E block physics today

Hey gang,

I'm not in school today.  Here's what you should work on:

1.  Review the HW problems with your table.

2.  Come up with definitions (and drawings, where relevant) for:

- crest and trough

- wavelength

- amplitude 

- frequency

- wave speed

Thanks.

A and E block HW

1.  Calculate the period of a 2-m long pendulum.

2.  How would the period of this pendulum be affected by relocating it to the Moon?

3.  How long should a pendulum be if it is to have a 1 second period?

4.  What exactly is a "wave"?  Try to come up with some type of definition.

A and E block HW

1.  Make a graph of T (time for one oscillation, in seconds) vs. length (in m).  T is on the y-axis.  What type of mathematical relationship seems to represent the data?

2.  Look up an equation for "period of simple pendulum".  What type of curve does this equation suggest?  Does your data seem to represent this?

3.  How could you tell how "good" your data is?  How can you test it in relation to the equation above?  Try it, if possible.

A and E block HW for Thursday (to be collected)

1.  What is the location, relative to the center of the Sun, of the CG of the Sun-Jupiter system?   You may look up needed data to perform this calculation.  Comment on whether or not this CG lies within the Sun itself.

2.  Consider a meter stick (fulcrum located at the 30 cm mark) that is balanced.  The mass of the meter stick is centrally located and is 75 g.  What is the smallest mass that will balance the stick?

3.  Write out your own definition for “energy.”

BONUS:

Consider a 10-feet long 100-lb beam supported on each by cables.  If a 150-lb person is sitting on the beam, 3.5-feet from the left end, what is the tension in each cable?  Believe it or not, this can be treated like a (slightly complex) lever problem.

One more thing

Some of you have asked about extra credit.  See me tomorrow (Friday) and I'll give you something to try in the next few days.  

To play with (A and E)

1.  Using Earth and Moon data, calculate the location of the CG of the Earth-Moon system.

The Center of Gravity!

A very useful concept in physics is Center of Gravity (AKA CM, Center of Mass - they are usually the same point).  

Recall the demo with the mass on a stick.  Same mass, held at a further distance from the "fulcrum", is harder to support.  It twists your wrist more - it requires a greater "torque".

So, what is torque?

Torque - a "rotating" force

T = F L

For an object to be "in equilibrium," not only must the forces be balanced, but the torques must also be balanced.

Consider a basic see-saw, initially balanced at the fulcrum:  See image below.

You can have two people of different weight balanced, if their distances are adjusted accordingly:  the heavier person is closer to the fulcrum.  

Mathematically, this requires that the torques be equal on both sides.

Consider two people, 100 lb and 200 lb.  The 100 lb person is 3 feet from the fulcrum.  How far from the fulcrum must the 200 lb person sit, to maintain equilibrium?

Torque on left = Torque on right

100 (3) = 200 (x)

x = 1.5 feet

NOTE:  The weights are NOT equal on both sides of the balance point.  But the torques ARE EQUAL.

We call the "balance point" the center of mass (or center of gravity).  

It is the point about which the object best rotates.

It is the average weighted location of mass points on the object.

It does not HAVE to be physically on the object - think of a doughnut.

The principle is believed to originate with Archimedes (287 - 212 BC).  He is believed to have said, "Give me a place to stand on, and I will move the Earth."

FYI:  http://en.wikipedia.org/wiki/Archimedes

E and A block mini-lab followup HW

You have some data from today's class.  Check that the left side and right side "balance" out mathematically.

For example, if you had one mass located on the left side, and 2 masses on the right side (where the majority of the stick is also located), the equation would resemble:

m1 x1 = m2 x2 + m3 x3 + Ms Xs

m = individual hanging masses
x = distance between the hanging mass and the fulcrum
Ms = mass of stick
Xs = distance from fulcrum to center of mass of stick (assumed to be at 50 cm)

Note that we are adding up the effects on the right side.  This is ok to do, as several things are generating torque on this side.

How close are the left and right values?  Find the percent difference between the sides, and try to account for why there is a difference at all.

HW for E and A

Do a little research about the "center of gravity" (CG) concept and bring a definition to our next class.

Also, consider the following problem:

A meter stick is used in an experiment, with the fulcrum located at the 28 cm point.  If a 100 g mass balances when placed at the 15 cm point, what is the mass of the meter stick?  Use the CG concept to solve this problem.  Recall that the CG is the point where we can pretend that ALL of the mass of something is located.

Another question to consider.  Regarding the CG of an object:  how do you think an object's stability (resistance to falling or flipping over) is related to its CG?

One more:  Think about the famous leaning tower in Pisa, Italy.  Why do you suppose it does not fall over?  Think in terms of the CG.

HW reminder

You have some data related to the lever.  What conclusion(s) can you draw?  How does the relationship from part 1 apply to part 2?

If you're feeling ambitious, look into the concept of "center of gravity."