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The Force Table
Introduction:
"The Force Table" is a simple tool for demonstrating Newton’s First Law and the
vector nature of forces. This tool is based on the principle of “equilibrium”. An object is
said to be in equilibrium when there is no net force acting on it. An object with no net
force acting on it has no acceleration. By using simple weights, pulleys and strings placed
around a circular table, several forces can be applied to an object located in the center of
the table in such a way that the forces exactly cancel each other, leaving the object in
equilibrium. (The object will appear to be at rest.) We will use the force table and
Newton’s First Law to study the components of the force vector.
Theory:
As we saw in the inclined-plane experiment, any vector can be decomposed into
several other vectors which, when added together, produce the original vector. This was
essential to our study of the inclined plane, where the force we were concerned with was
the component of the weight vector which was parallel to the inclined plane. Sometimes,
when doing calculations which involve adding several vectors, it is useful to break up the
individual vectors into components and then add the components.
How could this extra step actually facilitate the solution? Most vectors are given
only by their magnitude and direction, with magnitude being some scalar positive number
and direction given by some angle. If you are trying to add the vectors using a protractor
and ruler by the "parallelogram method", you will have to draw all the vectors, then add
them up graphically, one by one, until you have completed the task and with questionable
precision in your result. The component method reduces the addition to one step.
Furthermore, this step is analytical (adding numbers) rather than graphical (drawing
pictures), yielding the best possible precision.
In the inclined-plane experiment, the down-hill force was the component of the
weight vector which was parallel to the plane. We found this component by multiplying
the weight by the sine of the angle of the plane. Now let us consider a more general case.
In the Cartesian coordinate system, a point on the graph is specified by two scalar
numbers, x and y. The coordinate x gives the distance and direction along the x-axis, and
the coordinate y gives the distance and direction along the y-axis, from the origin to get to
the point in question. The absolute value of the coordinate indicates the length along the
