Stopping Distance vs. Velocity
(uses a Pasco Interface)
-> Mr. Stanbrough ->
AP Physics-> Kinematics-> this
What is the relationship between stopping distance and initial
velocity for an object subject to a constant deceleration?
When you apply the brakes of a car, the brakes applies a (more or
less) constant force to stop the car, which produces a (more or less)
constant deceleration for the car. Most people believe that they know
the relationship between the velocity that the car has before the
brakes are applied and the distance required to stop the car, but
they're wrong! (The theory
was discussed in the simulation.)
The purpose of this experiment is to check this out - without
wrecking any cars! A friction force between an object and a table is
also (more or less) constant, so in this lab you simulate the
stopping of a car by sliding a cylindrical mass across a horizontal
Here's what happens: you slide the mass through the photogate,
which measures the time that its light beam is blocked. This, along
with the diameter of the cylinder, allows you to calculate the
cylinder's average velocity, v, through the photogate. (Note:
The Science WorkshopTM photogate is automatically
programmed to calculate this velocity for you, and we will use
this feature - next time. For this lab, you will create your own
calculation for starting velocity.) You will measure and record the
distance that the cylinder slides before stopping manually. Given
enough good data, you should be able to discern the quantitative
relationship between velocity and stopping distance. There is an
PhysicsTM simulation of this situation, also.
Pasco Science WorkshopTM interface
Setting Up the Pasco Interface:
Turn on "Show Balloons" in the Help Menu. It will explain
the purpose of the various icons in the Pasco interface - which
is a big help.
Hook up and
initialize the Pasco Science WorkshopTM
Here is what the Calculator
Window would look like for a cylinder 0.022 m in
- Set up a
to measure the time the cylinder blocks the gate.
- Create a new
for the velocity of the cylinder through the gate.
keyboard entry ()
for the stopping distance of the cylinder.
- Create a data
to display time, starting
velocity and stopping distance.
- Create a
to display starting velocity vs.
the Graph Setup dialog (),
and uncheck "Connect Points". You can also re-title the graph,
and enable point protectors if you wish.
- Resize and arrange the windows for a convenient display.
the Record icon ()
in the Experiment Setup WIndow.
- Slide the mass through the photogate. Start
easy! - aim for a first slide of 5 cm or so.
Don't hit the photogate!! - they are
expensive! If you hit the side of the photogate or something else
bad happens, record this information along with the trial number
so that you can identify the "bad" data later.
- Measure the distance that the mass slid after passing through
the photogate. It might be good to think about the best way of
doing this. (Hint: Instead of moving the meter stick (and
probably the photogate) to measure each trial, you could leave the
photogate and meter stick in place for each trial, and use a 3x5
card or piece of paper as a 90o index ("square" to the
meter stick) to measure the distance. This may or may not provide
more consistent results that whatever method you can think of -
ti's just a hint...) Record the distance and press
<Return>.(Of course, as you make your measurements, be
- Remember that your lab book should be an "as it happens"
account of your work, and should contain a diagram of your lab
setup and a brief description of the procedure that you are
- When you have enough data (Ha!), click on "Stop Sampling". You
can make another run by clicking on Record ()
The analysis of your experimental data can proceed pretty-much as
it did in the simulation,
except that this is real data, and you will need to determine
the probable uncertainty in your measurements and calculations, and
add error bars to your
graphs. You can copy your data to the Clipboard, and paste it into
the Graphical AnalysisTM program if you like, and
then analyze it like you did in the simulation, or you can use the
Science WorkshopTM graphing tools. The links below
point to Science WorkshopTM notes on analysis of
- Stopping Distance: Having measured several stopping
distances, you should have a pretty good idea of the process, and
be able to decide on and justify an uncertainty for your
measurements. What factors contributed to this uncertainty?
- Starting Velocity: The starting velocity is the
diameter of the cylinder divided by the time interval recorded by
the photogate, so the relative uncertainty
in the starting velocity equals the sum of the relative
uncertainties of the diameter measurement and the time
measurement. You should be able to estimate and justify the
uncertainty in your diameter measurement. You can consider the
in the time measurement to be in the range 1.4 ms to 2 ms (1.4
x 10-4 s to 2 x 10-4 s). Instead of
calculating a relative
uncertainty for each trial, you can use the average
time (The uncertainty is an estimate, remember.) and
calculate one relative uncertainty for the velocity.
horizontal and vertical error bars (if appropriate) to your
graph, and do a curve
fit to check how your data compares to theory. To plot a graph of
v2 vs. x, create
the v2 calculation (shown at right) and add
a new column to your data table to hold it. Then create
a new graph of v2
So, what do you think? In particular,
- Does your data support the hypothesis that stopping distance
is proportional to the square of the initial valocity? Why do you
- What was the measurement that contributed the most uncertainty
to your results? How could this be improved if you were to do this
- What was the acceleration of the object in your experiment,
anyway? (Show a calculation, please.)
-> Mr. Stanbrough ->
AP Physics-> Kinematics-> this
last update July 12, 2000 by JL