Relating Position and Velocity for Constant Velocity



Name_______________________________ Date_________________

Pre-Lab Preparation Sheet for

Changing Motion

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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CHANGING MOTION – Part 1: Fan Carts

Objective: To study the concepts of acceleration.

APPARATUS: Ultrasonic motion detector, LabPro interface, computer, Logger Pro software, cart , track or table, fan attachment with 4 AA batteries, printer cable.

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 constant acceleration. The cart should move away from the motion detector and speed up. When you obtain a good data run (relatively straight line acceleration), Store Latest Run (under Experiment menu) give your graph the same title as the activity plus some identifying initials for your group e.g.“Speeding Up Away_GB”. (click on Graph options under the Options 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 the magnitude of acceleration indicated on an acceleration-time graph?

5. How is direction of acceleration indicated on an acceleration-time graph?

Activity 2 – Statistics and Linear Fit, Revisited

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:________ m/s/s

Using linear fit to find the slope : You can use the 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 and click on the linear fit icon (“R=”).

2. Record the equation of the best-fit curve:____________________

This equation is in the form v = mt + b. Explain what the m and the b in this equation actually represents for the moving cart. Don’t use terms like slope, or y-intercept. Instead, explain what they tell you about where the cart is, or what the cart is doing:

m

b

3. Slope (∆v/∆t) m/s/s = ______________

4. How does this value compare with the mean acceleration obtained from the acceleration graph?

4. Is the sign of the acceleration values the same, or opposite to that of the sign of the velocity graph values?

5. State the relationship between the acceleration graph and the slope of the velocity graph:

6. Write a general equation (symbols only) to describe the velocity (v) of an object with constant acceleration, a and initial velocity, v0:

7. Print your graph, with analysis boxes not blocking the actual data. When you have your graph in hand, Clear All Data (Data menu).

Investigation 2 – Direction of velocity and acceleration

Activity 1 – Slowing down away

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. Title should now be (you guessed it) Slowing Down Away_your initials.

1. Describe the position-time graph. Comparing it to speeding up away, what feature (if any) shows slowing down (compress graph to see better)?

2. Describe the velocity-time graph. Comparing it to speeding up away, what feature (if any) shows slowing down?

3. Describe the acceleration-time graph. Comparing it to speeding up away, what feature (if any) shows slowing down?

4. Is the sign of the acceleration values the same as, or opposite to that of the sign of the velocity graph slope? Why would you expect that?

5. Is the sign of the acceleration values the same, or opposite to that of the sign of the velocity graph values?

Activity 2 – Slowing down towards

Repeat the above procedure for the motion described above. 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. Title your graph appropriately.

1. Describe the position-time graph. Comparing it to the previous graphs, what feature (if any) shows motion towards the detector, (compress graph to see better)?

2. Describe the velocity-time graph. Comparing it to the previous graphs, what feature (if any) shows motion towards the detector?

3. Describe the acceleration-time graph. Comparing it to the previous graphs, what feature (if any) shows motion towards the detector (make sure you look at both graphs before answering)?

4. Is the sign of the acceleration values the same as, or opposite to that of the sign of the velocity graph slope? Why would you expect that?

5. Is the sign of the acceleration values the same, or opposite to that of the sign of the velocity graph values?

Activity 3 – Speeding up towards

Get your prelab back with your prediction for this motion. Is there anything on your prediction that you want to change?

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?

2. Is the sign of the acceleration values the same, or opposite to that of the sign of the velocity graph values?

3. Go back and look at all your graphs. When velocity values and acceleration value have the same sign, what is the cart doing?

4. When velocity values and acceleration value have opposite signs, what is the cart doing?

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

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2. For each part of the motion, indicate in the table below whether the velocity and acceleration vectors are positive, negative or zero.

| |Moving away |The turning point |Moving toward |

|Velocity | | | |

|Acceleration | | | |

B. Experiment

Test your predictions. Give the cart enough of a push so it travels about one 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 know where each of these points is?

4. Did the cart “stop” at its turning point? Does this agree with your prediction? How much time did it spend 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.

Questions

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. 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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6. 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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7. 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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11. Sketch the following graphs. Assume constant acceleration and also assume a case like the lab; position can only be positive::

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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