Motion Graphs
Activity 1: Position vs. Time Graphs
Materials
PASPORT Xplorer GLX (PS-2002)
PASPORT Motion Sensor (PS-2103)
Purpose:
The purpose of this activity is to explore graphs of motion (position vs. time) using a motion sensor to measure your motion as you move back-and-forth along a straight line at different speeds.
Background:
When describing the motion of an object, knowing where it is relative to a reference point, how fast and in what direction it is moving, and how it is accelerating (changing its rate of motion) is essential. A sonar ranging device such as the PASPORT Motion Sensor uses pulses of ultrasound that reflect from an object to determine the position of the object.
As the object moves, the change in its position is measured many times each second. The change in position from moment to moment is expressed as a velocity (meters per second). The change in velocity from moment to moment is expressed as an acceleration (meters per second per second). The position of an object at a particular time can be plotted on a graph. A graph is a mathematical picture of the motion of an object. For this reason, it is important to understand how to interpret a graph of position versus time. In this activity you will plot a graph of your motion in real-time, that is, as the motion is happening.
Procedure:
1. Turn on the GLX
2. Connect the Motion Sensor to one of the sensor ports on the top end of the GLX.
3. Put the range selection switch on the Motion Sensor to the “far” (Person) setting.
4. Place the motion sensor on the table or another flat surface. Aim the sensor (using the dial on the side) towards the person who is going to do the walking.
5. Create a graph that has a slope of +2
a. Pick a person to do the walking (either towards or away from the sensor).
b. When the walker is ready, have another person hit the Start/play button on the sensor. by walking either towards or away from the motion sensor.
c. When the person is done walking, hit the Start/play button again to stop taking data.
6. Create a graph that has a slope of -3. (follow steps a-c from above)
7. Create two different graphs that have an area under the curve of |4| (follow steps a-c from above)
8. Have one person in the group create a position vs. time graph for another group member to recreate.
a. Have one group member make a graph.
b. Once the initial graph is made, press F4 to open the Graphs menu.
c. Select #5 Two Runs by using the up and down buttons and then hitting the Check to select.
d. Now have a second member of the group try to match the initial graph. If after the first attempt you are not happy with the trial, then try again by pressing start and redoing the trial.
The Challenge:
When your group feels they have a good grasp of position vs. time graphs, get the Challenge Graph from your teacher. Plot out exactly how to recreate the Challenge Graph. Your group will only get one shot at recreating the Challenge graph. When your group is ready call your teacher over to recreate the graph.
Activity 2: Acceleration on an inclined plane.
Materials:
PASPORT Xplorer GLX (PS-2002)
PASPORT Motion Sensor (PS-2103)
1.2 m PASCO Track
GOcar (ME-6951)
Books or Binders
Purpose:
The purpose of this activity is to investigate the relationship between position, velocity, and acceleration for linear motion.
Background:
Constant acceleration means a constant change of velocity. This could mean a constant change of speed, a constant change of direction (such as uniform circular motion), or a combination. Although constant velocity is straightforward, the graphical representation of constant acceleration involves many fundamental concepts of kinematics. The slope of a plot of velocity versus time for an object is the acceleration of the object. The ratio of the units along the vertical and horizontal axes of a graph of velocity and time give the units for the object’s acceleration. Whether the slope of velocity is positive or negative reveals the direction of the object’s acceleration relative to the sensor.
If a cart moves on a plane that is inclined at an angle q, the component of force acting on the cart in a direction that is parallel to the surface of the plane is mg sin q, where m is the mass of the cart, and g is the acceleration due to gravity. If the friction on the cart is ignored, the acceleration of the cart should be g sin q.
Prelab Questions:
1. Is there constant acceleration (or deceleration) at anytime as the cart rolls up and down the ramp? If so, when?
2. What would constant acceleration look like on an acceleration vs. time graph?
3. What is causing the acceleration after the cart leaves the person’s hand?
Procedure:
Equipment Set Up:
1. Place the PASCO track on a table and attached the Motion Sensor to one of the track.
2. Use a couple of books to raise the motion sensor send of the track so that track is inclined at a small angle.
3. Place the cart at the bottom of the tack so the cart is facing the sensor. Aim the sensor so its signal will reflect from the cart as the cart moves up and then back down the track.
*** Have someone ready to catch the cart on its way back down. DO NOT let
the cart fall off the back of the track.
4. Make sure the Motion sensor is connected to the port on the top of the GLX. Put the range selection switch on the motion sensor to the “near” (cart) setting.
Data Collection:
NOTE: The procedure is easier if one person handles the cart and a second person operates the Xplorer GLX.
1. Press Start (the play/arrow button) on the GLX to begin measuring the sensor signal.
2. Give a cart a firm push toward the Motion Sensor. (Don’t let the cart get closer than 15 cm to the sensor.) Start collecting data as soon as the cart leaves the person’s hand. Stop taking data right before the person catches it at the bottom of the ramp.
3. Press Start (the play/arrow button) to end data recording just as the cart reaches the end of the track.
4. The graph screen will display the plot of position and time.
Analysis
Lab Write-Up (What to turn in)
Each person needs to turn in a paper with:
Title, Purpose for each activity, and answer the following…
Activity 1: Position vs. Time Graphs
Pre-lab Questions:
1. What will happen an a real-time graph of position vs. time as you move the Motion Sensor away from a wall? (draw a sketch of how the graph will look)
2. What will happen on the real-time graph of position vs. time as you move the Motion Sensor toward a wall? (draw a sketch of how the graph will look)
Post-Lab Questions:
1. Draw your graph with a slope equal to +2 and describe the motion.
2. Draw your graph with a slope equal to -3 and describe the motion.
3. Draw your two graphs that have an area under the curve of 4 and describe the motion for each graph.
4. Draw the graph your group member made and describe the motion.
Answer the following questions based on the Challenge Graph
5. Position-Match Score: _____________________
6. How well did your motion graph match the provided graph?
7. What was the meaning of the part of the position plot where the slope was positive?
8. Were certain parts of the plot easier to match than other parts? Why or why not?
9. Make a sketch of a velocity vs. time graph from the position vs time graph (don’t forget your units).
10. Describe your motion.
Activity 2: Acceleration on an inclined plane.
Pre-lab Questions:
1. Is there constant acceleration (or deceleration) at anytime as the cart rolls up and down the ramp? If so, when?
2. What would constant acceleration look like on an acceleration vs. time graph?
3. What is causing the acceleration after the cart leaves the person’s hand?
Data:
· Sketch your graph for Position vs. Time
· Sketch your graph for Velocity vs. Time
· What is the cart’s acceleration based on the slope of your velocity graph?
· What is the cart’s average acceleration based on the acceleration graph?
Post-Lab Questions:
1. Describe the position vs time plot of the Graph screen. Why does the distance begin at a maximum and decrease as the cart moves up the incline?
2. Describe the velocity cs time plot.
3. Describe the acceleration vs time plot.
4. How does the acceleration determined in the plot of velocity compare to the average value of acceleration from the plot of acceleration?