VECTORS

Your challenge for this laboratory period will be to design and execute an experiment that will demonstrate that the net force on a system in static equilibrium is 0. You will be expected to pay particular attention to the problems of accuracy and precision. The following information is presented to give you some guidance, on possible alternatives, but part of your grade will be based on your experimental design.

Force is a vector quantity, having magnitude and direction. Using the force table apparatus, several forces can be applied to the small circular ring such that the total force on the ring is zero. The system is then in a state of static equilibrium.

Mathematically,

You might choose the x-axis to pass through the 0º and 180º markings, and the y-axis to pass through the 90º and 270º markings. The magnitude of each force acting on the ring can be represented by the total amount of mass attached to a particular string. The direction of each force can be determined by measuring the angle from the x-axis that a particular string makes.

For this experiment, you might attach three forces to the circular ring and adjust the magnitudes (masses) and directions (angles) such that the system is in static equilibrium. (The net force then is zero. This occurs when the ring is exactly centered on the center stop. When any string is pulled, the system returns to the original position when the string is let go.) Decompose each force into x and y components. Vectorially add the three force vectors, i.e. add the components:

Rx = R1x + R2x + R3x , Ry = R1y + R2y + R3y

You could then find the magnitude R or the resultant force: R = 

Also you could find the angle that the resultant vector makes with respect to the x-axis (provided that . In what quadrant does  lie? If you have calculated a non-zero resultant vector , but your system is in static equilibrium, what may be the reasons?

You might choose 5 different sets of masses and angles & do each set 3 times.

(I.e. masses and angles must be different)

Record the angles to the nearest 0.10º. Do standard deviations on your data. Be sure to display your data and your calculations neatly and clearly. What else could you do to demonstrate this principle?

Points to be woven into your conclusion narrative:
What is a vector?
 What is the difference between a vector & scaler quantity?
 What is meant by drawing a vector to scale?
 What are the two methods of solving a vector problem?
 What is the difference between a resultant & equilibriant vector & what do they
physically mean?
Which is determined experimentally?
How is what you set up a vector?
 What is static equilibrium?
 Why should the sum of the vectors be 0 in a system in static equilibrium?
 How have you demonstrated/assured your system is in static equilibrium?

Last Updated: 4 August 2000
http://www.iun.edu/~woz/pweb/vector/vector.htm
Comments: Laboratory Supervisor
Copyright 1999, The Trustees of Indiana University