Periodic
Motion
Periodic
Motion
Objective:
Devop knowledge about periodic motion and relate it to the movement of a pendulum. To discover that the period of a pendulum is dependent on the length of the pendulum and independent of the bob and the amplitude.
Indiana Science Standards Addressed:
5.1.4 Give examples of technology, such as telescope, microscopes, and cameras that enable scientists and others to observe things that are too small or too far away to be seen without them and to study the motion of objects that are moving very rapidly or are hardly moving.
4.2.5 Write descriptions of investigations, using observations and other evidence as suport for explanations
Materials:
string
bob - infant stacking rings provide colorful bobs of different sizes and
mass
right angle clamp
ringstand
rod
Estimated Time:
This demonstration and the processing will take about forty-five minutes.
Procedure:
Step 1:
Begin the class period with a discussion of what the students think periodic
motion is. After a few minutes, bring out a pendulum from behind the lab
table
and use it as an example of periodic motion. Point out its various parts -
bob,
length, pivot point. Demonstrate what is meant by period and amplitude.
Spend
a few minutes discussing the accuracy of measuring a single period. The
students should realize that timing how long it takes for ten cycles and
dividing by 10 will lessen the effects of reaction time and result in a more
accurate measurement of the period.
Step 2:
As a class use the materials to construct a pendulum, students will need to tell the teach what supplies will work where to make a pendulum like the on already displayed for them. As a class find the period of their made pendulum by timing it for 10 cycles and using an amplitude of 10 cm. After doing so, experiment with other amplitudes (5 cm, 15 cm, 20 cm, etc.) to determine if the amplitude effects the period. All studentswill help to record the data in the class data table on the board under the following headings: Color of bob, Time for 10 cycles, Period, Effect of changing the amplitude.
When all the data is recorded, have a class discussion about the results. It should be apparent that the shape and mass of the bob and the amplitude have no effect on the period. Small differences can be explained by experimental error. If the students are not sure that the rings are actually different masses, bring out a scale and prove it. If you are using infant stacking rings, there will be about a 50% difference between the largest and smallest ring's mass.
Step 3:
Now use a different length of string to create a new pendulum. Lengths should vary from 25 cm to 2 m. Ffind the period of their pendulum using the different lengths. This time they will graph the results on the board on a length versus period graph.
Step 4:
Hang a piece of end roll paper about 21/2 meters long on a wall and label the
axes. The vertical axis is marked off to the actual length of the
pendulum. The horizontal axis is the period marked in a convenient scale.
When the students have found the period of each length of string on the
pendulum remove it from its support bar and hang it on the graph at its
corresponding period. Remind the students that the actual length of the pendulum
is measured from the pivot to the center of gravity of the bob. When using
rings for bobs, the center of gravity is at the center of the ring, therefore it is important that
the centers of the rings be lined up on the horizontal axis. By using this
self
graphing technique, it is not necessary to measure the pendulum's length
and the effect of the length of the pendulum on the period is shown quite
dramatically.
Step 5:
Once all pendulums are on the graph discuss the results. The graph
should look like a y-parabola. If it is not obvious that it is a parabola
remember that the origin is a point on the graph - zero length will have zero
period. With a marker sketch the curve on the graph. Discuss withthe
students the shape of the graph and what it represents mathematically. Hopefully
they will come up with the idea that there is a direct relationship between the
length and the square of the period. (This depends on their level of math
ability.) If this relationship is not obvious, lead the students by a
discussion of what needs to be done to straighten out the graph. This
approach usually gets to the idea of squaring the period. The students
should now verify these predictions by squaring their period and regraphing on
the second end roll graph. The students should transfer their pendulums
from the first to the second graph. The resulting graph should be a
straight line through the origin. At this point the class can discuss the
results that the square of the period is directly proportional to the length of
the pendulum. This would be a good point to start a discussion of the
equation and theory of a pendulum.
Step 6:
This activity will take more than the usual lab period. A good breaking
point
would be after finding the effect of the bob and the amplitude. This
activity
can be used with elementary students up to the first graph. The student's
understanding of this material can be evaluated by having them use the graph to
predict what the period of a pendulum will be for a specific length. They
can then experimentally verify their prediction.
Step 7: (Assessment)
Students will need to write a paragraph about what they learned from this demnstration, and the will be grade on the scientific knowledge that they are able to demonstrate in this paper.
Rationle:
Ths demonstration will give the teacher a chance to make sure that al th students are learning the same inforation about motion, and student will be able to ask questions about what they do not understand as the demonstration progress, by the end students will all be on the same track of knowledge about motion.
*To extend this activity students could draw a picture of a pendulum using their art supplies. This activity would integrate art into this activity wich was an objective for the week.