How things balance

FYI - exams are not yet graded.  Sorry!

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.  There may be a single torque on each side of a lever, or there may be multiple torques on each side.  Actually, there may be an infinite number of torques on either side.  Furthermore, there don't have to just be 2 sides - if this is a 3-dimensional (real) body, it can have an infinite number of "lever arms".  Consider a frisbee - it is round, but it still balances about a single point.  What is this special point called?  See below.


Center of Mass

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










Comments

Post a Comment

Popular posts from this blog

Newton's take on Gravitation - the inverse square law

Image
Newton's take on gravity and orbits - which is the genesis of our modern conception of it, is based on: Universal Gravitation (1687, Principia) Newton's take on orbits was quite different. For him, Kepler's laws were a manifestation of the bigger "truth" of universal gravitation. That is: All bodies have gravity unto them. Not just the Earth and Sun and planets, but ALL bodies (including YOU). Of course, the gravity for all of these is not equal. Far from it. The force of gravity can be summarized in an equation: or.... the force of gravitation is equal to a constant ("big G") times the product of the masses, divided by the distance between them (between their centers, to be precise) squared. Big G = 6.67 x 10^-11, which is a tiny number - therefore, you need BIG masses to see appreciable gravitational forces. This is an INVERSE SQUARE law, meaning that: - if the distance between the bodies is doubled, the force becomes 1/4 of its ...
Read more

Lenses and how they form images

Image
Lenses As shown and discussed in class, light refracts TOWARD a normal line (dotted line on the left image, perpendicular to surface of lens) when entering a more dense medium. Note in this  convex  lens that this direction of bend changes from down (with the top ray) to up with the bottom ray. This is due to the geometry of the lens. Look at the picture to make sure that this makes sense.  As a result, the rays will intersect after leaving the lens.  An image can form! The FOCAL LENGTH (f) of a lens (or curved mirror) where the light rays would intersect, but ONLY IF THEY WERE INITIALLY PARALLEL to each other. Otherwise, they intersect at some other point, or maybe not at all (if the object is too close to be focused on)! Note that your (human) eye lenses are convex - slightly thicker in the middle.  Thus, your eyes form "real" images on the retina - upside-down!  Unless, of course, the object is too close. If an image is projected onto ...
Read more

Electromagnetism and Electromagnetic Induction

Image
Electromagnetism Recall that the motion of charges leads to magnetic fields.   If you have charge traveling through a wire, electrons can be thought of as moving together – this causes a magnetic field, also known as electromagnetism.  The magnetic field caused by a current passing through a wire is often small, but if you coil the wire upon itself, the magnetic fields “add up”.  Several hundred turns of wire (with current running through it) can produced quite a strong electromagnet.  A coil with current running through it can naturally react to a permanent magnet – if this is engineered well, we have a motor.  See illustrations and demos in class. Below:  basic motors Electromagnetic Induction So, current causes magnetism – something shown in the early 19 th  century by Hans Oersted.  As it happens, the reverse is also true – magnetism can cause current, but there must be some relative CH...
Read more