Weight

Claimed by mxu86 (Michael Xu)

A page about weight as a property of matter.

The Main Idea

In physics, weight describes the Gravitational Force upon a mass, usually relative to Earth or a planet. Depending on the source, weight may be defined as a scalar - the magnitude of the gravitational force on an object - or a vector equal to gravitational force. An object's weight is commonly confused with mass, but instead it is a force that depends on another body of matter, while mass is an intrinsic property of matter.

A Mathematical Model

A mass m's weight near the surface of the Earth is represented by [math]\displaystyle{ {\vec{W} = \vec{F}_{g} = {m}\vec{g}} }[/math] where g is the gravitation acceleration of Earth, [math]\displaystyle{ {{\lt 0,-9.8,0\gt } \frac{m}{{s}^{2}}} }[/math].

Scalar weight would simply be the magnitude of the gravitational force, [math]\displaystyle{ {\left\vert{\vec{W}}\right\vert = \left\vert{\vec{F}_{g}}\right\vert} }[/math], and it can be simplified to [math]\displaystyle{ {\left\vert{\vec{W}}\right\vert = mg} }[/math].

A Computational Model

A simple segment of code that calculates the both scalar and vector weight (gravitational force) exerted upon a ball.

    # Initializing sphere object
    
    ball=sphere(pos=vec(0,0,0), radius=0.02, color=color.yellow, make_trail=true)

    # Defining constants
    g = vec(0,-9.8,0) #gravitational acceleration
    ball.m=0.1        #mass of the ball in kg
    W = ball.m*g      #weight of the ball on Earth

    # Printing values
    print("Scalar weight of the ball:", mag(W), "kg m/s^2 or N")
    print("Force of gravity exerted on the ball:", W, "kg m/s^2 or N")

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Determine the weight in Newtons of a 55 kilogram barbell on the surface of Mars, given the gravitational acceleration [math]\displaystyle{ {g}_{Mars} = 3.75\frac{m}{{s}^{2}} }[/math].

[math]\displaystyle{ \left\vert{\vec{W}}\right\vert = m{g}_{Mars} }[/math]

[math]\displaystyle{ \left\vert{\vec{W}}\right\vert = 55kg*3.75\frac{m}{{s}^{2}} }[/math]

[math]\displaystyle{ \left\vert{\vec{W}}\right\vert = 206.25 N }[/math]

Connectedness

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2. How is it connected to your major?
3. Is there an interesting industrial application?

History

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See also

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Further reading

Chabay & Sherwood: Matters and Interactions -- Modern Mechanics Volume 1, 4th Edition

External links

Internet resources on this topic

References

1. "Weight." Wikipedia. Wikimedia Foundation. Web. 1 Dec. 2015. <https://en.wikipedia.org/wiki/Weight#Gravitational_definition>.

2. "Types of Forces." Types of Forces. Physics Classroom. Web. 1 Dec. 2015. <http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Types-of-Forces>.

3. "The Value of G." The Value of G. Physics Classroom. Web. 1 Dec. 2015. <http://www.physicsclassroom.com/class/circles/Lesson-3/The-Value-of-g>.