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| Acceleration Due to Gravity |
Small variations
in the acceleration due to gravity, g, occur at different
places on Earth. This is because g varies with distance from
the center of Earth and is influenced by the subsurface geology. In
addition, g varies with latitude due to Earth’s rotation.
For motion with constant acceleration, the displacement, df
– di = vi(tf
– ti) + ½a(tf
– ti)2
. If di = 0 and
ti = 0, then the
displacement is df = vitf
+ ½atf2.
Dividing both sides of the equation by tf
yields the following: df
/tf = vi
+ ½atf . The slope
of a graph of df /tf
versus tf , is equal to
½a. The initial velocity, vi
, is determined by the y-intercept. In this activity, you
will be using a spark timer to collect free-fall data and use it to
determine the acceleration due to gravity, g.
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Question
How does the value of g vary from place to place?
- Measure free fall data.
- Make and use graphs of velocity versus time.
- Compare and contrast values of g for different
locations.
- Keep clear of falling masses.
spark timer
timer tape
1-kg mass
C-clamp
stack of newspapers
masking tape
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- Attach the spark timer to the edge of the lab table with the
C-clamp.
- If the timer needs to be calibrated, follow your teacher’s
instructions or those provided with the timer. Determine the period
of the timer and record it in the Data
Table.
- Place the stack of newspapers on the floor, directly below
the timer so that the mass, when released, will not damage the
floor.
- Cut a piece of timer tape approximately 70 cm in length and
slide it into the spark timer.
- Attach the timer tape to the 1-kg mass with a small piece of
masking tape. Hold the mass next to the spark timer, over the
edge of the table so that it is above the newspaper stack.
- Turn on the spark timer and release the mass.
- Inspect the timer tape to make sure that there are dots marked
on it and that there are no gaps in the dot sequence. If your
timer tape is defective, repeat steps 4-6 with another piece of
timer tape.
- Have each member of your group perform the experiment and collect
his or her own data.
- Choose a dot near the beginning of the timer tape, a few centimeters
from the point where the timer began to record dots, and label
it 0. Label the dots after that 1, 2, 3, 4, 5,
etc. until you get near the end where the mass is no longer in
free fall. If the dots stop, or the distance between them begins
to get smaller, the mass is no longer in free fall.
- Measure the total distance to each numbered dot from the zero
dot, to the nearest millimeter and record it in the Data
Table. Using the timer period, record the total time associated
with each distance measurement and record it in the Data
Table.
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- Use Numbers Calculate the values for
speed and record them in the Data
Table
.
- Make and Use Graphs Draw a graph of speed versus
time. Draw the best-fit straight line for your data.
- Calculate the slope of the line. Convert your result
to m/s2.
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- Recall that the slope is equal to ½a. What is
the acceleration due to gravity?
- Find the relative error for your experimental value of
g by comparing it to the accepted value.
| Relative error = |  |
- What was the mass's velocity, vi ,
when you began measuring distance and time?
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What is the advantage of measuring several centimeters
away from the beginning of the timer tape rather than from
the very first dot?
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Why do designers of free-fall amusement-park rides design
exit tracks that gradually curve toward the ground? Why
is there a stretch of straight track?
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| Share Your Data
Communicate the average value of g
to others. Post the name of your school, city, state, elevation above
sea level, and average value of g for your class in the Share
Your Data fields. Obtain a map for your state and a map of the United
States. View student
data and mark the values for g at the appropriate locations
on the maps. Do you notice any variation in the acceleration due to gravity
for different locations, regions, and elevations?
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