# Motion Measurement

 Write down your expectations. Make a guess about how fast you can turn a stopwatch on and off. 1 second? 10 seconds? 0.1 seconds? 0.01 seconds? If you just sit the wooden channel up on the wooden block and roll the ball down it, what is you guess about how long it will take to roll down the incline? Suppose you measured the time for the ball to roll down the ramp from a given height. If you raise the ramp to twice as high, will it cut the time in half? more than half the time? less than half the time?

Physical measurements are never exact, and it is important to assess the uncertainty in measurements. One way to do this is to repeat measurements and average the results. The maximum deviation from the average is one way to assess uncertainty (although not the best way). In the following measurements, measure each case at least three times and take an average. Then record the number like the following example.

 Measured times: 5.6 sec 6.0 sec 6.2 sec Sum 17.8 sec  ÷ 3 = 5.9 sec average

Experimental time: 5.9 ± 0.3 sec since the maximum deviation from the average is 0.3 sec.

(Checking one-by-one: 5.9-5.6 = 0.3, 5.9-6.0 = -.1, 5.9-6.2 = -.3, so the biggest difference has a size 0.3 . Using this maximum deviation from your average as your estimate of measurement uncertainty gives you a sort of "worst case" estimate of the uncertainty of your measurement.)

1. Start and stop the stopwatch as quickly as you can. This will give you a measure of your reaction time.

 Reaction time __________ __________ __________

Experimental reaction time    ___________  ±   ___________ sec.

2. Drop the ball provided from a height of one meter and measure the time required to hit the floor. Find an experimental fall time by the above procedure.

3. Assemble the track so that the bottom of the ball in its starting position may be positioned 2 cm above the flat surface (basically, this will mean just sitting the end of the track on top of the supporting block). Let the ball roll down the incline and measure the time when it leaves the track at the bottom end. Measure the length of the track so that you may calculate the average speed.

4. Will doubling the height of the upper end of the incline cut the time in half? Measure it and find out.

5. What height will cut the roll time in half? Experiment and find out. Record the height and the times for your closest approach to half the time in part 3.

6. Referring to your data in part 3:
What uncertainty in time measurement would you expect to come from your starting and stopping the stopwatch? (Hint: see part 1). __________

What is the average velocity for part 3?  __________

What is the velocity of the ball at the bottom of the track in part 3?  ___________

## Equipment: Motion Measurement

• Wooden channel made of corner molding
• 3 x 3 inch wooden blocks, drilled for dowel rod
• 1/4" dowel rod
• metal clip for use in adjusting height
• stopwatch
• meter stick
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