# Vectors Are a Snap Lab

 Materials: Force Board (only available in class), Protractor Time Allotment: 3 Class Days

### Purpose:

The purpose of this activity is to add three force vectors using a scaled vector addition diagram and to experimentally determine the resultant force for an object that is in a condition of static equilibrium; finally, you will use trigonometric functions to resolve the three forces into vector components and complete a mathematical analysis to show that the object is in a condition of static equilibrium.

### Pre-Lab Analysis:

In this lab, the forces acting upon a "point object" will be analyzed. The "point object" will be at rest and not accelerating. Thus, it would be expected that the "point object" satisfies the condition of static equilibrium. The diagram to the right depicts the actual classroom situation which will be analyzed.

1. If the vector components of the forces acting upon that "point object" are carefully added as vectors, then what will be the magnitude of the resultant force? Explain.

2. The two strings are pulling upward and horizontally upon the point object. The magnitude (B and C) and direction of these forces will be measured; the angles Q1 and Q2 can be determined from the direction (see diagram above). Write four equations involving trigonometric functions which can be used to determine the horizontal and vertical components of these forces.

 Bx = _____________________ By = _____________________ Cx = _____________________ Cy = _____________________

3. Given that the point object is at static equilibrium, how would you expect the magnitudes of By and Cyto compare? How about A and Bx and Cx? Explain fully.

### Collection of Data:

The procedure for collecting data involves utilizing a "force board" to measure the magnitude and direction of three forces acting upon an object. The "center ring" is the object upon which the three forces act. The forces are the result of a chain pulled to a given tension (and measured by a spring scale). A protractor can be used to determine the direction of each force. It is best to align one of the scales in the direction of due east and to measure the other scales as counter-clockwise angles of rotation from due East.

### Magnitude (N) Direction (degrees) Force A   _________________   _________________ Force B   _________________   _________________ Force C   _________________   _________________

Once the magnitudes and direction of the three forces are measured, use a separate page to construct a vector addition diagram and to determine the resultant force. The diagram should be a scaled drawing; the scale should be clearly indicated and the magnitude and direction of each vector should be clearly labeled. Label the magnitude and direction of the resultant on the diagram.

• Explain (in the space below) how your scaled diagram demonstrates that the "center ring" was in a condition of static equilibrium. Explain fully.

### Trigonometric Analysis to Determine Static Equibrium:

Use the trigonometric functions (as written in the Pre-Lab section) to determine the horizontal and vertical components of each force. Show your work in each individual cell of the data table. List both magnitude and direction (north, south, east, west) for the components. Then, sum the individual components to determine the vector sum (last row).

### Force A

_________________

_________________

### Force B

_________________

_________________

### Force C

_________________

_________________

### Vector Sum

_________________

_________________

• Explain (in the space below) how the above trigonometric analysis demonstrates that the "center ring" was in a condition of static equilibrium. Explain fully.

### Conclusion:

Using complete sentences, explain what is meant by static equilibrium and discuss the two methods which can be used to establish that an object is at static equilibrium. Do a bang-up job!