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Gravitational Attraction Between People
by Ron Kurtus (updated 30 May 2023)
You can find the gravitational force of attraction between people—such as between a boy and a girl—by applying the Universal Gravitation Equation, provided you know the mass of each person and their separation.
Questions you may have include:
- What is an example of the force between two people?
- What is the Universal Gravitational Equation?
- How do you determine the mass of each person?
- What is the force of attraction between the boy and the girl?
This lesson will answer those questions. Useful tool: Units Conversion
Example
For example, suppose a boy who weighed 165 lb-f on a scale (74.8 N or kg-f) sat near a 110 lb-f (50 N) girl, what would be the gravitational attraction between them, assuming the separation from their centers was 19.7 inches (0.5 meters)?
Note:
Metric weights are in kilograms-force or newtons (N). To use in the gravitation equation, newtons must be converted to kilogram-mass by dividing by 9.8 m/s^{2}.
In the British and United States systems of units, weights are usually stated as pounds (lb-force). To use in the gravitation equation, lb-f must be converted to pound-mass by dividing by 32 ft/s^{2}.
(See Confusion about Mass and Weight Units for more information.)
Universal Gravitation Equation
The solution requires an application of the Universal Gravitation Equation:
F = GMm/R^{2}
where
- F is the force of attraction between two objects in newtons (N)
- G is the Universal Gravitational Constant = 6.674*10^{−11} N-m^{2}/kg^{2}
- M and m are the masses of the two objects in kilograms (kg)
- R is the separation in meters (m) between the objects, as measured from their centers of mass
Determine mass of each person
To calculate the force of attraction, you must first convert the weight on Earth of each person to his or her mass, using the relationship:
W = mg or m = W/g
where
- W is the weight in newtons or pound-force
- m is the mass in kilogram-mass or slugs (pound-mass)
- g is the acceleration due to gravity on Earth; g = 9.8 m/s^{2} or 32 ft/s^{2}
Thus, the mass of the boy is:
M = (74.8 kg-force)/(9.8 m/s^{2}) = 7.6 kg-mass
Th mass of the girl is:
m = (50 kg-force)/(9.8 m/s^{2}) = 5.1 kg-mass
Resulting force between boy and girl
Next, substitute the values into the equation:
F = GMm/R^{2}
where
- M = 7.6 kg
- m = 5.1 kg
- R = 0.5 m
The result is:
F = (6.674*10^{−11} N-m^{2}/kg^{2})(7.6 kg)(5.1 kg)/(0.5 m)^{2}
F = 258.7*10^{−11}/0.25
F = 1035*10^{−11} N
F = 1.035*10^{−8} N
Approximate answer
The force of attraction is approximately:
F = 10^{−8} N
That is a very small gravitational attraction, but it can be measured on a sensitive instrument, such as one using piezoelectric sensors.
Summary
You can find the gravitational force between a boy and a girl by applying the Universal Gravitation Equation, provided you know the mass of each person and their separation.
The result is a very small gravitational attraction.
Think clearly and logically
Resources and references
Websites
Measure small forces with high initial load
Converting units of mass to equivalent forces on Earth - Wikipedia
Weight - Wikipedia
Mass - Wikipedia
Kilogram - Wikipedia
Mass and Weight: the Gravity Force - Engineering Toolbox
Books
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Top-rated books on Gravitation
Students and researchers
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Gravitational Attraction Between Boy and Girl