Unit Summary # 5

During this unit, we covered the following topics:

1. Work and Power
2. Work and Kinetic Energy
3. Conservation of Energy
4. Simple Machines

Work and Power

The formula for work is

Work= Force * Distance

One thing to remember is that force and distance must be parallel to calculate work.

So, when you carry a box down a hallway, no work is done. When you first lifted the box, work was done.

Another example of work is walking up stairs.

You would multiply your force by the vertical height of the stairs to find the amount of work done.

Work is measured in joules(J).

One think associated with work is power.

The formula for power is

Power= Work / Time

The units for power are Joules/Second but thats a lot to say, so instead we use Watts(W).

Here is the video my group and I made about this topic:

Work and Kinetic Energy

Kinetic energy is the energy of movement

Formulas you need to know for this relationship are

Work= Change in KE

KE=1/2mv² 

Also, since work is equal to the change in KE, you must also know how to find that 

Change in KE= KEfinal - KEinitial

Conservation of Energy/Potential Energy

The Law of Conservation of Energy states that energy can be neither created nor destroyed, only converted.

So, when something is not moving, it has Potential Energy. 

Potential Energy is the energy of position. (height)

As this ball swings, it has varying amounts of potential and kinetic energy.

At the top of its swing, it has only potential energy.

Mid-swing, it has both potential and kinetic. 

The formula you must remember for this is

PE= Mass * Gravity * Height

Simple Machines

Today we have a misconception of how simple machines work. 

We think that simple machines reduce the amount of work you have to do.

This is not true.

Machines reduce the amount of force you use over a longer time. 

The ramp on the truck is a simple machine.

It would take a big force to lift something directly into the truck.

The ramp allows you to use a smaller force over a greater distance.

The work you put in will always equal the work you get out. 

Unit Summary # 4

In Unit 4 we cover 6 main topics
   1. Rotational and Tangential Velocity
     2. Rotational Inertia
     3. Conservation of Angular Momentum
     4. Center of Mass/Center of Gravity
     5. Torque
     6. Centripetal Force

Rotational and Tangential Velocity

Rotational Velocity is the number of rotations made per unit of time

>>An example of Rotational Velocity that can be found everyday is the RPM of your car. It measures how many rotations your car wheels are making per minute.

Tangential Velocity is the distance covered per unit of time

An example of Rotational Velocity that can be found everyday is the RPM of your car. It measures how many rotations your car wheels are making per minute.

>>When thinking about tangential velocity, you must remember Radial Distance. Radial Distance is the distance something is from the axis of rotation. The longer the Radial Distance, the faster the objects tangential velocity will be.

To better understand this in class, we went outside and linked arms in a line. We went around in a circle. We noticed that the people on the outside had to run to keep up the same rotational speed as the people in the middle.

Example Problem:
Which of the animals has the faster tangential velocity, the panda or the dragon?

Rotational Inertia

Rotational inertia is an objects resistance to spin.

Rotational inertia is dependent on the distribution of mass. The father the mass is from the axis of rotation, the larger rotational inertia it will have.

Lets say all of these balls have the same mass and are rolling down a hill. The golf ball will reach the bottom of the hill first because it mass is more closely concentrated around its axis of rotation.

Conservation of Angular Momentum

Angular Momentum before must equal the angular momentum after. 

Rotation Inertia before * Rotation Velocity before = Rotation Inertia after * Rotation Velocity after

The figure on the left has extended mass and a slower velocity, the figure on the right has a condensed mass and a faster velocity, but their angular momentums are equal.

Center of Mass/ Center of Gravity

Center of Gravity is the average position of all of its mass.

The Base of Support is the plane in which the object is supported by the ground.

An object will fall when the center of gravity gets outside the base of support.

In A, the center of gravity is directly over the base of support. In B, the center of gravity is shifted to the left but still over the base of support. In C, the center of gravity is no longer over the base of support, thus, the person will fall.

Here is a video my group and I made about this topic

Torque

Torque is the force that causes rotation.

Torque= Force*Lever arm

Torque is created when the center of gravity goes outside the base of support.

Also, its what happens when you're turing a bolt with a wrench, or shutting a door.

You can create a large torque by having a large lever arm, a large force, or both.

Things are balanced when clockwise and counterclockwise torques are equal.

Centripetal Force

Centripetal Force is a center-seeking force

As the car rounds the curve, you get thrown against the side of the car. This is because when the car rounds the curve, it has centripetal force on it. But, there is no centripetal acting on you. So, you keep going straight until the car runs into you. This sensation is what we incorrectly call centrifugal force.