Tension Free Body Diagram

If a vine is hung over a tree branch in the forest and two monkeys are hanging on both ends then the tension in the vine will be equal throughout the whole rope, since if it wasn’t the vine would snap or go slack.

The tension force for one monkey’s side will be equal and opposite to the tension force on the other monkey’s side.

The vine itself will also require a different amount of force to slide across the top of the branch depending on how the vine and the tree branch interact.

The force required for movement is unique depending on the materials (which defines a coefficient of friction).

Objects will have different coefficients of friction, denoted as mu, based on how they act together.

In analyzing situations it is good to draw a picture or “free body diagram” and decide what the axes are, including which directions should be understood as positive and negative.

The free body diagram should  only be applied to simple situations (generally one or a few objects involved).

When the situation is complicated, like the effect of huge numbers of electrons hitting an object, other theories come into play.

Even with fifty forces that are three dimensional, you would have to add up 150 components (x, y, z for each) and that wouldn’t be fun.

Changing Coordinate Systems to Make Problems Easier

One day a physicist comes across a perplexed student in the library.

It seems that the student had only learned to place his axes with the positive y axis going up and the positive x axis going to the right.

Unfortunately this system wasn’t working so well with a situation involving pulleys and curved directions.

The physicist decides to help the engineer by telling him that the x-y coordinate system can be changed to better suit the problem at hand, much like polar coordinates can be more convenient than cartesian coordinates.

If an object travels in a curved path he reasons that the x-y coordinate system may also be curved in parts for simplicity.

Gravity may be thought of as positive or negative and up may be considered down.

The physicist also says that simply using common sense to check an answer will often times be effective, for instance if a block is sitting on a wall with no forces it will probably just stay there.

Newtons Second Law F=ma

As the village blacksmith walks along one day he sees a group of monks circling around an apple tree and chanting something about the truth being expanded.

When he stops and listens he learns that a man named Newton became inspired by falling of apples.

The monks explain that Newton then came up with the equation ΣF = ma (where F and a are both vectors) which means that the sum of the forces in a direction is equal to the mass, not to be confused with weight, multiplied by the acceleration, one example being gravity, in a direction.

The F and a are vectors, indicated by bold.

The monks are rejoicing since they had only previously been able to understand the motion of objects.

Now they can understand interaction of objects with mass through the use of vector components, the old testament of the truth, and their newfound equation.

Circular Motion Centripetal Acceleration Arc Length

One day a little kid is playing with a yo-yo and swinging it around in a circle for his own amusement.

Suddenly a crazed physicist walks up and decides to explain the physics of the circular motion.

First he asks the kid to spin the yo-yo around without any acceleration and the kids tries, but this turns out to be a trick question since there always is an acceleration towards the center (centripetal or center seeking force) because the velocity changes directions.

The physicist next shows how components can be used for measuring velocity vectors.

He then explains that describing certain aspects of circular motion with rectangular coordinates is pure silliness and that sometimes polar coordinates with an angle and a radius are much simpler.

He notes however that unlike in navigation, the angle is measured from the positive x-axis in physic.

Finally the physicist gives a nifty trick (s=rφ) for finding the arc length of pizza, or any circle, if one knows the radius and angle phi, but speaking of pizza he thinks about how good some would be and walks off.

Michael Jordan Flies Through the Air (statue) from Esparta on Flickr

The stadium is packed with fans as Michael Jordan flies through the air on his way to the rim. Gravity seems suspended in this “hang time” phenomenon.

The hot dog dealer casually explains that by using THE TRUTH, and possibly a know/don’t know table, it can easily be calculated that it is true that Jordan spends 2/3 of the time actually in the air and with a vertical leap of over forty inches this can be a long time.

The hot dog dealer continues to explain the physics of the game by showing how vector analysis can track the motion of basketball stars.

A vector has direction and magnitude and can be added or subtracted using normal additive rules.

Thus he explains that the offense can jump both forward and up, but if the defense has the same vertical component they will both land at the same time since horizontal and vertical motion components are independent.

The dealer then continues on his way and warns not to use tangent for the x or y components

Instead, multiply the vector by sin(θ) to find the y component (magnitude in the y direction) and multiply the vector by cos(θ) for the  x component (magnitude in the x direction.

Also, by convention you should measure θ from the positive x-axis (this is physics convention anyway).

Michael Jordan top 40 moments

One Dimensional Motion Formulas

v = u + at

v2 = u2 + 2as

s = ut + 1/2 at2

average velocity = (v + u)/2

v: velocity (this is the velocity u combined with increases or decreases due to acceleration)

u: velocity (in this case before any acceleration)

a: accelation

t: time

s: distance

Relative Motion & Reference Points

When something is observed it is always observed from some vantage point.

If two people are running next to each other it will not seem as if the other is moving, since their relative motion is the same.

Since the motion is really the same from any vantage point the reference point used to analyze physics can be chosen to be anywhere.

However, some reference points are more useful than others (depending on the situation).

For instance, with gravity- the lowest point in a certain situation could be ten meters above ground if an object is sitting on top of a roof, thirty two meters below ground if there is a hole, or at ground level.

Setting a convenient reference point will often make the manipulation of equations simpler though.

For instance, setting the reference point on the ground=0 level can make an integral easier because the bound of zero may cancel out terms.

Having zero at ground level may not always be convenient though, and always using zero to cancel out terms can be deceiving since it will not always work that way.

Car velocity physics – physics velocity

A physics professor drives along in his camry on the highway and covers about 88 feet per second or a velocity of 100 km/h when he observes a mitsubishi GT 3000 that races out onto the freeway.

This vehicle has an initial velocity of 100 km/h and smoothly accelerates, with the increase in velocity being constant over time, up to 250 km/h which is about 220 ft/s.

A police helicopter spots the GT 3000 and calls in squad car to lay a spike strip. The GT 3000 slams on the breaks and leaves skid marks for 160 feet. The police officer who finds the driver calmy whips out the stone tablet of THE TRUTH (v=v0 + at and x-x0 = v0 + 1/2 at2) and using this and his knowledge of the GT 3000’s breaking capabilities calculates the initial velocity and cuffs the driver for reckless driving.

The physics professor continues at a constant velocity on the highway, passes the arrest, and hears the driver cursing physics, but he knows the power of THE TRUTH.