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.
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.
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.
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.
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:
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.
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.
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?
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?
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?
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.)
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.
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)
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.)
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 -?
Question 1-15: Does this agree with your answer to Question 1-8? Explain.
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.
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?
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.
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?
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.
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.
Test your predictions.
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.
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?
Question 2-4: How can you tell the sign of the acceleration from a velocity–time graph?
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.)
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.)
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 -?
Question 2-11: Does this agree with your answer to Question 2-3?
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.
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.
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.)
Test your predictions.
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?
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.)
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?
Question 2-16B: According to your graphs, are they in the same or different directions? Explain.
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.
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.
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.
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.
Question 2-26: Was your general rule in Question 2-13 correct? If not, modify it and restate it here.
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 -.
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.
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.
Test your predictions
You will want to try a few times to get a good round trip.
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.
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?)
Question 2-29B: Does this agree with your prediction?
Question 2-29C: Did it spend much time at the turning point before it started back down the ramp? Explain.
Question 2-30: According to your acceleration graph, is the acceleration at the instant the IOLab reaches its turning point +, 0 or -?
Question 2-31A: Is the acceleration significantly different from that during the rest of the motion?
Question 2-31B: Does this agree with your prediction?
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?)
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?
What was the sign of the acceleration for the stop?
Question 2-34: Explain why the acceleration has this sign in each case.
Push
Stop
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
Moving up after release
At the highest point
At the highest point
Moving down
Moving down
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?
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).
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.
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.
To test your prediction you will need the following:
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?
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.
Question 3-4: What was the sign of the acceleration as the IOLab moved to the right?
Question 3-5: What about to the left?
Question 3-6: Explain your answers to these two questions by your rule in Question 2-12.
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?
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.
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.