Vectors

Learning Objectives

	Describe the relationship between resultant vectors and their components,
	Add vectors utilizing both graphical and Vector Sums methods, and
	Confirm accuracy of these methods by balancing the vectors on a Force Table.

Equipment

Graph paper, ½ meter sticks, protractors, Force Table, assorted masses.

Procedure

Your group will be assigned one group of vectors (#1,2,3,4, or 5). Each group contains three vectors (A,B, and C). See either PHY 111 Vector Data Collection Tool or PHY 112 Vector Data Collection Tool.

Hiking Trip - Triangle Method

1. Determine a scale (for example, 40 Newtons for each centimeter on the ruler) which will allow enough room to connect two vectors .

2. Next, draw a line in the middle of a graph page to create a top graph and a bottom graph. Locate an origin near the bottom of the top half.

Vector A represents a hike on the first day. The origin is your base camp and the head of the arrow is your first stop.

	Use the scale to draw the distance (magnitude) you hiked from camp.
	Use a protractor (horizontal to the x-axis) to mark the degrees of direction in which you traveled.

Vector B represents your second day hike. Start from your last position - not base camp.

	Start at the Arrow head of Vector A.
	Use the scale to draw the distance (magnitude) you hiked the second day.
	Use a protractor (horizontal to the x-axis) to mark the degrees of direction in which you traveled.

R₁ represents the first rendezvous of your trip. R₁ gives the distance and direction in which your friend would hike from the base camp. R₁ is the Vector sum of A + B.

Connect the base camp to your position after the second day. Tail of Vector A (origin) to the Head of Vector B.

Measure its magnitude with the ruler and direction with a protractor (horizontal to the x-axis).

3. On the bottom half, redraw R₁.

Vector C represents your third day hike after you and your friend meet. R₂gives the distance and direction in which another friend would hike from the base camp to rendezvous with you. R₂is the Vector sum of R₁+ C or A + B + C.

Draw Vector C from your last point. Record the magnitude and direction of Vector R₂. Record your data in the Triangle Method of Part II on your Data Collection worksheet. HINT: R₂ angle should be measured horizontal to the x-axis!

Tractor Pull - Common Origin

1. Use the parallelogram method to add the three common origin vectors.

	Draw the tail of all three vectors at a common origin.
	Draw a parallel vector to Vector B so the tail of B starts at the Arrow head of A. Draw a parallel vector to Vector C so the tail of C starts at the Arrow head of B.
	Draw the resulting vector from the origin to the Arrow head of C with a dotted line and label it R2.

2. Record the R₂ vector magnitude and direction of the parallelogram method in Part II of your Data Collection worksheet.

Vector Sum

PHY 111 should skip to Check the Accuracy. PHY 112 refer to Vectors A, B, and C drawn on the triangle method graphs. Identify the components for each vector and complete Part III of the Vector Data Collection Tool.

PHY 112 Example:

Check the Accuracy

1. Refer to the common origin graph. Draw -R₂ magnitude and direction from the origin.

	Imagine three students pulling a boat on the water, and each vector represents the magnitude and direction of their effort. R₂ would be the final magnitude and direction of their effort.
	Next, imagine another person pulling in the opposite direction to prevent the boat from moving. That would be -R₂. The forces should cancel each other with a net force of zero.

2. Use the Force Table to check the accuracy of your vector sum method from Part III.

	Align three pulleys to match the angles of Vectors A, B, and C.
	The fourth pulley should match the -R₂ vector angle.
	Apply appropriate masses in grams to represent the magnitude.
	If you were careful and your vector sum calculations are accurate, the center ring will not touch the center pin of the Force Table.

3. Print and complete the Lab Homework:

	PHY 111 Homework Assignment
	PHY 112 Homework Assignment

Homework and Lab Report are both due at the next class.