Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lab Investigation 4B, 2F
TEKS 4B Describe and analyze motion in one dimension using equations
Descriptive
with the concepts of distance, displacement, speed, average velocity,
instantaneous velocity, and acceleration. TEKS 2F Demonstrate the use of course apparatus,
equipment, techniques, and procedures, including multimeters (current, voltage, resistance), triple
beam balances, batteries, clamps, dynamics demonstration equipment, collision apparatus, data
acquisition probes, discharge tubes with power supply (H, He, Ne, Ar), hand-held visual spectroscopes,
hot plates, slotted and hooked lab masses, bar magnets, horseshoe magnets, plane mirrors, convex
lenses, pendulum support, power supply, ring clamps, ring stands, stopwatches, trajectory apparatus,
tuning forks, carbon paper, graph paper, magnetic compasses, polarized film, prisms, protractors,
resistors, friction blocks, mini lamps (bulbs) and sockets, electrostatics kits, 90-degree rod clamps,
metric rulers, spring scales, knife blade switches, Celsius thermometers, meter sticks, scientific
calculators, graphing technology, computers, cathode ray tubes with horseshoe magnets, ballistic carts
or equivalent, resonance tubes, spools of nylon thread or string, containers of iron filings, rolls of
white craft paper, copper wire, Periodic Table, electromagnetic spectrum charts, slinky springs, wave
motion ropes, and laser pointers.
Lab 2F, 4B: Measuring Distance and Displacement
Introduction
Vectors have many uses. For example, you can use vectors to describe the distance an object travels and
the displacement that results from an object’s movement. Before you can make use of vectors, you must
first select a frame of reference.
To use vectors to describe an object’s position or movement on a flat surface, you must first define a
frame of reference that includes the origin—a specific point that does not move. Two imaginary lines, or
axes, that pass through the origin at right angles are then chosen, as shown in Figure 1 on the next page.
These two lines are the x-axis and the y-axis. Using the axes, you can describe the position of an object in
terms of its x- and y-coordinates—for example, the point (4, 8) on a graph. Note that the coordinates of
the origin are (0, 0).
Figure 1 shows that you can also define a vector to describe an object’s position by drawing an arrow
from the origin to the object’s position. The object’s coordinates (7, 2) determine the length and direction
of the vector. Figure 2 shows that any vector in the frame of reference can be broken down into x- and ycomponents. Therefore, any vector is also the resultant vector of its own x- and y-components. Resultant
vectors are also used to represent the result of vector addition.
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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lab Investigation 4B, 2F
Descriptive
Figure 1: Position vector
Figure 2: Vector components
You can use a similar method to define a vector describing an object’s displacement. To do this, draw a
vector from the object’s starting point to its ending point. Figure 3 shows the x- and y-coordinates of an
object’s starting and ending points. Note that the x- and y-components of the displacement vector are
simply the difference between the x- and y- coordinates of the starting and ending points.
Figure 3: Displacement vector
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TEKS
Name ___________________________ Class ________ Date ___________
Physics
Lab Investigation 4B, 2F
In this investigation, you will compare two methods of determining the length
of a displacement vector.
Descriptive
Materials
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•
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masking tape
meter stick
calculator
string
Safety
• Put on safety goggles. Use caution to avoid bumping into people or objects when moving around the
room. Note all safety alert symbols next to the steps in the Procedure, and review the meaning of
each symbol.
Pre-Lab Discussion
Read the entire investigation first. Then work with a partner to answer the following questions.
1. How will you determine the x- and y-coordinates of each position?
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2. How will you determine the x- and y-components of the displacement vector?
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3. How will you calculate the length of the displacement vector?
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TEKS
Name ___________________________ Class ________ Date ___________
Physics
Lab Investigation 4B, 2F
4. How will you measure the length of the displacement vector?
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Descriptive
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Procedure
1. Work with a classmate. Mark a dot on a small piece of masking tape. Mark the origin of your frame
of reference by sticking a piece of masking tape on the floor, away from furniture and other
obstacles.
2. Use the width of the classroom as the x-direction and the length of the classroom as the y-direction.
Attach a 2-meter strip of tape to the floor, running from the origin in the x direction. This is the xaxis. Attach a second 2-meter strip of tape to the floor, running from the origin in the y direction.
This is the y-axis. Note that the x- and y-axes should be at right angles to each other.
3. Select a point 1 to 4 meters from the origin as your starting point. Mark this point by sticking a piece
of masking tape on the floor and marking a dot on it. Label this piece of tape Start.
4. Walk from the starting point to another point 1 to 4 meters from the origin. Mark this point by
sticking a piece of masking tape on the floor and marking a dot on it. Label this piece of tape End.
5. Use a meter stick to measure the x-coordinate of the starting point to the nearest centimeter, as
shown in Figure 4. Be careful to measure parallel to the x-axis. Record your measurement in the
data table.
Figure 4
6. Repeat Step 5, measuring parallel to the y-axis, to determine the y-coordinate of the starting point.
Record your measurement in the data table.
7. Measure and record the x- and y-coordinates of the ending point in the same way that you
determined the coordinates of the starting point.
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TEKS
Name ___________________________ Class ________ Date ___________
Physics
Lab Investigation 4B, 2F
8. Determine the x-component of the displacement vector by subtracting the
x-coordinate of the starting point from the x-coordinate of the ending
point. Record this value in the data table as the vector component in the
x-direction.
9. Repeat Step 8 with the y-coordinates of the starting and ending points to
Descriptive
calculate the y-component of the displacement vector. Record this value in the data table
as the vector component in the y-direction.
10. Calculate and record the square of the vector component in the x-direction. Calculate and
record the square of the vector component in the y-direction.
11. Use the following formula to calculate the length of the displacement vector
L=
x2 + y2
where L is the length of the displacement vector and x and y are the x- and y-components of the
displacement vector. Record this value in the data table as the vector length of the displacement
vector.
12. Working with your partner, stretch a string from the starting point to the ending point. While holding
the string in this position, mark the string at both points. Use a meter stick to measure the distance
between the two marks on the string. Record this measurement in the data table as the measured
vector length of the displacement vector.
Observations
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TEKS
Name ___________________________ Class ________ Date ___________
Physics
Lab Investigation 4B, 2F
Descriptive
Analyze and Conclude
1. Measuring What tool can you use to measure the distance moved by an object?
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2. Measuring How can you measure the distance an object has moved?
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3. Measuring How can you measure the magnitude of the displacement of an object?
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4. Calculating How can you calculate the displacement of an object?
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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lab Investigation 4B, 2F
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Descriptive
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TEKS
Name ___________________________ Class ________ Date ___________
Physics
Lab Investigation 4B, 2F
5. Controlling Variables How could using a large book as the displaced
object produce a significant error in your results?
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6. Comparing and Contrasting How did the calculated length of the displacement vector compare
with the measured length of the displacement vector?
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7. Inferring Describe a condition in which it would be impossible to actually measure a displacement.
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TEKS
Name ___________________________ Class ________ Date ___________
Physics
Lab Investigation 4B, 2F
8. Comparing and Contrasting How does the distance moved by an
object between its starting point and ending point compare with the
displacement vector between the same points?
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Descriptive
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Go Further
In this investigation, you determined the distance between two points by measuring and calculating the
displacement vector. How could you determine displacement by using a graph? Write a procedure you
would follow to answer this question. Have your teacher approve your procedure before you carry out the
investigation. How does the displacement determined by this graphing method compare with the actual
measurement of the displacement?
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