LAB 3: CHANGING MOTION

Please list the members of your group:

OBJECTIVES

OVERVIEW

In the previous lab, you looked at position–time and velocity–time graphs of the motion of the IOLab. The data for the graphs were collected using the Wheel on the IOLab. Your goal in this lab is to learn how to describe various kinds of motion in more detail.

You have probably realized that a velocity–time graph is easier to use than a position–time graph when you want to know how fast and in what direction an object is moving at each instant in time (even though you can calculate this information from a position–time graph).

It is not enough when studying motion in physics to simply say that “the object is moving toward the right” or “it is standing still.” When the velocity of an object is changing, it is also important to describe how it is changing. The rate of change of velocity with respect to time is known as the acceleration.

To get a feeling for acceleration, it is helpful to create and learn to interpret velocity–time and acceleration–time graphs for some relatively simple motions of the IOLab on a smooth ramp. One of the easiest ways to get the IOLab to move with its velocity changing at a constant rate is to have it move under the influence of the Earth’s gravitational force. This can be most easily accomplished by raising one end of the ramp to form an inclined plane.


Copyright © 2018 John Wiley & Sons, Inc.

INVESTIGATION 1: VELOCITY AND ACCELERATION GRAPHS

Activity 1-1: Speeding Up

In this activity you will look at velocity–time and acceleration–time graphs of the motion of the IOLab, and you will be able to see how these two representations of the motion are related to each other when the IOLab is speeding up.

This could be done by moving the IOLab with your hand, but it is difficult to get a steadily changing velocity in this way. Instead you will use an inclined ramp to accelerate the IOLab. Note that the direction down the ramp is the +y direction.



Prediction 1-1: Which of the following graphs would represent position vs. time as the IOLab rolls down the ramp shown above, speeding up at a steady rate in the +y direction.

A B C D E

Activity 1-1: Speeding Up



Prediction 1-2: Which of the following graphs would represent velocity vs. time as the IOLab rolls down the ramp shown above, speeding up at a steady rate in the +y direction.

A B C D E

Activity 1-1: Speeding Up



Prediction 1-3: Which of the following graphs would represent acceleration vs. time as the IOLab rolls down the ramp shown above, speeding up at a steady rate in the +y direction.

A B C D E

Activity 1-1: Speeding Up

In this activity you will observe the shapes of velocity–time and acceleration–time graphs of the IOLab moving along a smooth inclined ramp. You will focus on motions with a steadily increasing velocity.

You will need the following materials:

Activity 1-1: Speeding Up

    IMPORTANT WARNING: Never click the Restart button by mistake. Clicking this button will cause the IOLab to save your work and go back to the beginning. If you do click Restart, follow the instructions about IOLab given to you to retrieve your saved work and start again.

  1. Elevate the ramp to about 20°, as shown. Measure the angle with the protractor.
  2. Ensure the graph axes to the right are for the Wheel for position, velocity and acceleration vs. time.
  3. Hold the IOLab near the top of the ramp with its front (the eye bolt) pointing down the ramp.
  4. Click Record, release the IOLab, collect graphs as it rolls down the ramp, and stop it at the bottom of the ramp.
  5. Repeat the experiment a couple of times, to make sure you captured a good example of speeding up as the IOLab rolled down the ramp. You can graph another run by clicking on +Add Run at the top of this slide
  6. NOTE: Remember that the IOLab and software afford you the opportunity to repeat measurements very quickly. Get into the habit of repeating your measurements until you get a clear representation of what you are exploring.

  7. Once you have a good graph, you should remove any others you made by clicking Remove next to them above the graph. The remaining graph will remain on the screen when you move on, for comparison to future graphs that you make. Adjust the position, velocity and acceleration axes to display the graphs as clearly as possible.

Activity 1-1: Speeding Up

At what time did the following events occur, according to your graphs:

Question 1-1A: The moment you released the IOLab

Question 1-1B: the moment you stopped the IOLab

Question 1-2: Does the position-time graph agree with your prediction? If it is different, what is different, and why?

Question 1-3: How does this position-time graph of the IOLab differ from the position-time graphs for steady(constant velocity) motion that you observed in Lab 1: Introduction to Motion?

Activity 1-1: Speeding Up

Question 1-4: Does the velocity-time graph agree with your prediction? If it is different, what is different, and why?

Question 1-5: What feature of your velocity graph indicates that the motion of the IOLab was in the positive direction?

Question 1-6: What feature of your velocity graph indicates that the IOLab was speeding up? How does a graph of motion with a constant velocity (as in Lab 1) differ?

Activity 1-1: Speeding Up

Adjust the acceleration axis so the graph fills the axes and answer questions below.

Question 1-7: Does the acceleration-time graph agree with your prediction? If it is different, what is different, and why?



Question 1-8A: During the time that the IOLab was speeding up, was the acceleration positive or negative?

Positive Negative

Question 1-8B: How does speeding up while moving in the positive direction result in this sign of acceleration?

(Hint: Remember that acceleration is the rate of change of velocity. Look at how the velocity is changing. It takes two points on the velocity–time graph to calculate the rate of change of velocity.)

Activity 1-1: Speeding Up

Question 1-9A: How does the velocity vary in time as the IOLab speeds up?

Question 1-9B: Does it increase at a steady (constant) rate or in some other way?

Question 1-10A: How does the acceleration vary in time as the IOLab speeds up?

Question 1-11B: Is this what you expect based on the velocity graph? Explain.

Activity 1-1: Speeding Up

The diagram below shows the positions of an IOLab at equal time intervals as it speeds up. Assume that the IOLab is already moving at t1.

Question 1-12: Use the symbols ---> to represent the velocity vectors at the four different times, and label them 1, 2, 3 and 4. Be sure to indicate the magnitude of the velocity at each time with the length of the vector. (For example --> and -----> would represent small and larger velocity to the right, while <-- and <---- would represent velocities to the left)



Activity 1-1: Speeding Up

The diagram below shows the positions of an IOLab at equal time intervals as it speeds up. Assume that the IOLab is already moving at t1.

Question 1-13: Choose from the choices below how you would find the vector representing the change in velocity Δv between the times t3 and t4 (at 2 and 3 s) in the diagram above. (Hint: Remember that the change in velocity is the final velocity minus the initial velocity, and the vector difference is the same as the sum of one vector and the negative of the other vector.)



A B C

Activity 1-1: Speeding Up

Question 1-14: Based on the direction of this vector and the direction of the positive y axis, what is the sign of the acceleration +, 0 or -?

Positive Negative Zero

Question 1-15: Does this agree with your answer to Question 1-8? Explain.

Activity 1-2: Speeding Up More

Prediction 1-2: Suppose that you accelerate the IOLab at a faster rate. How would your velocity and acceleration graphs be different than those above? Describe precisely how your velocity graph would be different than your graphs from Activity 1-1 and also how your acceleration graph would be different.

Test your predictions.

  1. Elevate the track to 30° or more. Again, measure the angle with the protractor.
  2. Click Record and collect velocity-time and acceleration-time graphs. Repeat if necessary to get nice graphs.
  3. Compare your graphs from this activity and the ones persistently displayed from Activity 1-1 to answer these questions.

Question 1-16: Did the changes in the velocity and acceleration graphs agree with your predictions?

Question 1-17: How is the velocity-time graph different for a larger acceleration? How is the magnitude (size) of acceleration represented on a velocity–time graph?

Question 1-18: How is the acceleration-time graph different for a larger acceleration? How is the magnitude (size) of acceleration represented on an acceleration–time graph?

INVESTIGATION 2: SLOWING DOWN AND SPEEDING UP

In this investigation you will look at the IOLab moving up the inclined ramp and slowing down. You will position the ramp so that the IOLab is moving in the positive direction while slowing down. A car being driven along a road and brought to rest when the brakes are applied is a similar type of motion.

Later you will examine the motion of the IOLab speeding up while moving in the negative direction. In both of these cases, we are interested in how velocity and acceleration change over time. That is, we are interested in the shapes of the velocity–time and acceleration–time graphs (and their relationship to each other), as well as the vectors representing velocity and acceleration. You will need the same materials as for Investigation 1.

Activity 2-1: Slowing Down

In this activity you will look at the velocity and acceleration graphs of the IOLab moving in the positive direction and slowing down.

The IOLab and ramp should be set up as shown below. The ramp should be inclined about 20°.

Now, when you give the IOLab a quick push up the ramp (in the positive y direction) it will slow down after it is released. You will stop it at the top before it rolls back down again.

Prediction 2-1: If you give the IOLab a short push up the ramp (in the positive y direction) and release it, will the acceleration be positive, negative, or zero after it is released?

Positive Negative Zero

Activity 2-1: Slowing Down

The IOLab and ramp should be set up as shown below. The ramp should be inclined about 20°.

Now, when you give the IOLab a quick push up the ramp (in the positive y direction) it will slow down after it is released.

Prediction 2-2: Select your prediction for the velocity–time graph from the choices above.

A B C D E

Activity 2-1: Slowing Down

The IOLab and ramp should be set up as shown below. The ramp should be inclined about 20°.

Now, when you give the IOLab a quick push up the ramp (in the positive y direction) it will slow down after it is released.

Prediction 2-3: Select your prediction for the acceleration–time graph from the choices above.

A B C D E

Activity 2-1: Slowing Down

Test your predictions.

  1. Click Record to begin graphing, give the IOLab a short push up the ramp and release it, stopping it near the top of the ramp. Use your hand to prevent it from rolling back down the ramp. You may have to try a few times to get a good set of graphs.
  2. Carefully read and record the times of the following points on your graphs:

    Question 2-1A: at the spot where you started pushing.

    Question 2-1B: at the spot where you stopped pushing (released the IOLab).

    Question 2-1C: the region where you were not pushing the IOLab.

    Question 2-1D: at the spot where the IOLab came to rest (and you stopped it with your hand).

    Question 2-1E: Describe how you identified each of the points A, B, C and D on your graphs.

Activity 2-1: Slowing Down

Question 2-2: Did the shapes of your velocity and acceleration graphs agree with your predictions? If they differed, describe how and why.

Question 2-3: From your graphs, what is the sign of the acceleration during the time interval when the IOLab was slowing down?

Positive Negative Zero

Question 2-4: How can you tell the sign of the acceleration from a velocity–time graph?

Activity 2-1: Slowing Down

Question 2-5: How can you tell the sign of the acceleration from an acceleration–time graph?

Question 2-6: Is the sign of the acceleration (which indicates its direction) what you predicted? How does slowing down while moving in the positive direction result in this sign of acceleration? (Hint: Remember that acceleration is the rate of change of velocity with respect to time. Look at how the velocity is changing.)

Activity 2-1: Slowing Down

Question 2-7: The diagram above shows the positions of the IOLab at equal time intervals. (This is like overlaying snapshots of the IOLab at equal time intervals.) Describe in words the directions of the vectors you could draw above the IOLab at each time that might represent the velocity of the IOLab at that time while it is moving up the ramp in the positive direction and slowing down.

Question 2-8: Use the symbols ---> to represent the velocity vectors at the four different times, and label them 1, 2, 3 and 4. Be sure to indicate the magnitude of the velocity at each time with the length of the vector.

Question 2-9: Choose from the choices below how you would find the vector representing the change in velocity Δv between the times t3 and t4 (at 2 and 3 s) in the diagram above. (Hint: Remember that the change in velocity is the final velocity minus the initial velocity, and the vector difference is the same as the sum of one vector and the negative of the other vector.)

A B C

Question 2-10: Based on the direction of this vector and the direction of the positive y axis, what is the sign of the acceleration +, 0 or -?

Positive Negative Zero

Question 2-11: Does this agree with your answer to Question 2-3?

Yes No

Activity 2-1: Slowing Down

Question 2-12: Based on your observations in this lab, state a general rule to predict the sign (the direction) of the acceleration if you know the sign of the velocity (i.e., the direction of motion) and whether the object is speeding up or slowing down.

Activity 2-2 Speeding Up While Moving In the Negative Direction

Prediction 2-4: Suppose now that you start with the IOLab at the top of the ramp, and let it roll down in the negative direction. See the diagram above. Select the graph below that correctly describes velocity vs. time for this motion, speeding up as the IOLab moves down the ramp in the negative direction.

A B C D E

Prediction 2-5: Select the graph below that correctly describes acceleration vs. time for this motion, speeding up as the IOLab moves down the ramp in the negative direction. (Use your general rule from Question 2-13.)

A B C D E

Activity 2-2 Speeding Up While Moving In the Negative Direction

Test your predictions.

  1. Click Record to begin graphing and release the IOLab from rest from the top of the ramp. Stop the IOLab before it reaches the bottom of the ramp.
  2. Repeat as needed. Adjust the axes as needed to make your graphs clearer.
  3. When you feel your graphs accurately depict the situation, continue on to the questions on the next slides.

Activity 2-2 Speeding Up While Moving In the Negative Direction

Question 2-13: How does your velocity graph show that the IOLab was moving in the negative direction? Explain.

Question 2-14A: During the time that the IOLab was speeding up, is the acceleration positive, zero, or negative?

+ Positive - Negative Zero

Question 2-14B: Does this agree with your prediction? If not, explain why.

Question 2-15: Compare the acceleration you observed on your graphs to that from Activity 2-1 that was persistently displayed. Does this agree with your prediction? Explain how speeding up while moving in the negative direction results in this sign of acceleration.(Hint: Look at how the velocity is changing.)

Activity 2-2 Speeding Up While Moving In the Negative Direction

Question 2-16A: When an object is speeding up, what must be the direction of the acceleration relative to the direction of the object’s velocity?

Same Opposite No acceleration

Question 2-16B: According to your graphs, are they in the same or different directions? Explain.

Activity 2-2 Speeding Up While Moving In the Negative Direction

Question 2-17: The diagram above shows the positions of the IOLab at equal time intervals. Describe in words the directions of the vectors you could draw above the IOLab at each time that might represent the velocity of the IOLab at that time while it is moving down the ramp in the negative direction and speeding up.

Question 2-18: Use the symbols ---> to represent the velocity vectors at the four different times, and label them 1, 2, 3 and 4.

Question 2-19: Choose from the choices above how you would find the vector representing the change in velocity Δv between the times t3 and t4 (at 2 and 3 s) in the diagram above.

A B C

Activity 2-2 Speeding Up While Moving In the Negative Direction

Question 2-20: Was your general rule in Question 2-12 correct? If not, modify it and restate it here.

Question 2-21: There is one more possible combination of velocity and acceleration directions for the IOLab: moving in the negative direction and slowing down. Using your general rule predict the sign of the acceleration in this case, +, - or 0.

Postive Negative Zero

Question 2-22: Explain why the acceleration should have this sign in terms of the sign of the velocity and how the velocity is changing.

Activity 2-3: Slowing Down While Moving in the Negative Direction

Question 2-23: The diagram above shows the positions of the IOLab at equal time intervals for the motion described in Question 2-21. Describe in words the directions of the vectors you could draw above the IOLab at each time that might represent the velocity of the IOLab at that time while it is moving up the ramp in the negative direction and slowing down. Assume that the IOLab is moving at t1 and t4.

Question 2-24: Use the symbols ---> to represent the velocity vectors at the four different times, and label them 1, 2, 3 and 4. Be sure to indicate the magnitude of the velocity at each time with the length of the vector.

Question 2-25: Choose from the choices above how you would find the vector representing the change in velocity Δv between the times t3 and t4 (at 2 and 3 s) in the diagram above.

A B C

Question 2-26: Was your general rule in Question 2-13 correct? If not, modify it and restate it here.

Activity 2-4: Reversing Direction

In this activity you will look at what happens when the IOLab slows down, reverses its direction, and then speeds up in the opposite direction. How does the velocity change with time? What is the IOLab’s acceleration?

The setup should be the same as in Activities 2-1 and 2-2. The ramp should be inclined to 20°.

Prediction 2-6: You give the IOLab a very short push up the inclined ramp (positive direction). It moves up the ramp, slows down, reverses direction, and then moves back down the ramp. For each part of the motion—up the ramp, at the turning point, and back down the ramp—indicate below whether the velocity will be positive, zero, or negative. Also indicate whether the acceleration will be +, 0, or -.

Velocity moving up the ramp v > 0 v < 0 v = 0 Acceleration moving up the ramp a > 0 a < 0 a = 0 Velocity at the turning point v > 0 v < 0 v = 0 Acceleration at the turning point a > 0 a < 0 a = 0 Moving down the ramp v > 0 v < 0 v = 0 Moving down the ramp a > 0 a < 0 a = 0

Activity 2-4: Reversing Direction

Prediction 2-7: Select the graph below that correctly describes velocity vs. time for this motion, slowing down as the IOLab moves up the ramp in the positive direction, coming to rest, reversing direction and speeding up as the it moves down the ramp in the negative direction.

A B C D E

Activity 2-4: Reversing Direction

Prediction 2-8: Select the graph below that correctly describes acceleration vs. time for this motion, slowing down as the IOLab moves up the ramp in the positive direction, coming to rest, reversing direction and speeding up as the it moves down the ramp in the negative direction.

A B C D E

Activity 2-4: Reversing Direction

Test your predictions

  1. Begin with the IOLab near the bottom of the ramp with the eye bolt pointing up the ramp (positive y direction).
  2. Click Record to begin graphing. Give the IOLab a short push up the ramp and release, so that it travels almost to the top of the ramp. The IOLab will slow down, and then it will reverse its direction and roll down the ramp again. Stop it with your hand when it reaches the bottom.
  3. You will want to try a few times to get a good round trip.

  4. When you get a good round trip, adjust the axes to display the graphs as clearly as possible. Then move on to the next slide and answer the questions.

Activity 2-4: Reversing Direction

Question 2-28A: At what time did you start pushing the IOLab?

Question 2-28B: At what time did the IOLab push end? (where your hand left the IOLab)

Question 2-28C: At what time did the IOLab reach its highest point? (and was about to reverse direction)

Question 2-28D: At what time did you stop the IOLab with your hands?

Question 2-28E: You found the points A, B, C, and D on both graphs. Explain how you know where each of these points is.

Activity 2-4: Reversing Direction

Question 2-29A: Did the IOLab “stop” at its turning point? (Hint: Look at the velocity graph. What was the velocity of the IOLab at its turning point?)

Yes No

Question 2-29B: Does this agree with your prediction?

Yes No

Question 2-29C: Did it spend much time at the turning point before it started back down the ramp? Explain.

Activity 2-4: Reversing Direction

Question 2-30: According to your acceleration graph, is the acceleration at the instant the IOLab reaches its turning point +, 0 or -?

Positive Negative Zero

Question 2-31A: Is the acceleration significantly different from that during the rest of the motion?

Yes No

Question 2-31B: Does this agree with your prediction?

Yes No

Question 2-32: Explain the observed sign of the acceleration at the turning point. (Hint: Remember that acceleration is the rate of change of velocity. When the IOLab is at its turning point, what will its velocity be in the next instant? Will it be positive or negative?)

Activity 2-5: Sign of the Push and Stop

Question 2-33: Find on your acceleration graph for Activity 2-4 the time intervals when you pushed the IOLab to start it moving and when you stopped it.

What was the sign of the acceleration for the push?

Positive Negative Zero

What was the sign of the acceleration for the stop?

Positive Negative Zero

Question 2-34: Explain why the acceleration has this sign in each case.

Push

Stop

Activity 2-6: Challenge

Challenge: You throw a ball up into the air. It moves upward, reaches its highest point, and then moves back down toward your hand. Assuming that upward is the positive direction, indicate below whether the velocity is positive, zero, or negative during each of the three parts of the motion. Also indicate if the acceleration is positive, zero, or negative. (Hint: Remember that to find the acceleration, you must look at the change in velocity.)

Moving up after release

v > 0 v < 0 v = 0

Moving up after release

a > 0 a < 0 a = 0

At the highest point

v > 0 v < 0 v = 0

At the highest point

a > 0 a < 0 a = 0

Moving down

v > 0 v < 0 v = 0

Moving down

a > 0 a < 0 a = 0

Question 2-35: In what ways is the motion of the ball similar to the motion of the IOLab that you observed in Activity 2-4? What causes the ball to accelerate?

INVESTIGATION 3: MOTION SIMILAR TO AN INCLINED RAMP OR BALL TOSS

Now you will observe another example of the IOLab reversing its motion. Suppose it is on a smooth level surface as shown below. The mass hung from fishing line attached to the back of the IOLab provides a constant force to the left (the negative y direction).

Activity 3-1: The Motion of the IOLab Pulled by a Hanging Mass

The IOLab is given a short push to the right and released.

Prediction 3-1: Select the graph below that correctly describes velocity vs. time for this motion after release, slowing down as the IOLab moves in the positive direction, coming to rest, reversing direction and speeding up as the it moves back in the negative direction.

A B C D E

Prediction 3-2: Select the graph below that correctly describes acceleration vs. time for this motion after release, slowing down as the IOLab moves in the positive direction, coming to rest, reversing direction and speeding up as the it moves back in the negative direction.

A B C D E

Activity 3-1: The Motion of the IOLab Pulled by a Hanging Mass

To test your prediction you will need the following:

  1. Attach one end of the fishing line to the mass and the other end to the back of the IOLab (the wire rod). Ensure that the hanging mass is not swinging wildly.
  2. Click on Record to collect graphs of velocity and acceleration for the motion of the IOLab along the horizontal surface as you give it a short push to the right (in the positive y direction), release it and then stop it when it returns to its original position.
  3. Adjust the velocity and acceleration axes to display the graphs as clearly as possible.

Activity 3-1: The Motion of the IOLab Pulled by a Hanging Mass

Question 3-1A: At what time did you start pushing the IOLab?

Question 3-1B: At what time did the IOLab push end? (where your hand left the IOLab)

Question 3-1C: At what time did the IOLab reach its furthest point to the right? (and was about to reverse direction)

Question 3-1D: At what time did you stop the IOLab with your hands?

Activity 3-1: The Motion of the IOLab Pulled by a Hanging Mass

Question 3-2: Describe your graphs. Did they agree with your predictions?

Question 3-3: Would you describe this motion as having constant velocity or constant acceleration? Explain.

Activity 3-1: The Motion of the IOLab Pulled by a Hanging Mass

Question 3-4: What was the sign of the acceleration as the IOLab moved to the right?

Postive Negative Zero

Question 3-5: What about to the left?

Postive Negative Zero

Question 3-6: Explain your answers to these two questions by your rule in Question 2-12.

Activity 3-1: The Motion of the IOLab Pulled by a Hanging Mass

Question 3-7: What was the sign of the acceleration of the IOLab when it was at its furthest point to the right, positive, zero, or negative?

Postive Negative Zero

Question 3-8: Explain this value for acceleration.

Question 3-9: Are your graphs similar to any set of the graphs in Investigation 2? Which ones? Explain why these sets of graphs are similar in shape.

ALL DONE!

Please remember to edit the report (insert your name - and if necessary your partners), export the report and submit it on D2L.


Now do the homework associated with this lab.


Copyright © 2018 John Wiley & Sons, Inc. and David Sokoloff, Erik Jensen, and Erik Bodegom.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise.