# Stopping Distance vs. Velocity

### (uses a Pasco DataStudioTM Interface)

[Lab Index]

BHS -> Staff -> Mr. Stanbrough -> AP Physics-> Kinematics-> this page

## Purpose:

What is the relationship between stopping distance and initial velocity for an object subject to a constant deceleration?

## Discussion:

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 Experiment:

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 table.

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 speed, v, through the photogate. You will measure and record the distance that the cylinder slides before stopping. Given enough good data, you should be able to discern the quantitative relationship between velocity and stopping distance. (There is an Interactive PhysicsTM simulation of this situation, also.)

## Pasco DataStudioTM interface photogate with stand the experiment file "v_vs_stopdist.ds" cylindrical mass meter stick vernier caliper poster board or large sheet of paper Setting Up:

1. Connect the Pasco Science Workshoptm 500 Interface to a USB port of your computer.
2. Switch the interface on. The green light on the front of the interface should be illuminated.
3. Open the experiment file "v_vs_stopdist.ds".
4. Plug the photogate into digital channel 1 on the interface, as shown in the Experiment Setup window. The photogate's red LED should light when you block the photogate.
5. Measure the diameter of the cylindrical mass and enter this value (in cm) in the dialog box in the Calculator window. This enables the interface to calculate the average speed of the mass (distance/time) as it passes through the photogate.
6. Place the poster board or a large sheet of paper on your lab table to protect its surface from the sliding mass.
7. Draw a reference line on the poster board and place the photogate on the line. This will enable you to replace the photogate in case it is accidentally bumped during the experiment.

## Procedure:

1. Click theStart button () in the toolbar at the top of the screen. (It turns into a Keep/Stop button ().)
2.
3. 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! The time that the mass blocked the photogate (in seconds) and its average speed through the photogate (in cm/sec) appear in read in the data table.
4. 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...) Highlight the "Stopping Distance) box in the data table and record the distance, then press <Return>.(Of course, as you make your measurements, be thinking about uncertainties.)
5. Press the Keep button () to record the data. The elapsed time and speed values change from red to black, and a point is plotted on the stopping distance vs. valocity graph.
6. You want to take a reasonable amount of data over as wide a range of velocities/distances as you can manage. As you work, you can refer to the graph to see what distances you are missing and try to "shoot for" those distances. Remember to press the Keep button after each data set. When you believe that you have enough data (Ha!), press the Stop button().
7. If you have time, another trial or two might be interesting - particularly if you can find a different surface on which to slide the mass.

## Results:

1. Add error bars to your graph by clicking the Options button () in the Graph Window tool bar, and selecting the "Error Estimates" tab.
2. The Graph Window's tool bar contains a Fit Menu () in which you can find an appropriate mathematical model for your data. Remember: the question is "Does the data support or reject the theoretical model?" - not "Can I find some strange random function that more-or-less fits the data?"
3. Print copies of your data table(s) and graph(s) for your lab notebook.

## Conclusions:

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 think so?
• What was the measurement that contributed the most uncertainty to your results? How could this be improved if you were to do this experiment again?
• What was the acceleration of the object in your experiment, anyway? To what extent was the acceleration constant? (Show a calculation or two, please.)

[Lab Index]
BHS -> Staff -> Mr. Stanbrough -> AP Physics-> Kinematics-> this page
last update March 17, 2004 by JL Stanbrough