Weight

A page about weight as a property of matter.

Created by Michael Xu (mxu86)

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 its mass, but instead it is a force that depends on another body of matter, while mass is an intrinsic property that measures the amount of matter within an object.

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")

Example

Most problems involving weight calculation are simple; complex problems usually instead involve gravitational force and space.

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?
   1. Since most or all of my future work in engineering will be on planet Earth, future calculations and research may revolve around weight, mass, and other properties of matter. In addition, weight as well as weightlessness and space intrigue me, and I intend to do work in materials science that relates to space exploration.
2. How is it connected to your major?
   1. Materials science involves engineering, physics, and chemistry, so understanding the intrinsic properties of matter is crucial to eventually manipulating and creating new combinations of materials. Weight is one property, among many, that must be taken into consideration when choosing a material for an application or designing a new material altogether.
3. Is there an interesting industrial application?
   1. The idea of weight is used on most United States highways as a form of tax collection and safety. Weigh stations, built out of tough concrete and steel, use a series of conductive wires or sensors to determine the change in voltage that a load creates when acting upon these wires and sensors. Calculations then determine the corresponding weight based on that voltage difference. These weigh stations check every large tractor trailer to enforce taxes and maintain a safe load that travels upon the roads.

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>.
4. "How do truck weigh stations work?" 01 May 2001. HowStuffWorks.com. Web. 1 Dec. 2015.<http://science.howstuffworks.com/engineering/civil/question626.htm>