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Gravitational Attraction Between Boy and Girl

by Ron Kurtus (15 September 2016)

You can find the gravitational force of attraction between a boy and a girl by applying the Universal Gravitation Equation, provided you know the mass of each person and their separation.

For example, suppose a boy who weighed 165 lb (74.8 kg-force) sat near a 50 kg-force (110 lb) girl, what would be the gravitational attraction between them, assuming the separation from their centers was 0.5 meters (19.7 in)?

Note that 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/s2.

(See Confusion about Mass and Weight Units for more information.)

Questions you may have include:

This lesson will answer those questions. Useful tool: Units Conversion



Universal Gravitation Equation

The solution requires an application of the Universal Gravitation Equation:

F = GMm/R2

where

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

Thus, the mass of the boy is:

M = (74.8 kg-force)/(9.8 m/s2) = 7.6 kg-mass

Th mass of the girl is:

m = (50 kg-force)/(9.8 m/s2) = 5.1 kg-mass

Substitute values

Next, substitute the values into the equation:

F = GMm/R2

where

Resulting force

The result is:

F = (6.674*10−11 N-m2/kg2)(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

Ron Kurtus' Credentials

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

Gravitation Resources

Books

Top-rated books on Gravity

Top-rated books on Gravitation


Questions and comments

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.


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