<< Chapter < Page Chapter >> Page >

Phet explorations: pendulum lab

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 g on planet X. Notice the anharmonic behavior at large amplitude.

Pendulum Lab

Section summary

  • A mass m size 12{m} {} suspended by a wire of length L size 12{L} {} is a simple pendulum and undergoes simple harmonic motion for amplitudes less than about 15º size 12{"15"°} {} .

    The period of a simple pendulum is

    T = L g , size 12{T=2π sqrt { { {L} over {g} } } } {}

    where L size 12{L} {} is the length of the string and g is the acceleration due to gravity.

Test prep for ap courses

A ball is attached to a string of length 4 m to make a pendulum. The pendulum is placed at a location that is away from the Earth’s surface by twice the radius of the Earth. What is the acceleration due to gravity at that height and what is the period of the oscillations?

Got questions? Get instant answers now!

Which of the following gives the correct relation between the acceleration due to gravity and period of a pendulum?

  1. g = 2 π L T 2
  2. g = 4 π 2 L T 2
  3. g = 2 π L T
  4. g = 2 π 2 L T

(b)

Got questions? Get instant answers now!

Tom has two pendulums with him. Pendulum 1 has a ball of mass 0.1 kg attached to it and has a length of 5 m. Pendulum 2 has a ball of mass 0.5 kg attached to a string of length 1 m. How does mass of the ball affect the frequency of the pendulum? Which pendulum will have a higher frequency and why?

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Problems&Exercises

As usual, the acceleration due to gravity in these problems is taken to be g = 9.80 m / s 2 , unless otherwise specified.

What is the length of a pendulum that has a period of 0.500 s?

6.21 cm

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

What is the period of a 1.00-m-long pendulum?

2.01 s

Got questions? Get instant answers now!

How long does it take a child on a swing to complete one swing if her center of gravity is 4.00 m below the pivot?

Got questions? Get instant answers now!

The pendulum on a cuckoo clock is 5.00 cm long. What is its frequency?

2.23 Hz

Got questions? Get instant answers now!

Two parakeets sit on a swing with their combined center of mass 10.0 cm below the pivot. At what frequency do they swing?

Got questions? Get instant answers now!

(a) A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is 9 . 79 m/s 2 size 12{9 "." "79"`"m/s" rSup { size 8{2} } } {} is moved to a location where it the acceleration due to gravity is 9 . 82 m/s 2 size 12{9 "." "82"`"m/s" rSup { size 8{2} } } {} . 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 ( 0 . 01 ) 2 = 0 . 01% size 12{ \( 0 "." "01" \) rSup { size 8{2} } =0 "." "01"%} {} so it is necessary to have at least 4 digits after the decimal to see the changes.

Got questions? Get instant answers now!

A pendulum with a period of 2.00000 s in one location ( g = 9 . 80 m/s 2 size 12{g=9 "." "80"`"m/s" rSup { size 8{2} } } {} ) 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?

Got questions? Get instant answers now!

(a) What is the effect on the period of a pendulum if you double its length?

(b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?

(a) Period increases by a factor of 1.41 ( 2 size 12{ sqrt {2} } {} )

(b) Period decreases to 97.5% of old period

Got questions? Get instant answers now!

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 1 . 63 m/s 2 size 12{1 "." "63"`"m/s" rSup { size 8{2} } } {} .

Got questions? Get instant answers now!

At what rate will a pendulum clock run on the Moon, where the acceleration due to gravity is 1 . 63 m/s 2 size 12{1 "." "63"`"m/s" rSup { size 8{2} } } {} , 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.

Slow by a factor of 2.45

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

If a pendulum-driven clock gains 5.00 s/day, what fractional change in pendulum length must be made for it to keep perfect time?

length must increase by 0.0116%.

Got questions? Get instant answers now!

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 1

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask