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What is the Function of a Force Table?
The Force Table
A Force table is a tool to demonstrate Newton's First Law and how vectors work. It is common in most physics classroom labs.
Newton's First Law:
An object at rest remains at rest and an object in motion conitnues in motion with constant velocity (that is constant speed in a straight line) unless it experiences a net external force.
The force table is based on the principle of "Equilibrium."
Equilibrium is reached when there is no net force acting upon an object. An object with no net force acting upon it has no acceleration.
The force table uses pulleys, strings, and weights placed around a circular table.
Weights are placed at the end of strings supported by pulleys located on a circular tabletop. When equal amounts of weight (or force) are added the string will find equilibrium and acceleration in a certain direction will halt.
Data is collected from a series of quantitative markings on the tabletop. The direction that the string was moving prior to equilibrium and the amount of the weights needed to bring the string to equilibrium give the string both direction and magnitude making the string a vector. Multiple strings can be placed on the table as stated above and more data can be collected. This data can then be used to determine resultant vector quantities through addition, subtraction, or using trigonometric functions.
The Addition, Subtraction, and Resolution of Vectors
Physical quantities are seen as either being scalar or vector quantities.
A scalar quantity has magnitude without direction, and a vector quantity has magnitude and direction.
Velocity, acceleration, and force are examples of vectors.
Two vectors are equal if they have the same magnitude and direction.
Addition of Vectors
There are many ways to add vector quantities. The graphical approach is to line the vectors onto a graph and add one vector to another at the angles given and determine the geometric shape formed.
When two or more vectors are added together they must have the same units of measurement. When a vector quantity is handwritten it has an arrow over the letter (->). For clarity V and W will be two vector amount that need to be added together for a resultant vector quantity.
To add V to W, first you would draw V on a piece of graph paper to determine a scale for its measurement, whatever units the vector maybe, keeping in mind its direction. Then W will be drawn, starting from the tip of vector V and heading in the direction needed to represent it. R or the resultant vector will be R=V+W.
This is known as the triangle method of addition.
A resultant vector can be the sum of many vectors of R=A+B+C+D etc. as long as each vector is drawn from the tip of the last vector.
The analytical method may vary depending on the whether the triangle formed is a ninety-degree triangle. In the case of a ninety degree triangle the resultant can be determined by trigonometric functions by breaking the triangle into its ninety degree components and using the Pythagorean theorem to determine the resultant.
There is another option for the addition of vectors. Instead of using a geometrical approach one can use what is called a component approach. The component approach places the vectors on x or y axis and also uses the Pythagorean theorem to find resultant vector quantities.
A negative vector has the same magnitude yet opposite direction.
Subtraction of Vectors
Negative vectors can be added to positive vectors thus allowing the subtraction of vectors.
Rules for Using the Component Approach
When two or more vectors are added together the following rules can be followed:
1. Select a coordinate system.
2. Draw a picture of the vectors to be added or subtracted and label them accordingly.
3. Find your x and your y coordinates.
4. Find your resultant components in both the x and the y directions. This is done by using the triangle method of addition as stated above.
5. Use the Pythagorean Theorem to find the magnitude of the resultant vector.
6. Use a trigonometric function to find the angle the resultant vector makes with the x axis.
There is so much that can be learned about vectors and Newton's First Law from a Force Table.
All students in Physics whether High School or University should have a chance to use a Force Table to help get a visual understanding of force, acceleration, and velocity.