Relating Position and Velocity for Constant Velocity
Name_______________________________ Date_________________
Pre-Lab: Acceleration and Velocity
1. In Investigation 1, Activity 1, how do you expect that your position-time graphs will differ from those where you were moving with a constant velocity? How about your velocity-time graph?
2. In Investigation 1, Activity 2, what quantity are you using the linear fit function to find?
3. In Investigation 2, Activity 1, explain how to use the fan to make the cart slow down instead of speed up:
4. Draw your predictions for Speeding Up Towards the Motion Detector (Investigation 2, Activity 3):
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Lab Group Members: Date:
Acceleration and Velocity
purpose: Analyze the sign of acceleration for motion with changing velocity.
EQUIPMENT: Motion detector, USB cable, computer, Logger Pro software, cart, track, fan attachment with 4 AA batteries.
Investigation 1 – Measuring acceleration
Activity 1 – Speeding up away
PROCEDURE:
Open Logger Pro Experiments folder to Additional Physics, RealTime Physics, Mechanics, L02A1-1 (Speeding Up ).
Set up the cart, ramp and motion detector as indicated below. Make sure the ramp is level and that the cart is at least 20 cm in front of the motion detector, and that the fan is attached securely.
Conserve batteries and fight noise pollution by turning fan on only when collecting data.
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Turn on the fan, release the cart and collect the data. The fan makes the cart move with a reasonably constant acceleration. We can ignore slight variations. The cart should move away from the motion detector and speed up. When you obtain a good data run (relatively horizontal line acceleration), Store Latest Run (Experiment menu).
1. Examine the position-time graph. How is it different from a position graph for constant velocity? To see the differences more clearly, move the cursor to the time axis, where it will turn into a wavy line. Use that to compress the position graph. Before moving to the next question, go to Edit and Undo your changes.
2. Examine the velocity-time graph. How is it different from a velocity graph for constant velocity?
3. Examine the acceleration-time graph. What feature indicates that it is constant acceleration?
4. How is direction of acceleration (different from direction of motion!) indicated on an acceleration-time graph?
5. Explain why acceleration is positive for this motion:
Activity 2 – Statistics and Curve-Fit
Using statistics: You can use the statistics feature to find the mean acceleration from the acceleration graph. Click on the acceleration graph to make it active. Select the portion of the acceleration graph that you want to use and click on the “STAT” icon:
1. Mean acceleration: magnitude:________ m/s/s sign___________
2 . Compare the acceleration and velocity graphs. Are the signs of acceleration and the velocity the same, or different (circle the correct answer)?
Using linear-fit: You can use the linear-fit feature to find the equation of the best-fit curve for the velocity graph. Select the portion of the velocity graph that you want to use (same as the acceleration graph) and click on the linear fit icon (“R=”).
3. Δv/Δt (slope): magnitude:_______ units________ sign__________
4. State explicitly the relationship between the value of the acceleration graph and the slope of the velocity graph for motion with constant acceleration:
5. Record the equation of the best-fit curve with the given values:___________________
Using curve-fit: Use the curve-fit feature to find the equation of the best-fit curve for the position graph. Select the portion of the position graph that you want to use (same as the acceleration graph) and click on the curve-fit icon (f(x)=). The position graph for constant acceleration is described by a quadratic equation. Click on the “try fit” button to generate the curve-fit.
4. Record the equation of the best-fit curve with the given values:___________________
5. Can you recognize any of the coefficients (A,B,C) from the best-fit curve for of the velocity graph? Which one (or ones)?
6. Print your graphs, with analysis boxes not blocking the actual data. Title the graph “Speeding up Away”.
Investigation 2 – Direction of velocity and acceleration
Activity 1 – Slowing down away
DO NOT CHANGE EXPERIMENT FILE. For this activity, the fan should be pushing the cart towards the motion detector. Now if you push the cart away, it will slow down. Turn the fan unit on and begin graphing. Give the cart a gentle push away from the motion detector. The relevant part of the graph occurs from after you’ve stopped pushing, (i.e. cart is moving on its own) until the cart stops. Identify this portion of your data for analysis. When you get a good data run, print your graphs (no further data analysis). Title should now be (you guessed it) Slowing Down Away.
Mark the start and end of the relevant portion of your data with a pencil, so I can see that you know where it is.
1. Describe the position-time graph. Comparing it to Speeding Up Away, what feature shows slowing down (compress graph to see better)?
2. What is the sign of the velocity values? _________ The sign of the slope _________?
3. The sign of the acceleration graph should be negative (Verify!). Why is the sign of the acceleration opposite to that of the sign of the velocity graph values for this motion? Choose the best hypothesis:
A. Slowing down always results in negative acceleration.
B. When an object slows down, velocity and acceleration have opposite signs.
Activity 2 – Slowing down towards
1. Based on your answer to the above multiple-choice question, predict the sign of the acceleration graph for this motion. This question is graded on logic, not correctness! ________________
2. Clear all data from the previous graph, including title, and repeat the above procedure for slowing down towards the detector . The relevant part of the graph occurs from after you’ve stopped pushing, (i.e. cart is moving on its own) until the cart stops. Identify this portion of your data for analysis. When you get a good data run, print your graphs. Mark the start and end of the relevant portion of your data with a pencil. Title your graph Slowing down towards.
3. Describe the position-time graph. Comparing it to Slowing Down Away, what feature shows motion towards the detector, (compress graph to see better)?
4. Explain why the sign of the velocity values are negative during the time the cart is slowing down. Recall that for “Slowing Down Away” velocity values were positive.
3. What is the sign of acceleration? ______________
4. Why is the sign of the acceleration opposite to that of the sign of the velocity graph values for this motion? Choose the best hypothesis:
A. Slowing down always results in negative acceleration.
B. When an object slows down, velocity and acceleration have opposite signs.
Did you change your hypothesis from the last time this question was asked?
Activity 3 – Speeding up towards
Get your prelab back with your prediction for this motion.
Clear all data from the previous graph and repeat the above procedure for the motion described above. Don’t let the cart hit the motion detector!! When you get a good data run, print your graphs, with the appropriate title.
1. How did the shapes of your velocity and acceleration graphs compare with your predictions? If they were not the same, explain:
2. Fill in the table:
|Type of Motion |sign of velocity |sign of acceleration |
|Speeding Up in Positive Direction | | |
|Slowing Down in Positive Direction | | |
|Slowing Down in Negative Direction | | |
|Speeding Up in Negative Direction | | |
4. How do the signs of velocity and acceleration relate when
a) the object is speeding up
b) the object is slowing down
5. Which one or more of the graphed quantities always shows the direction of the motion?
INVESTIGATION 3 – REVERSING DIRECTION - THE TURNING POINT
In this activity you will look at what happens when the cart slows down away from the motion detector, reverses direction and then speeds up towards the motion detector.
A. Prediction
1. Using your previous observations as a guide, draw a prediction of this situation on the axes that follow.
REVERSING DIRECTION
2. For each part of the motion, indicate in the table below whether signs of velocity and acceleration vectors are positive, negative or zero.
| |Moving away |The turning point |Moving toward |
|Velocity | | | |
|Acceleration | | | |
B. Experiment
Test your predictions. Clear all data from the previous graph and give the cart enough of a push so it travels about one-half meter before it returns. Don’t let the cart hit the motion detector!! When you get a good data run, (A, B, and C, below, must be visible), print your graphs. Make an identifying title for your graph. The relevant part of the graph occurs from after you’ve stopped pushing, (i.e. cart is moving on its own) until just before you stop the cart on its return trip.
3. With pen or pencil, label the following points on both graphs:
A. where your hand left the cart
B. the turning point
C. where you stopped the cart
How did you determine where each of these points is? If any of these points is NOT on your graph, state this explicitly?
4. Did the cart stop at its turning point (i.e. v = 0)? Does this agree with your prediction? Did it spend any time at the turning point velocity before starting back toward the detector? Explain:
5. According to the graph, what is the acceleration at the instant the cart reaches its turning point? Does this agree with your prediction? Using the definition of acceleration (∆v/∆t) explain how the acceleration can be non-zero when the velocity is zero at some instant.
INVESTIGATION 5 GRAPH ANALYSIS
After studying the acceleration and velocity graphs you made, answer the following questions.
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1. An object moving along a line (the + distance axis) has the acceleration-time graph above. How might the object move to create this graph
A. If it is moving away from the origin
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B. If it is moving toward the origin
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2. Sketch on the axes below the velocity-time graphs that go with the above acceleration-time graph (for cases A and B). Label your graphs.
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3. How would an object move to create each of the three labeled parts of the acceleration-time graph above?
a:____________________________________________________________
b:________________________________________________________________
c:________________________________________________________________
4. Sketch below a velocity-time graph which might go with the above acceleration-time graph.
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5. For each of the velocity-time graphs below, sketch the shape of the acceleration-time graph that goes with it.
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6. A car moves along a line [the + distance (position) axis]. Fill in the table below with the sign (+ or -) of the velocity and acceleration of the car for each of the motions described.
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7. Which position-time graph below could be that for a cart that is steadily accelerating away from the origin?
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11-13. A car can move in either direction along a line (the + distance axis). Sketch velocity-time and acceleration-time graphs which correspond to each of the following descriptions of the car's motion. Use the axes provided on the following page.
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14. The following is a velocity-time graph for a car.
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What is the average acceleration of the car? Show your work below.
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15. A ball is tossed in the air. It moves upward, reaches its highest point and falls back downward. Sketch a velocity-time and an acceleration-time graph for the ball from the moment it leaves the thrower's hand until the moment just before it reaches her hand again. Consider the positive direction to be upward.
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16. Sketch the following graphs. Assume constant acceleration:
a. an object speeding up in a positive direction:
b. an object speeding up in a negative direction:
c. an object slowing down in a positive direction:
d. an object slowing down in a negative direction:
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