Abeka Physics Section 10.2 Flashcards
Describe a simple pendulum
> consists of freely swinging mass hanging from thin, massless connector
since no means of suspension can be totally devoid of mass, true pendulum does not exist in real world
true pendulum idealization can be approximated by any swinging device that has most of its mass concentrated at moving end
is at equilibrium when it is vertical and angle of displacement, theta, is then 0
motion of simple pendulum is almost simple harmonic, restorative force due to gravity is nearly proportional to angle of displacement
List the laws of a pendulum
> “the period of a pendulum depends on the square root of its length”
“the period of a pendulum is inversely dependent on the square root of the acceleration due to gravity”
“the period of a pendulum does not depend on its mass”
“the period of pendulum does not depend on its amplitude”
Describe the law of pendulum that states “the period of a pendulum depends on the square root of its length
> long pendulum has longer period than short pendulum
to double period, length must be increased fourfold
to triple period, length must be nine times as long
factor of increase in period is square root of factor of increase in length
Describe the law of pendulum that states “the period of pendulum is inversely dependent on the square root of acceleration due to gravity”
> at high elevation, pendulum swings bit more slowly than it does at sea level because magnitude of “g” is lower at higher elevations
Describe the law of pendulum that states “the period of a pendulum does not depend on its mass”
> when big teenager and delicate child are swinging side by side at playground, each completes full cycle in about same time
in reality, there is some difference because teenager encounters more air resistance
in a vacuum, however, any 2 simple pendulums of same length have same period, regardless of their masses
Describe the law of pendulum that states “the period of pendulum does not depend on its amplitude”
> as long as amplitude is not so great that motion ceases to be nearly simple harmonic, the period of pendulum does not depend on its amplitude
for small amplitudes, period of given pendulum is constant
to use playground swing as example again, child who is content to sway gently will have same period when swinging at slightly higher level
Solve this: Find the period of a simple pendulum that is 0.75 m long.
Equation T = 2pi(square root of l/g) may be used directly since l is 0.75 m and g is 9.80 m/s^2
T = 2pi(square root of 0.75 m/9.80 m/s^2)
T = 1.7 s
Solve this: What is the length of a simple pendulum whose period is 1.00 s at a location where g = 9.81 m/s^2?
Solve equation T = 2pi (square root of l/g) for l. Reversing, isolating the radical, and squaring give l/g = T^2/4pi^2
Then solving for l gives
l = gT^2/4pi^2
where g is 9.81 m/s^2 and T is 1.00 s. Substituting,
l = (9.81 m/s^2)(1.00s)^2/4pi^2
l = 0.248 m
Describe and define physical pendulum
> no simple pendulum exists in real world
swinging mass cannot be suspended on massless connector, but real devices resembling simple pendulum exist, they are called physical pendulums
“any rigid body mounted so that it can swing in a plane about a point of support”
is close approximation of simple pendulum if mass at end is much greater than mass of connector
examples: hanging flower basket, baseball bat in grip of batter, weather vane, wrecking ball, and tree branch exposed to breezes
Describe natural frequency
> every physical object has natural frequency of vibration
to discover natural oscillating frequencies of (inanimate) objects about you, try banging them with pencil
sound raised by vibration of piece of metal is clear and ringing; whereas, book makes high, muffled sound, and a drum’s sound is deep and hollow
predominant pitch of each sound indicates natural frequency of vibration
is possible for an object to oscillate under influence of external force
response of object to forced oscillation depends on relationship between object’s natural frequency and driving (imposed) frequency
theoretically, in absence of friction or some other damping force acting to reduce amplitude of oscillation, amplitude of oscillator driven at its natural frequency can increase to infinity
Describe resonance
> as driving frequency approaches natural frequency, amplitude of oscillation increases
when 2 frequencies are same or nearly same, oscillator is said to be in resonance
example: adult pushing child on swing (if frequency of pushing did not match frequency of swinging, very little motion would result, but since they are matched, child swings higher and higher with very little effort required from adult
well-known example: ringing of crystal glass at certain notes sung by opera singer (both glass and voice naturally vibrate at more than 1 frequency simultaneously. If frequencies of one closely match frequencies of other, and if vocal sound producing resonance is loud enough, glass may shatter)
