Group member names:
-Bo White
-Jeremy Cossel
-Aaron Hawkins
Laboratory Activity 3:
Acceleration Graphs
Objectives

Explore how motions are related to acceleration-time graphs

Relate acceleration-time graphs to velocity-time graphs and position-time
graphs

Learn to use vectors to represent motion
Equipment

Computer

Ultrasonic motion sensor

USB Link

Dynamics cart

Track for cart

Fan attachment
Activity One: Speeding up
Velocity
Acceleration
Prediction 1: Using the line tool on the drawing toolbar of Word, draw a line on
both the velocity and acceleration graphs below predicting the shape of a curve
for a cart starting at rest and moving away, speeding up at a constant rate.
Time
Time
Set up the equipment: Obtain a USB Link and a motion detector as in the
previous lab. Open the experiment file called SpeedingUp.ds to display
acceleration and velocity graphs. You can find it by going to the networked disk
“PLAB” (usually disk G:), in that opening the folder “Plab”, then finding the folder
for Physics 201, and then looking in the folder for Lab 3. Set the detector up as
in the previous lab, except make sure the switch on top is set to the ‘cart’ instead
of ‘person’ setting. Lay the track on the table and set the motion detector on the
table at the end of the track that does not have the post. Check that the track is
reasonably level by setting the cart in the middle and seeing if it has a tendency
to roll to one end. If so, level the track by adjusting the base screw at one end.
Look under the fan and check that it has two batteries installed along with two
aluminum cylinders that are taking the place of batteries. Attach the fan to the
cart and put a rubber band on to make sure it doesn’t fall off.
Experiment: Place the cart on the track with the fan pointing away from the
motion detector about 30 cm (1 foot) away from the detector and turn it on, with
one person holding it in position. Have another team member start taking data.
Let go of the cart as soon as the clicking sound is heard, careful to not get any
hands between the detector and the cart, and let the cart speed away. Catch it
just before it crashes into the other end of the track. When you have a nice
graph, copy the graph and paste it in the section below.
Question 1: How did the result compare to your prediction? What feature of the
velocity graph shows that the cart is speeding up at a constant rate? What
feature of the acceleration graph shows that the cart is speeding up at a constant
rate? What does it mean that both the velocity and acceleration graphs are
positive (above the axis) the whole time?
Our velocity prediction was correct, but the acceleration prediction wasn’t. The
velocity graph showed the line was getting farther from the x-axis. On the
acceleration graph, it stayed as a horizontal line, which shows no acceleration.
Both graphs showing positive numbers means that the motion was speeding up
and moving away from the detector.
Velocity
Acceleration
Prediction 2: How will the graphs look if you start the cart at the far end of the
track and let it speed up towards the detector?
Time
Time
Experiment: Set the cart on the far end with the fan pointing toward the detector
and let it speed up toward the detector while taking data. Catch the cart when it
gets about 30 cm from the detector, so it doesn’t crash. Past your graph below.
Question 2: How did the result compare to your prediction? What feature of the
velocity graph shows that the cart is speeding toward the detector up at a
constant rate? What feature of the acceleration graph shows that the cart is
speeding up towards the detector at a constant rate? What does it mean that
both the velocity and acceleration graphs are negative (below the axis) the whole
time?
The result matched our prediction fairly accurately. The velocity graph shows it’s
moving towards and speeding up because the line is moving in the negative
direction getting farther from the x-axis. The acceleration graph shows the line
moving negative below the x-axis. Both of them being negative means that the
cart is moving toward the detector and speeding up.
Velocity
Acceleration
Prediction 3: Now imagine that you return the cart to the far end of the track,
only this time with the fan pointing away from the detector. You give it a quick
push toward the detector, with the fan blowing to slow it down, and you then
catch the cart when it comes to a momentary stop. Draw velocity and
acceleration graphs for this motion.
Time
Time
Experiment: Set the cart on the far end with the fan pointing away the detector
and push it toward the detector so that it slows down while taking data. Catch
the cart when it is about stopped. Past your graph below.
Question 3a: First identify what part of the velocity and acceleration graphs
corresponds to when you pushed on the cart, and which part correspond to when
the cart was moving freely. Focus on the second part in the following questions.
How did the result compare to your prediction? What feature of the velocity
graph shows that the cart is moving toward the detector? What feature shows
that the cart is slowing down at a constant rate?
Our predictions were not correct. The velocity graph shows that it’s moving
toward the detector because the values are starting negative and move toward
the x-axis. The velocity is steadily going towards zero.
Question 3b: Do the acceleration and velocity graphs have the same sign during
the whole time? The acceleration graph has the same sign as what feature of
the velocity graph? What do the relative signs of the velocity and the
acceleration graphs tell you about the motion?
No, the velocity graph is negative but the acceleration graph is positive. The
velocity graph is negative, but it is going towards positive, so that is the feature
that the acceleration graph has the same sign as. It tells us that the cart is
slowing down while moving towards.
Velocity
Acceleration
Prediction 4: In this final case, you will start with the cart about 30 cm from the
detector, with the fan pointing towards the detector, and give it a push away from
the detector. Let the cart slow down and come back, catching it before it hits the
detector. Draw a prediction of the velocity and acceleration graphs.
Time
Time
Experiment: Set the cart about 30 cm from the detector with the fan blowing the
cart towards the detector. Give the cart a quick push, being careful to not let
your hand get in front of the detector. (You may find it easier to grab the sides of
the cart or the end away from the detector.)
Question 4: First identify what part of the velocity and acceleration graphs
corresponds to when you pushed on the cart, and which part correspond to when
the cart was moving freely. Focus on the second part in the following questions.
What does it mean that the velocity graph changes signs? What does the point
that it is zero correspond to in the motion of the cart? Does the acceleration
graph change signs, or is it ever zero?
When the graph changed signs, the object changed directions. The point that it’s
at zero is where the cart makes the transition from moving towards to moving
away. The acceleration is always positive and is never zero.
Activity Two: Vector representations
Vectors (arrows) are an alternative way to indicate the motion of an object. A
velocity vector can be drawn at the location of the object at a particular time with
the length of the arrow representing the relative velocity of the object.
Question 6a: On the picture below, use the arrow drawing tool to draw a velocity
vector underneath each carat in the figure below.
(from RealTime Physics (Electronic Version) by David Sokolof, et al., John Wiley and Sons, NY, 1999)
Question 6b: Compare the method of representing velocity with a graph and
that of using vectors. What aspects indicate the relative time? What aspects
indicate the velocity at a given time? What tells us how the velocity is changing?
Fill the chart out below
Graph
Vectors
Time
Velocity
Direction
Change in
velocity
Question 6c: How would you draw a vector to represent the acceleration of the
cart at each point? Draw vectors on the above diagram below the velocity
vectors to represent the acceleration.
Question 7: Draw velocity and acceleration vectors for the cart speeding up
toward the detector.
(from RealTime Physics (Electronic Version) by David Sokolof, et al., John Wiley and Sons, NY, 1999)
Question 8: Draw velocity and acceleration vectors for the cart slowing down as
it moves toward the detector.
(from RealTime Physics (Electronic Version) by David Sokolof, et al., John Wiley and Sons, NY, 1999)
Summary
The following questions will help you get the main ideas out of this lab. You
should find these straightforward questions, but take the time to talk it over with
your team and write complete answers to these questions. You may find your
answers here to be the most useful part of this lab down the road.
Summary 1: In an acceleration graph, what does the vertical distance from the
axis mean? What does it mean if the line is above the axis, on the axis, or below
the axis?
The vertical distance tells how or if it’s increasing. If the line is above the axis,
the acceleration is positive, if it’s on the axis, there’s no movement, and if it’s
below the axis, the acceleration is negative.
Summary 2: How are velocity and acceleration graphs related? What aspect of
an acceleration graph and what aspect of a velocity graph tell us how something
is changing its motion?
When the velocity is starting negative and moving towards positive, the
acceleration graph is a constant positive line. And vice versa. When the values
cross the x-axis, that’s when the object changes direction.
Summary 3: How do you know your above statements are true? What
experimental observations and/or logical reasoning can you give to justify what
you said in summary questions 1&2?
Our statements are true from observing the results of Dr. Bonham’s experiment.
The graphs clearly showed data that was relatively easy to interpret, and our
answers came from that.
Summary 4: Look over your graphs. How can you tell if an object is speeding up
or slowing down from velocity and acceleration graphs? If both acceleration and
velocity are positive, how is it moving? Both negative? One positive and one
negative? Explain your reasoning.
On the velocity graph, if the values are moving away from the x-axis on either
side, it’s speeding up. If the values are moving toward the x-axis on either side,
it’s slowing down. If the object is moving toward then away, then acceleration will
be on the positive side of the x-axis, and if the object is moving away then
toward, then acceleration will be on the negative side of the x-axis. If they’re
both positive, then the object is moving towards then away. If they’re both
negative, then the object is moving away then towards. The values might be
negative but the slope can be positive. And the values might be positive but the
slope can be negative. When the velocity graph has a positive slope, the
acceleration was positive, and when the velocity graph has a negative slope, the
acceleration was negative.
Summary 5: Describe how to use vectors to represent velocity and acceleration
of an object. How can you tell from the directions of the velocity and acceleration
vectors if the object is speeding up or slowing down?