Read pp. 134-136
Do 6, 11, 12, 28
Pendula
(or Pendulums, in the vernacular)
What is a pendulum?
Pendulum: Consists of a massive object called a bob suspended by a string.
What is it good for?
• Keeping time• Galileo (what other options did he have?)• Clocks• Calculating acceleration due to gravity
• Other, less obvious things• Verifying the rotation of the earth• Understanding Energy: Potential and Kinetic• Study of simple harmonic motion
Velocity, acceleration & the Pendulum
Conservation of Energy & The Pendulum• Definitions
– Potential energy describes the possibility of converting stored energy into motion
– Kinetic energy describes the energy of motion– Since (mass)energy can be neither created nor destroyed,
potential and kinetic energy can be exchanged interchangeable
Kinetic energy is a measure of how fast the bob is moving.
This height indicates the distance the pendulum bob “falls” under the influence of gravity. It and gravity determine how much potential there is for motion
We are back at the same height!And at ½ of a cycle.
Conservation of Energy & The Pendulum
We are back at the same height!And at ½ of a cycle.
Kinetic and Potential Energy
Kinetic Energy = ½ m v2
Potential energy = mg h
With pendula, we are usually interested in the period
What things might affect the period?
- mass- angle- length- gravity- wind resistance
What do you think the form of the equation might be?
Pendulum: Consists of a massive object called a bob suspended by a string
Pendula go through periodic motion as follows:
Where:T = period, or the time to go through one cyclel = length of pendulum stringg = acceleration of gravity
Note: 1. This formula is true for only small angles of θ.2. What would you expect to find in this equation and is not
there?
g
lT 2
The motion of a pendulum is independent of the mass• As long as the mass is big enough so that air resistance
can be ignored• As long as the mass of the string holding the pendulum is
very small compared to the mass of the bob
Where:T = periodl = length of pendulum stringg = acceleration of gravity
g
lT
g
lT 22 42
As we increase l, what happens?
As we increase g, what happens?
g
lT
g
lT 22 42
As we increase the angle, what happens?
As we increase the mass, what happens?
g
lT
g
lT 22 42
1) What is the period of a pendulum on Earth with a length of 1m?
2) What is the period of a pendulum on Jupiter with a length of 1m? (ag = 3g)
3) What is the period of a pendulum on the moon with a length of 2m? (ag = 1/6g)
4) What is the length of a pendulum (on Earth) with a period of 10 sec?
5) What is the length of a pendulum (on Earth) with a length of 0.1 sec?
Examples:
1) What would the graph of period vs. length look like?
2) What would the graph of period2 versus length look like?
3) What would the graph of period2 versus g look like?
Examples(2):