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):