Free 125 Physics Projects for the Evil Genius by Jerry Silver Page B

gravitational acceleration is
constant
and affects an object in free-fall,
regardless of whether it is moving up or down
.

    Figure 19-4
Velocity versus time for a falling ball. The slope of each line gives the acceleration of the ball in free fall. Courtesy PASCO
.
Why It Works
     
    Part 1 is a direct measurement and application of the basic motion formula:
    a = 2d/t 2
    where we find the acceleration due to the force of gravity.
    Part 2 measures the same thing, but it uses a much more precise measurement of the distance traveled in a given time. We know from Projects 1 and 2 that the slope of the distance versus the time graph gives a measure of velocity. Similarly, the slope of the velocity versus the time graph gives acceleration. Each bounce provides a replication of this experiment that can provide a separate data point.
Other Things to Try
     
    A motion sensor reveals the brief time that a ball encounters the ground as it compresses, decompresses, and eventually reverses direction. Some balls do this more quickly than others. This can be seen in time-lapse photography but can also be noticeable in the distance versus time graphs generated by motion sensor.
    There is another method for measuring the Earth’s gravitational acceleration using a pendulum. See Project 22 . Compare this with the results you get with the motion sensor.
The Point
     
    This experiment gives two ways to measure the acceleration on any object caused by the gravitational force of the Earth. The first way is a direct measurement limited by the reaction time to record how long it takes an object to fall. The second method uses a motion sensor that captures this data with greater resolution and precision, and when interpreted graphically gives a more accurate value for gravitational acceleration. In either case, the correct value is 9.8 m/s 2 or 32 ft/s 2 .

Project 20
The buck stops here (the falling dollar). Using a meterstick to measure time .
     
The Idea
     
    This experiment explores the nature of
free-fall
: the longer an object falls, the greater the
distance
it falls. Measuring the distance an object falls can give an indication of the
time
. This can be used to estimate a person’s reaction time. You use both a dollar bill and a meterstick to prove this point.
What You Need
     
meterstick
Method
     
     
This requires two people. The first person holds a meterstick upside down, so the end that reads 0 cm is directed downward.
The second person holds their fingers at the bottom of the meterstick ready to grab the meterstick, as shown in Figure 20-1 .
The meterstick is dropped, and then caught as shown in Figure 20-2 .
The
distance
the meterstick falls is an indication of the person’s reaction
time
. Under gravitational acceleration, distance is related to time according to the equation d = ½ gt 2 where
g
is the gravitational acceleration constant, 9.8 m/s 2 , and time is measured in seconds. This equation gives the distance in meters. This relationship is tabulated in Table 20-1 :

    Figure 20-1
Ready to catch the meterstick
.

    Figure 20-2
The position where the meterstick is caught is an indication of the time it was falling
.
    Table 20-1

Expected Results
     
    The reaction
time
can be determined by the
distance
that the meterstick falls before being caught. The meterstick will typically fall about 10–20 centimeters before being caught, but this will vary with the individual.
Why It Works
     
    The distance an object falls increases with the
square
of the time it falls. Similarly, the time it takes to fall is proportional to the
square
root of the distance.
Other Things to Try
     
    A dollar bill is about 15.2 cm (6 inches) in length. According to the previous chart, it will take a dollar bill nearly 0.18 seconds to fall. Challenge someone to catch the dollar. Unless the person anticipates that release, the bill will fall (almost every time).

    Figure 20-3
Money often seems to fall through our hands. It falls through its own length in