# Stopping Distance vs. Velocity

### (uses a Pasco Interface)

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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 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 Interactive PhysicsTM simulation of this situation, also.

## Pasco Science WorkshopTM interface photogate meter stick cylindrical mass Setting Up the Pasco Interface:

### Hint:

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.

1.  Here is what the Calculator Window would look like for a cylinder 0.022 m in diameter.
Hook up and initialize the Pasco Science WorkshopTM interface.
2. Set up a photogate () to measure the time the cylinder blocks the gate.
3. Create a new calculation () for the velocity of the cylinder through the gate.
4. Enable keyboard entry () for the stopping distance of the cylinder.
5. Create a data table () to display time, starting velocity and stopping distance.
6. Create a graph () to display starting velocity vs. stopping distance.
1. Open the Graph Setup dialog (), and uncheck "Connect Points". You can also re-title the graph, and enable point protectors if you wish.
7. Resize and arrange the windows for a convenient display.

## Procedure:

1. Click the Record icon () in the Experiment Setup WIndow.
2. 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.
3. 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 thinking about uncertainties.)
4. 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 using.
5. When you have enough data (Ha!), click on "Stop Sampling". You can make another run by clicking on Record () again.

## Results:

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 the data.

### Measurement Uncertainties:

• 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 absolute uncertainty 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.

### The Graphs:

Add 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 vs. x.

## 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? (Show a calculation, please.)

[Lab Index]
BHS -> Staff -> Mr. Stanbrough -> AP Physics-> Kinematics-> this page
last update July 12, 2000 by JL Stanbrough