Work Unit Summary

This Unit we studied Work and some other concepts pertaining to it.
First we learned...

Work and Power:

Work = Force x Distance 
Work is measured in joules

The force and distanced used to calculate the work you do on something must be parallel. For instance is a box weighs a certain number of Newtons(upwards), and you take it across the room(forward), then you don't do work on the box.

Work is fairly similar to what you may think it is. The only misleading thing about our idea of work is that sometimes we may feel as though we are putting more or less work in when the work is actually the same.

One way it is misleading is that you may get tired doing work faster and thus think you have done more work. This isn't more work, it is more power.

Power is the time in which you do work. Power is measured in watts.
(Power = Work / time)

So, if you do something faster an end up feeling more tired, you just used more power, your work probably didn't change.

Note: 746 watts = one horsepower.

We then learned that Work is also related to Kinetic Energy:

Kinetic Energy is basically energy that a moving object has. 
the formula is: 

KE = (1/2)m(v)^2

So, you can calculate the KE for anything that you know has mass and velocity. (an object that is not moving does not have KE. Neither does an object with no mass.)

What we learned is that the change in KE is equal to Work
change in KE = Work

Often, we will calculate the change in KE in an object that speeds up or slows down over a distance(the velocity changes). We can jump between Work and KE(and then power if we know the time) by subtracting the final KE from the initial KE and then finding the Force by plugging it into Work = Force x Distance using the distance it changed KE.

Once we learned about Kinetic Energy, we learned about Conservation of Energy:

We learned that, when an object moves(or doesn't), it does not lose energy. The energy may be lost to heat or sound or light, however it is all accounted for. You also do not add Energy. 

An example is when an object is swinging on a string. When it is at the top of it's path(and it may be a t rest), it has a lot of Potential Energy but no Kinetic Energy. When it swings down, it starts to lose potential energy and gain Kinetic Energy until at the nadir of the path, it has a lot of Kinetic Energy and no Potential Energy. This relationship, in fact, is equal and opposite. 

change in KE = change in PE

You could relate this to the law of conservation of momentum because in a given situation(like an airbag in a car), you could use the fact that the change in momentum/energy is always the same to determine the factors that increase or decrease your injury in a car crash. 

With these added equations, we add on to the amount of steps we could use to go from, say, PE to Work. We could use PE = KE, and then use KE = Work to find, say, distance or force. 

To Apply these to actual actions, we talked about Machines: 
Specifically, simple machines.

Three types of simple machines are:
a ramp, a pulley, and a jack(for a car).


The way Machines work is they increase the distance over which the work is done so that the force is decreased and it feels easier. This is a way in which what we are doing can feel deceiving because we may be tempted to say that the work decreases because it feels easier. However, it is rather the case that

Work in = Work out
F(D) = F(D)

For instance, a ramp with increase the distance of the work you put in which makes the force you put in less. However, it still equals the same work out regardless.

We did a podcast on Machines which includes some helpful examples about how machines work and how efficient they are. Watch below to learn more.



Thanks for reading!

Unit 4 Summary

This Unit we learned about rotation.

Rotational and Tangential Velocity:

When speaking about rotation, there are two different kinds of velocity. There is rotational(or angular) velocity, and tangential(or linear) velocity.

Rotational velocity: measures how many times something rotates in a given unit of time. 

Tangential velocity: measures distance over in a given unit of time. This is the kind of velocity we were already familiar with. 

There are many situations where these two seem similar but are different. For instance when two children are riding on a merry go round, one on the outermost horse, and one on the inner most horse, their rotational speed is the same. If you can imagine, they rotate the same number of times per minute. However, the outermost child must cover more distance and therefore has a higher tangential velocity. 

Rotational Inertia:

Regular Inertia represents something's resistance to change.

Rotational Inertia: Rotational Inertia is specifically an objects resistance to change rotation. 

Inertia in regular circumstances is usually represented as mass. With rotational inertia it refers specifically to the distribution of the mass. When the mass is distributed further from the axis of symmetry, the rotational inertia increases. Be careful to not mistake this for increased rotational velocity. Inertia is resistance, so when the inertia increases, the rotational velocity decreases. The converse is true for when the inertia decreases. 

An Example of this is when an ice skater spins. When the ice skate pulls their arms(mass) in closer to their axis of symmetry, their rotational velocity increases. And when they extend their arms, they slow down. 

Conservation of Angular Momentum: 

We know very well that momentum is conserved. That is total momentum before = total momentum after.
The switch to angular momentum is ridiculously simple: angular momentum before = angular momentum after. 

And Rotational Momentum is also similar to normal momentum: 

Angular Momentum = (Rotational velocity x (Rotational Inertia)

This principle of conservation simply states that, for example the ice skater, would have the same angular momentum when she pulled her arms in as when she extended them out. This is because of the way inertia and velocity act opposite to each other. When inertia increases, velocity decreases and vise versa. They are always balancing each other out. 

Torque:

Torque is the thing that causes the rotation.

Torque is made up of two components: Force and Lever arm. 
Torque = Force x Lever Arm 

For instance in this picture, the side of the see saw with the girl on it has a greater Torque because she has a greater force, so it rotates with a counterclockwise torque.

Each rotation has a clockwise torque and a counterclockwise torque. 

When something is balanced, the two torques are equal. That is, 

Clockwise Torque = Counter Clockwise Torque

Here is an example of a meter stick that has been balanced on the edge of a table with a 100 gram weight on one side and the calculations to prove it is balanced:

*Remember that the Force is the Center of Gravity. The Lever Arm is the distance from the Center of Gravity to the axis of rotation. 

Center of Mass/Gravity:

To keep balanced you must keep your Center of Gravity over your base of support.

For instance, The leaning tower of Pisa is tilted, however, it's Center of Gravity is still over it's base of support.

This is why football players keep their feet further apart, because widening your base of support makes it easier to keep your Center of Gravity over it. And they are less likely to fall over. 

When wrestlers bend their knees, they do so to lower their center of gravity closer so that is, again, harder to get it out of the base of support, and thus harder to knock them over. 

Centripetal Force: 

Centripetal Force is a force that goes inwards from an object to the center as it rotates. 

This is why it is also called a center seeking force. 

It is a combination of an object that is already moving forward and the force of gravity downwards. 

Here is a picture of centripetal force:

(ps. sorry this is the lamest diagram ever...but it was either super simple or super complicated. If you need visual help check out the podcasts.)

Remember that centrifugal force is not real!

And that was Unit 4!