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 textbook, 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

1. How is this topic connected to something that you are interested in?
2. How is it connected to your major?
3. Is there an interesting industrial application?

History

Since weight is essentially the force of gravitation, refer to Gravitational Force for more about the history of the Law of Gravitation.

See also

Vectors

Mass

Gravitational Force

Gravitational Potential Energy

Further reading

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

External links

Physics Classroom lessons and notes

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>.