Vectors

Force Table Lab: Vectors


  • The general idea of what a force is

    • A force is an interaction between two bodies that could potentially change the state of a system

      • A push or a pull on an object due to some other object

  • Two Forces we will deal with today:

    • Weight- We call this the force of interaction between earth and any massive object on Earth surface (Not to be confused with mass: how much stuff makes up an object)

    • Tension Force- The force that the string exerts on the mass (equal in magnitude to the forces that the string experiences from the mass)

  • Though forces are an important concept that we will talk about in the future in extensive detail, today we are Mainly interested in one Concept: FORCES ARE VECTORS!

  • A vector is a physical parameter that has two properties

    • A magnitude

    • A direction

  • Vectors can be broken up into components

    • Often times we will break up vectors into our coordinate system- for convenience

  • We can perform Vector addition

    • We can add Graphically

    • we can add components

  • We can perform scalar multiplication

    • These are just like scaling up or down a picture

    • We multiply by a constant value

  • In this Lab, you will

    • Find a vector that is equal and opposite to the addition of vectors A and B by randomly placing the third weight

    • Scale down your Force Vectors (A and B) and add them graphically

      • The result of this vector should be EQUAL and Opposite to Vector C

    • Break your vectors into components and calculate them mathematically

    • Use a force sensor to test your calculation

  • In order to practice dealing with vectors, let’s work as a class on the following problem.

    • Work with your lab partners for 15 minutes, then we will go over this together.

Problem:

Consider the following coordinate plane where vectors a and b are shown.

a) Find the components of a along the x-axis and along the y-axis (labeled ax and ay)


b) Now find the x and y components of b. (keep in mind that sign indicates direction)


c) Add the x component of a with the x component of b and the y component of a with the y component of b.


d) Use the results from above to draw the “resultant vector” (showing its components). The resultant vector is the vector that has its x component equal to the addition of the x components of a and b and has its y component equal to the sum of the y components of a and b. (use graph paper)


e) Use a ruler and a protractor to recreate the picture above but placing the tail of b on the head of a and drawing the resultant vector connecting the tail of a to the head of b. We call this head to tail addition. (use graph paper)