Unit 5 Reflection

This unit, we studied Work and Power, the relationship between Work and Kinetic Energy, the Conservation of Energy, and Simple Machines.I feel really good about this unit, and my only difficulty with this unit is remembering what I have to show to get full credit on tests/quizzes, though I know how to get to the right answer. My effort has been good, though my organization needs to get better.

Real world application:

I can connect this unit with daily life very easily. While walking around campus, I notice when I either go up stairs or an inclined plain, knowing that, when going to the same place, the stairs and the inclined plain require the same amount of work, they just have different forces and distances.

Work and Power

Equation: Work=(force)(distance)
Units: Joules (J)

Equation: Power=work/time

Units: Watts

For work to happen, force and distance must be PARALLEL!!

Example problem:

If a 600N person walks up stairs that are 4 meters high, how much work is done?

Work=F*d

Work=600N*4m

Work=2400J

When is there more work? When a person goes up the stairs to third or when the elevator carries them to third?

The work required is the same. The upward force against gravity (or weight) is the same, and the distance that is parallel to that force (height) is the same, therefore work is the same. Horizontal distance does not matter because it is perpendicular to the upward force, and therefore contributes nothing to the work done.

When considering work, only the height matters.

Work happens to an object when force is exerted on that object over a distance. The equation for work is work=force*time, and it is measured in m/s or Joules. For there to be work, the force and distance must be parallel. In this example, the person's wright, or force, is vertical, and therefore for there to be work, the distance must be vertical as well. Work does not happen when the distance is perpendicular to the force, or when there is no distance.

If the force of the person is 4N, and the staircase is 15m tall, how much work will there be? 

work=force*distance

        = 4N*15m

work= 60 Joules

Power is how quickly work is done. The equation for power is Power=(work)/(time) and is measured in Watts.

If it takes the person 10 seconds to reach the top, how much power is exerted?

Power=(work)/(time)

=60J/10s

Power=6 Watts

Work and Kinetic Energy relationship

Formulas:

Kinetic Energy= (1/2)mv² 
Change in KE=KE_final-KE_initial
Change in KE=work
Work=fd

Why do airbags keep us safe?

KE=(1/2)mv² 

Change in KE=KE_final-KE_initial

You go from moving to not moving regardless of what you hit, therefore the change in Kinetic Energy is the same regardless of what you hit

Change in KE=work

Since the change in Kinetic Energy is the same, the work is the same regardless of what you hit.

work=fd

Airbag work=f*d

Dash work=f*d

Since the work is constant regardless of what you hit, the airbags increase the distance it takes to stop you, and thus decrease the force. Small force means less injury.

Conservation of Energy

Formulas:

Potential Energy=mgh

Change in PE= Change in KE

How does potential energy change if someone jumps off of a cliff?

As they fall, PE goes down and KE goes up by the exact same amount. The sum of PE and KE at any point will be equal to the PE they had when they were at rest at the top. Energy must be conserved.

Top: let PE=1000J, KE=0

¼ of the way down: PE=750J, KE=250J

½ of the way down: PE=500J, KE=500J

¾ of the way down: PE=250J, KE=750J

Just before impact: PE=0J, KE=1000J

When PE goes down KE goes up by the exact same amount.

Energy cannot be created or destroyed, but it can be transferred to other forms such as heat, light, and sound.

************PE is equal to the work required to raise an object to a certain height*************

PE=mgh

Work=F*d

Work=mg*h (mg is the amount of upward force required, h is the distance (height) it is lifted)

Machines

Purpose of a ramp: A ramp increases the distance over which a force is applied, thereby decreasing the amount of force required to do the same amount of work (lifting an object to a certain height).

Why do bolt cutters have such long handles but such short blades?

The work done on the handles equals the work done by the blades (Work in=Work out). The long handles allow for a large distance over which the force is applied. The short blades do the same work, but over a very short distance. This shorter distance means the force the blades apply is much greater than the force on the handles.

In this picture, I drew two mice using a pulley system to lift up pieces of cheese. The mouse on the left has almost a whole block of cheese, and the mouse on the right has the sliver that is cut out of the block. The mouse on the left has a longer rope and more pulleys while the mouse on the right has a shorter rope and has one pulley.

The machines in this picture are the pulleys. What a machine does is reduce the force it takes to do a job. Notice that it reduces force and NOT work. A machine does this by increasing the distance it takes for complete the job, making the force smaller. We know that this happens because workin=workout. this means that force-in*distance-in=force-out*distance-out.

Since the left mouse's rope is longer, that mouse can pull with less force to get the same sized cheese (it is not the same sized in the picture) up than the mouse on the left has to. The big block of cheese signifies that since there is more distance to cover, the left mouse will be able to pull up a larger piece of cheese than the right mouse.

 ******FOR MORE MACHINE NOTES... WATCH THE VIDEO AT THE TOP*************


 Efficiency=Work out/Work in

Machine Recourse

In this picture, I drew two mice using a pulley system to lift up pieces of cheese. The mouse on the left has almost a whole block of cheese, and the mouse on the right has the sliver that is cut out of the block. The mouse on the left has a longer rope and more pulleys while the mouse on the right has a shorter rope and has one pulley.

The machines in this picture are the pulleys. What a machine does is reduce the force it takes to do a job. Notice that it reduces force and NOT work. A machine does this by increasing the distance it takes for complete the job, making the force smaller. We know that this happens because workin=workout. this means that force-in*distance-in=force-out*distance-out.

Since the left mouse's rope is longer, that mouse can pull with less force to get the same sized cheese (it is not the same sized in the picture) up than the mouse on the left has to. The big block of cheese signifies that since there is more distance to cover, the left mouse will be able to pull up a larger piece of cheese than the right mouse.

Work/Power Recourse

Work happens to an object when force is exerted on that object over a distance. The equation for work is work=force*time, and it is measured in m/s or Joules. For there to be work, the force and distance must be parallel. In this example, the person's wright, or force, is vertical, and therefore for there to be work, the distance must be vertical as well. Work does not happen when the distance is perpendicular to the force, or when there is no distance.

If the force of the person is 4N, and the staircase is 15m tall, how much work will there be? 

work=force*distance

        = 4N*15m

work= 60 Joules

Power is how quickly work is done. The equation for power is Power=(work)/(time) and is measured in Watts.

If it takes the person 10 seconds to reach the top, how much power is exerted?

Power=(work)/(time)

=60J/10s

Power=6 Watts

Unit 4 Reflection

Rotational and Tangential Velocity
Rotational Velocity:  

• number of complete rotations, revolutions, cycles, or turns per time unit
• same= with merry-go-rounds, train wheels, etc
• know something has the same rotational velocity when connected by a shaft

Tangential velocity:

• same= with gears, belts, etc
• different=  tapered train wheels
• know something has same tangential velocity when covers same amount of distance in the same amount of time.

The further away from the axis of rotation, the more tangential velocity something has.

Train Problem

We know that the wheels have the same rotational velocity because they are connected by a shaft, making them rotate with the same velocity. We know that the larger-inner parts of the wheels have a greater tangential velocity than the smaller-outer parts because they cover more distance in the same amount of time. This makes the wheels self correct because if the wheels start to get off track, the larger-inner parts will go faster, making the trains "correct" again.

Inertia
 Why does a Frisbee roll faster than a hula-hoop down a hill?

The Frisbee will go faster than the hoop because the distribution of mass is closer to its axis of rotation, causing the Frisbee to have less rotational inertia and the hoop.

Mass close to the axis of rotation= less rotational inertia
Mass away from the axis of rotation=more rotational inertia

Conservation of Angular Momentum
Rotational Inertia X Rotational Velocity = Angular/Rotational Momentum

Takes distribution of mass into account

Angular P before= Angular P after
(Rotational Inertia X Rotational Velocity) BEFORE = (Angular/Rotational Momentum) AFTER

The distribution of mass changing causes the Rotational inertia to change, which causes the Rotational velocity to change.

           

Torque
3 Ways to Cause a Larger Torque:

1. Larger lever arm
2. Large Force
3. Both

DISCLAIMER!!!!!!------- Torque is NOT a FORCE

The lower the center of gravity, and the wider the base of support, the more stable something will be

Center of Mass/Gravity

STEP 1:

This picture depicts an unbalanced meter-stick with a torque. It is unbalanced because the center of gravity is not supported. The force comes out of the center of gravity, causing it to tilt counter-clockwise. The lever arm is the distance from the Center of Gravity to the base of support. A Torque=(Force)(Lever Arm)

Step 2: 

This picture depicts a balanced meter-stick. It is balanced because the Center of Gravity is supported. The force comes out of the Center of Gravity, and since it is within the support, the meter-stick will not tilt or topple over. There is no lever arm because the meter-stick is balancing on its Center of Gravity.

Step 3:

A 100g weight was added to the meter-stick, which changed the system's center of gravity, but not the Center of Gravity of the meter-stick itself. On lever arm is from the edge to the base of support, and the other is from the base of support to the meter-stick's center of gravity. Since the Lever arm from the weight to the base of support is longer than the other one, to make the two Torques equal, which has to happen for something to be balanced, there needs to be a greater force on the side with the shorter lever arm. That makes the equation (Force(a))X(Lever Arm(a))=(Force(b))X(Lever Arm(b)) true.

Part 3:

Torque=Force X Lever Arm

We found the Center of Gravity of the meter-stick by itself, which was 50.25 cm. When we added the 100g weight, the lever arm with the weight is 29.5 cm, and the other lever arm is 20.75 cm. w=mg, which means w=0.1Kg*9.8-- Weight=0.98N Since I know the lever arm and the force of one side of the meter-stick, I can find the Torque. Torque=(0.1X9.8)(29.5)--- Torque=28.9 N cm. This is the Torque for both sides because for something to be ballanced, the clockwise Torque= the counter-clockwise Torque. This means that 28.91=20.75(F)--- 1.39=Force. w=mg---- 1.39=m(9.8)---1.39/9.8=0.1418 which, when converted from Kg to g, you get 141.8g. When we weighed our meter-stick, the weight was 142.9g.

Centripetal/Centrifugal Force
Why, when rounding a curve, you lean up against the door:

I am going straight, and want to keep going straight because of Newton's first law. Because of this, I have inertia and keep wanting to go straight. The car door pushes me inward, and I push the car door outward.

Centripetal Force: Center-seeking force
Centrifugal Force: Fictitious Force-- Center-fleeing force

Finding the Mass of a Meter Stick Without Using a Scale Lab

STEP 1:

This picture depicts an unbalanced meter-stick with a torque. It is unbalanced because the center of gravity is not supported. The force comes out of the center of gravity, causing it to tilt counter-clockwise. The lever arm is the distance from the Center of Gravity to the base of support. A Torque=(Force)(Lever Arm)

Step 2: 

This picture depicts a balanced meter-stick. It is balanced because the Center of Gravity is supported. The force comes out of the Center of Gravity, and since it is within the support, the meter-stick will not tilt or topple over. There is no lever arm because the meter-stick is balancing on its Center of Gravity.

Step 3:

A 100g weight was added to the meter-stick, which changed the system's center of gravity, but not the Center of Gravity of the meter-stick itself. On lever arm is from the edge to the base of support, and the other is from the base of support to the meter-stick's center of gravity. Since the Lever arm from the weight to the base of support is longer than the other one, to make the two Torques equal, which has to happen for something to be balanced, there needs to be a greater force on the side with the shorter lever arm. That makes the equation (Force(a))X(Lever Arm(a))=(Force(b))X(Lever Arm(b)) true.

Part 3:

Torque=Force X Lever Arm

We found the Center of Gravity of the meter-stick by itself, which was 50.25 cm. When we added the 100g weight, the lever arm with the weight is 29.5 cm, and the other lever arm is 20.75 cm. w=mg, which means w=0.1Kg*9.8-- Weight=0.98N Since I know the lever arm and the force of one side of the meter-stick, I can find the Torque. Torque=(0.1X9.8)(29.5)--- Torque=28.9 N cm. This is the Torque for both sides because for something to be ballanced, the clockwise Torque= the counter-clockwise Torque. This means that 28.91=20.75(F)--- 1.39=Force. w=mg---- 1.39=m(9.8)---1.39/9.8=0.1418 which, when converted from Kg to g, you get 141.8g. When we weighed our meter-stick, the weight was 142.9g.

Torque Resource

In this video, Mr. Hewitt explains Torque. By showing that an L-shaped piece of wood will either stand straight or topple over, depending on how it is positioned. Torque is equal to the force multiplied by the lever arm. Torque IS NOT equivalent to force! Lever arm is the distance from the axis to the center of gravity. With the L-shaped wood example, Mr. Hewitt shows that if the object's center of gravity is supported, it will stay standing up. However, if there is no support for the center of gravity, the object will fall down. This video is really helpful!

Angular/ Rotational Momentum

Angular/Rotational Momentum is the rotational inertia multiplied by the rotational velocity. Rotational inertia is an object's resistance to spinning around an axis. Rotational velocity is the number of rotations per unit of time. If the guy who flew off of the merry-go-round, had been closer to the axis of rotation (the center of the merry-go-round), it would have been harder for him to fly off of it, due to the tangential speed. Tangential speed increases the further away one is from the axis of rotation, therefore, if the guy had been closer to the center, he would not have spun as quickly, possible saving himself from flying off. The Distribution of mass is important because it affects the rotational inertia. The closer to the axis of rotation the mass is, the quicker the object will spin. The further away the mass is from the axis of rotation, the slower the object will spin. The Distribution of mass changing will cause the rotational inertia to change, which causes the rotational velocity to change.