now F (N) and (M1M2)/r2 referring to equation (3) above for which is the IV and which the DV.
Model the data with the best mathematical fit.
[Your response to this statement is extremely ‘telling’ about your lab analysis skills. There is much that goes into choosing
a ‘best mathematical fit.’ Critically and carefully observe the relationship between the IV and DV. Take into account that a
mathematical fit may cross an axis; what would this physically mean if it did? THINK! THINK! THINK!...you’re doing physics
here!!]
8.
Print a copy of your Data page (should be page 2) AND Graph page (should be page 3). Utilize these
pages for your responses.
2
Conclusion:
1.
2
Is your experimentally determined value within error of the accepted value of 𝐺 = 6.67 × 10−11 𝑁∙𝑚
?
𝑘𝑔2
Defend your response with meaningful supported details.
2.
2
The accepted value for the Universal Gravitational Constant is 𝐺 = 6.67 × 10−11 𝑁∙𝑚
. Calculate a
𝑘𝑔2
percent difference between your experimentally determined value of G and the theoretical value:
% 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
3.
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
× 100
𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
Utilizing equation (3) clearly derive the units of G.
3