Measuring acceleration due to gravity: the period of a pendulum
What is the acceleration due to gravity in a region where a simple pendulum having a length 75.000 cm has a period of 1.7357 s?
Strategy
We are asked to find
given the period
and the length
of a pendulum. We can solve
for
, assuming only that the angle of deflection is less than
.
Solution
Square
and solve for
:
Substitute known values into the new equation:
Calculate to find
:
Discussion
This method for determining
can be very accurate. This is why length and period are given to five digits in this example. For the precision of the approximation
to be better than the precision of the pendulum length and period, the maximum displacement angle should be kept below about
.
Knowing
can be important in geological exploration; for example, a map of
over large geographical regions aids the study of plate tectonics and helps in the search for oil fields and large mineral deposits.
Take home experiment: determining
Use a simple pendulum to determine the acceleration due to gravity
in your own locale. Cut a piece of a string or dental floss so that it is about 1 m long. Attach a small object of high density to the end of the string (for example, a metal nut or a car key). Starting at an angle of less than
, allow the pendulum to swing and measure the pendulum’s period for 10 oscillations using a stopwatch. Calculate
. How accurate is this measurement? How might it be improved?
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of
. Pendulum 2 has a bob with a mass of
. Describe how the motion of the pendula will differ if the bobs are both displaced by
.
The movement of the pendula will not differ at all because the mass of the bob has no effect on the motion of a simple pendulum. The pendula are only affected by the period (which is related to the pendulum’s length) and by the acceleration due to gravity.
Play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. It’s easy to measure the period using the photogate timer. You can vary friction and the strength of gravity. Use the pendulum to find the value of
on planet X. Notice the anharmonic behavior at large amplitude.
Section summary
A mass
suspended by a wire of length
is a simple pendulum and undergoes simple harmonic motion for amplitudes less than about
The period of a simple pendulum is
where
is the length of the string and
is the acceleration due to gravity.
Conceptual questions
Pendulum clocks are made to run at the correct rate by adjusting the pendulum’s length. Suppose you move from one city to another where the acceleration due to gravity is slightly greater, taking your pendulum clock with you, will you have to lengthen or shorten the pendulum to keep the correct time, other factors remaining constant? Explain your answer.
Some people think a pendulum with a period of 1.00 s can be driven with “mental energy” or psycho kinetically, because its period is the same as an average heartbeat. True or not, what is the length of such a pendulum?
(a) A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is
is moved to a location where it the acceleration due to gravity is
. What is its new period? (b) Explain why so many digits are needed in the value for the period, based on the relation between the period and the acceleration due to gravity.
(a) 2.99541 s
(b) Since the period is related to the square root of the acceleration of gravity, when the acceleration changes by 1% the period changes by
so it is necessary to have at least 4 digits after the decimal to see the changes.
A pendulum with a period of 2.00000 s in one location
is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?
Find the ratio of the new/old periods of a pendulum if the pendulum were transported from Earth to the Moon, where the acceleration due to gravity is
.
At what rate will a pendulum clock run on the Moon, where the acceleration due to gravity is
, if it keeps time accurately on Earth? That is, find the time (in hours) it takes the clock’s hour hand to make one revolution on the Moon.
Suppose the length of a clock’s pendulum is changed by 1.000%, exactly at noon one day. What time will it read 24.00 hours later, assuming it the pendulum has kept perfect time before the change? Note that there are two answers, and perform the calculation to four-digit precision.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
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before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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