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Uniform Motion

Purpose

Use graphical methods to analyze the motion of an object.

Introduction

In this activity, a strip of ticker tape will be attached to a constant-velocity car, as shown in Figure 1 below. The movement of the tape through a ticker timer equals the distance that the car has traveled. The distance between two successive dots on the tape is the same as the displacement of the car during a single up-and-down motion of the arm on the timer. If the distance between dots is large, then the tape was moving rapidly. If the distance is small, then the tape was moving slowly.

The time interval between successive strikes of the arm on the tape is constant. The dots on the tape can be used to measure time intervals. The ticker timer makes 60 strikes per second, or the time between each successive strike is 1/60th of a second. In this experiment, the car will take some 5 to 6 seconds to cross the lab table. We will use a time interval of a half second or 30 dots.

The distance represented by the 30 spaces between each 31 successive dots is equivalent to the distance traveled by the car during one time interval of 0.5 sec. This distance (∆d) divided by one time interval (∆t) represents the average velocity (v)during that interval of time:

v= ∆d∆t

If the distance is measured in centimeters (cm), then the velocity is expressed in cm per time interval. Since the time interval here is known, we can express the velocity in cm/s.

Materials

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·  ticker timer/ticker tape

·  constant-velocity car

·  meter stick/ruler

·  masking tape

·  C-clamp

·  graph paper

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Procedure

  1. Set up the ticker timer as shown in Figure 1. Insert about 2.0 meters of ticker tape into the timer. Make sure the tape moves freely through the timer. Use a piece of masking tape to secure the ticker tape to the constant-velocity car.
  2. Start the timer; then start the car and allow it to pull the tape through the timer. Stop the car and the timer when the car reaches the edge of the lab table. Repeat this procedure so that every member of the lab group has a ticker tape with a set of dots on it that resembles the tape in Figure 2.
  3. Write “Start” at the end of the tape that was attached to the car. Examine the dots on the tape. Notice that at the very beginning, the dots may be too close together to clearly distinguish them. Find the first clearly distinguishable dot and label this one “zero.” Count off 30 dots from the zeroth one and mark this dot “1” for the end of the first time interval. Continue until you have marked ten intervals.
  4. Measure the distance in centimeters from the zeroth dot and the dot marked “1;” record this value in your data table below. Continue measuring the length of the remaining intervals.
  5. Compute and record the average velocity for each time interval using the data table.
  6. Find the distance that the car was from its starting position at the end of each time interval by adding up the displacements and record this value as the position in the data table.

Data

Time Interval / Time from Start
(sec) / Displacement
(cm) / Average Velocity
(cm/s) / Position from Start
(cm)
1
2
3
4
5
6
7
8
9
10

Analysis

1.  Using your graphing calculator, plot the velocities (vertical axis) versus the corresponding time (horizontal axis). Enter the data into “lists” with time in L1 and velocity in L2. Use “Stat Plot.”

2.  Write an explanation for what the graph shows. Indicate where on the graph the velocity is constant or nearly constant, and where it is changing. Calculate the overall average velocity for the entire trip. Record this value and plot a horizontal line indicating the overall average velocity by using “Y=” option and Y1= your average value. How does this average compare with the values during each interval? Show me your graph. Sketch the graph for later use.

3.  Again using your calculator, plot the car’s position from its starting point (L2) versus time (L1).

4.  Write an explanation for what this second graph shows. What does the slope of this graph represent? Point out any places where the slope of the graph changes. Draw a “line of best fit” and find its slope using the statistic feature of your calculator: STAT → CALC → LinReg. The calculator should show the slope, intercept, and correlation coefficient. If R2 does not appear, use your “Catalog” (2nd, 0) to select “DiagnosticOn.” To draw a line of best fit, select “Y=,” clear any values for Y1=, and then “VAR,” “Statistics,” “EQ,” “RegEQ.” This will copy the linear regression equation. Displaying the graph will show both the equation and data points. Show me your graph and sketch it.

5.  Look at both graphs. Explain how the two graphs are related. How is the slope of the second graph related to the average value of the first one? Find the percent difference between these two values.

6.  In this experiment, which was the independent variable and which was the dependent variable?

What to Turn In

To complete this activity, turn in the following:

·  two graphs: velocity – time and position – time (shown to me)

·  answers to analysis questions and supporting calculations (average velocity, slope of best fit line, % difference)