Simple Machine Resource

http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/simmac.html

This resource from hyper physics reiterates all of the information about machines we have discussed in class.

Power resource

http://www.youtube.com/watch?v=RpbxIG5HTf4

In this Khan Academy resource, power is discussed. They describe work and its relation to power. Instantaneous power is also discussed, but we have not talked about this in class as of yet.

Unit 4 Reflection

In this unit I learned about…

Rotational and Tangential Velocity

-Tangential velocity is the velocity of something moving along a circular path. The direction of motion is tangent to the circumference of the circle. Another word for tangential speed is linear speed. Tangential speed depends on the radial distance ( distance from the axis).
-Rotational velocity involves the number of rotations or revolutions around an axis per unit time. Rotational velocity is often measured in RPM (rotations per minute). Rotational speed will be the same at any distance from the axis of rotation.

An excellent situation in which to observe rotational and tangential velocity is on a merry go round. All of these children are traveling at the same rotational velocity, because they are making the same number of revolutions in a given time. However, the kids on the outer edge of the merry go round are moving at a faster tangential velocity than the kids towards the center of the merry go round. This is because they are covering a much larger distance in the same amount of time that the kids toward the inside are covering a very small distance. 

Rotational Inertia

Rotational inertia is the property of an object to resist changes in spinning. It depends on mass and its distribution. When the mass is closer to the axis of rotation it has less rotational inertia, so it speeds up, and when it is farther from the axis, it has more rotational inertia, so it slows down. So why does velocity change?

Conservation of Angular Momentum

We've learned about the conservation of momentum, ptotalbefore = ptotalafter;  p = mv; mvbefore = mvafter. This same same rule applies to rotational or angular momentum. In this case, rotational speed is velocity is conserved, so angular momentum before = angular momentum after. Angular momentum is based on two things: rotational inertia and rotational velocity, so  angular momentum = rotational inertia x rotational velocity; rotational inertia x rotational velocity = rotational inertia x rotational velocity.

In this video, we can see how the ice skater's angular momentum is conserved when she lessens her rotational inertia by bringing her arms in and increases her rotational velocity:
http://www.youtube.com/watch?v=AQLtcEAG9v0


Torque

Torque causes rotation. It is equal to force x lever arm. A lever arm is the distance from the axis of rotation. There are three things that affect torque: changing the force, changing the lever arm, or both. Torque is measured in Nm (Newton meters). The more torque an object has, the easier it is to rotate.
My group made a podcast about torque that further explains it implications:

http://www.youtube.com/watch?v=fOPdbmeks4A


Center of Mass/Gravity

All objects have an average position of their mass, called their center of mass. When gravity acts on that center of mass, it is called center of gravity. Center of gravity affects balance. When an object's center of gravity is inside of its base of support, it is less likely to fall over than when it center of gravity is outside of its base of support. When center of gravity is outside of the base of support, a lever arm is created, and the force of gravity gives the object torque, causing it to fall over.
This is exemplified in the following image:

The object with the smaller base of support will fall over because its center of gravity is outside of its base of support, while the large one will remain standing.

Centripetal/Centrifugal Force

Centripetal force is a center-seeking force that keeps objects going into a curve when rotating. Centrifugal force is a fictitious, fleeing force that causes an object to feel as if it is being flung outward.

One example of centripetal force is a satellite orbiting earth. One might ask, how does a satellite not end up being flung out of orbit or crashing into earth? Satellites are able to stay in earth's orbit, because they have the perfect velocity, so they don't cancel out the centripetal force (gravity) acting on them.

Below is a satellite orbiting the earth and a diagram of the forces and velocity.

Satellites orbit, because they have the force of gravity pulling them towards earth, but how do things like airplanes turning have a centripetal force? Their centripetal force is a resultant of Flift and Fweight.

This is also exemplified in car on a banked race track. The resulting centripetal force keeps the car on the racetrack. 

What I have found difficult about what I have studied is accepting that centrifugal force does not exist, but we feel something and call it centrifugal force and study it. I overcame these difficulties by listening carefully to class discussions and realizing that centrifugal force is a feeling, not an actual force.

My problem-solving skills, effort, and learning…

In this unit, I have completed all of my homework in a timely manner and participated in class. My group members and I created a helpful podcast about torque, and we worked well together. I found that I improved my blog posts, because I found a useful drawing app and learned how to properly link my video sources.

My goals for the next unit are to continue completing my work on time and improve my blog posts by providing more visual explanations and thorough descriptions.

Meter Stick Challenge

In step one, we discussed the meter stick's center of gravity, and the torque on the meter stick depending on where it was located on the table and how much weight was added to the end.

In step two, we decided a plan on how to solve for the mass of the meter stick using the stick and a 100g lead weight. We were not allowed to use a scale. We found the tipping point of the stick without a weight on it (this is its center of gravity), which was 49.5 cm. We also found its tipping point with the weight which was 71 cm. We realized that the torque and center of gravity would be the same with or without the weight, which allowed us to solve for the mass, because torque = force times lever arm. When we found the weight of the meter stick, we could convert it to mass using w = mg. 

In step 3, which we performed as a class, my partner Princess and I  found that our meter stick had a different center of gravity than the others, causing our mass to be different. In the corrected method, we first had to know that the counter clockwise torque is equal to the clockwise torque. Since torque = force times lever arm, we could calculate the weight of the meter stick by plugging in the proper units in their respective places. The lever arm when it was balanced with the weight was .3 m, but we didn't know the force (this would be what we solved for, and it was the clockwise torque). The lever arm with the weight with a counter clockwise torque was .2 m with force of .98 (on the center of gravity). Thus we were able to solve for force and mass. The resulting number must be multiplied by 2, because it equals only half the mass of the meter stick.

The following link is a depiction of the meter stick on the table with the mass:
https://docs.google.com/drawings/d/1JH6rNL7vy14oYnYhB5W25tmBF3VMLc3q7PvhRTb97h0/pub?w=960&h=720

How to solve for the mass of the meter stick:

1) counter clockwise torque = clockwise torque
    Force time lever arm = force times lever arm

2) w = mg
    w = .1 (9.8)
    w = 0.98 N

3) F(.3) = (.98)(.2)
    F(.3) = .196
    F = .65 N

4) w = mg
   .65 = m(9.8)
   .066 kg = m

          

Center of Mass and Torque

Torque Resource:

http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html

This resource explains the relation between lever arm and force to create torque. It gives an example of torque when it explains how torque is involved when opening doors. It also tells us that in order for an object to rotate, the force must be perpendicular to the lever arm.

Center of Mass Resource:

http://www.youtube.com/watch?v=0-h1GUTKvCI#t=53

<iframe width="560" height="315" src="//www.youtube.com/embed/0-h1GUTKvCI" frameborder="0" allowfullscreen></iframe>

Hewitt-drew-it gives us an example of a dog on a plank hanging off of a cliff. He asks us how far the plank (and the dog) can hang off of the cliff, before falling over. He gives an equation to calculate this, and explains that the dog would fall if the plank overhung past the center of gravity of the plank and the  dog. He gives us the same question with a girl rather, than a dog, on the plank, showing that the center of gravity will be closer to the girl because of her greater weight.
He leaves us with a question: Two meter sticks are attached to create a ninety degree angle. Where should you place you finger on the sticks to balance them?

Angular Momentum Resource

Hewitt Drewit

http://www.youtube.com/watch?v=8I4ii1xEeG0

<iframe width="560" height="315" src="//www.youtube.com/embed/8I4ii1xEeG0" frameborder="0" allowfullscreen></iframe>

In this video, Hewitt tells us:

angular momentum = momentum times radial distance
angular momentum = mvr

An object or system of objects will maintain its angular momentum, unless acted upon by an external net torque.

gives us an example of this with planets and their moons

Shows a man spinning with weights pulling them out from his body (greater rotational inertia/ harder to spin)  and in closer to his body (smaller rotational inertia/easier to spin).

also gives example of ice skaters spinning in this same manner

if no external net torque acts on a rotating system, the angular momentum of that system remains constant (conservation of angular momentum)

Hewitt leaves us with a question: One is at an amusement park, in the middle of a turntable, that is set spinning freely. If one crawls towards the edge of the turntable, does its rotational rate increase, decrease, or remain the same? What physics principle supports your answer?

Unit 3 Explanation

In this unit I learned about…

Newton's Third Law
Newton's third law states that for every action, there is an equal and opposite reaction.

This picture of a book on a table is an example of an action reaction pair. The book pushes the table down and the table pushes the apple up. The table is resting on the ground, so the table pushes the earth down, and the earth pushes the table up. The earth is also reacting to the apple, so the earth pulls the apple down, and the apple pulls the earth up. 

Each of these action reaction pairs can be represented with arrows of equal length going in opposite directions. The format with which one writes an action reaction pair is as follows: 

Bat                        hits                 ball forward

Ball                       hits                 bat backward

Switch nouns       same verb        opposite directions

Newton's third law is reiterated in the following video:

http://www.youtube.com/watch?v=UKk8PNl8JoI&feature=youtu.be

<iframe width="560" height="315" src="//www.youtube.com/embed/UKk8PNl8JoI" frameborder="0" allowfullscreen></iframe>

Tug of War and Horse and Buggy

With knowledge of Newton's Third Law, one might wonder how a horse can push or pull something if each action has an equal and opposite reaction. This is exemplified in a horse pulling a buggy:

The horse pulls the buggy with the same force the buggy pulls the horse, so how can it move? The horse is able to pull the buggy forward, because the horse pushes harder on the ground than the buggy, causing the system to accelerate. There are three action reaction pairs when a horse pulls a buggy: Horse pulls buggy forward, buggy pulls horse backward, buggy pushes earth forward, earth pushes buggy backward; horse pushes ground backward, ground pushes horse forward. It should be noted that when drawing vectors for these action reaction pairs, it is crucial that the vectors for the horse and earth action reaction pair be larger than the others, as it has a greater force than the other pairs. 

The same principle can be applied to a game of tug of war, the team that has a greater push on the earth will win.

Forces in Perpendicular Directions

The movement of an object is dependent on the direction of the forces that act on it. For example, if a box is resting on a ramp, why does it slide down? While a box exerts a force on the ramp and vice versa, there is also a force of gravity on the box. Thus, the fnet is in the direction down the ramp.

Another example is of someone paddling in a river. If a rower wishes to reach something directly across the river, how should they paddle? Paddling straight across would not be effective because the resultant velocity would lead the rower downstream. To get directly across the river, the rower must paddle directly across, as the resultant velocity will lead him or her to their destination. 

Yet another example of how perpendicular forces affect the movement of objects is billiards. When a pool ball hits another ball, both balls will move, unless hit perfectly straight into the other. If the ball is hit perfectly straight, only the second ball will move, because it only has momentum in the x direction, and none in the y direction. When a ball hits another at an angle, they will both move, because they have momentum in both the x and y directions. Momentum is conserved when they hit at an angle, because their momentum's are equal and opposite. 

The final example is when a pall is hanging from a string. We want to know which side of the string has more tension. The Fweight and fnet up are drown perpendicular, equal and opposite. To find the tension, one must draw 2 lines parallel to each side of the string and intersecting the fnet up. From the ball to where the lines intersect the string on either side are the ftension. The side that is longer has a greater amount of tension. 

Gravity and Tides

Everything with mass attracts all other things with mass. The force an object undergoes depends on its mass F~m and its distance between other objects F=1/d^2. The farther away an object is from something, the less force it feels. An example of this is the force of gravity at sea level vs the force of gravity on a mountain top. The farther away one is from the center of the earth, the less force gravity has on them, so one experiences less gravity on a mountain than at sea level. Let's put the relation of mass distance and force together. The formula for gravity (G) is 6.67*10^11 Nm^2/kg^2. The formula for universal gravitational force is F=Gm1m2/d^2. Gravity is important, because it keeps us in orbit.

When one wishes to solve an equation for the force between 2 objects they must do the following: 1)separate numbers and exponents 2)multiply/divide them respectively 3)multiply these groups together 3)use Newtons as your units 

Example: F=(6.67*10^-11)(5.98*10^24)(6*10^1)/(6.37*10^6)^2

= (6.67)(5.98)(6)/(6.37)^2 * (10^-11)(10^24)(10^21)/(10^6)^2

= (5.90) * (10^14)/(10^12)

=5.90 * 10^2

DON'T FORGET TO SQUARE THE DISTANCE!

The force between the earth and the moon is what creates tides. The force between the moon and the earth is greater than the force between the sun and the earth. This is because the opposite sides of the earth experience a difference in force. It is also what causes tides. The side of the earth facing the moon and the opposite side will experience high tides, while the other sides experience low tides. As the earth spins every place will experience 2 high tides and 2 low tides a day. Tides are not at the same time every day because the moon moves as well. What about the moon and earth in relation to the sun. When they are all aligned, we experience tides at their extremes, high highs and low lows. These are called spring tides and occur during new and full moons. When they are not aligned, we experience neap tides, which are higher low tides and lower high tides. These occur during half moons.

Momentum-and Impulse Momentum Relationship

Momentum is inertia in motion. The formula for momentum is p=mv. When momentum changes, mass or velocity changes (acceleration). Impulse is force over time or J=Ft. Impulse is also equal to change in momentum (J=Δp or J=Δmv) Impulse and change in momentum are always linked. When a great force is applied for a long time, momentum increases. It takes the same impulse to decrease momentum, so to requires the same product of force and time. A long time interval reduces force and acceleration. When momentum changes in  short amount of time there is a greater force and when it changes in a longer time, there is a smaller force. The impulse an object undergoes will be the same no matter how it is stopped. This answers the question of how airbags keep us safe.

No matter how a person in a car is stopped it is going from moving to not moving. therefore, the change in momentum is the same regardless of how the car (and the person) are stopped. p=mv Δp=pfinal-pinitial

Since the change in momentum is the same no matter how one is stopped, the impulse is the same no matter how quickly the person is stopped. Δp=J

The airbags stop a person over a long period of time. Since the impulse is constant, the force on the person is smaller than it would be if there weren't an airbag present. A smaller force on the person means less injury.

This relation can be applied to many safety precaution that serve to decrease the force on an object or person.

Conservation of Momentum

The total momentum before a collision is equal to the total momentum after the collision.

How do we know this?

Well,

Fa=-Fb Force of a is equal and opposite to force of b

FΔta=-FΔtb  same amount of time (impulse)

Ja=-Jb j also equals change in p

Δpa=-Δpb

Δpa + Δpb = 0 no net change in momentum before or after a collision 

There are two types of collisions: elastic- when the objects do not stick together and inelastic-when the objects stick together.

To solve an equation for velocity for an elastic collision:

ptotalbefore = ptotalafter

mava+mvbv = mava+mvbv

plug in masses and velocity before the collision

solve

To solve an equation for velocity for an inelastic collision:

ptotalbefore = ptotalafter

mava+mbvb = ma+mb(vab)

plug in masses an velocities and solve for velocity after collision (tab)

My problem solving skills, effort, and learning

In this unit, I found that I struggled with many of the concepts we addressed. I participated in class, and completed my homework to the best of my ability, although sometimes I didn't turn it in on time or done completely. Group activities, like our lab were a struggle because of technological difficulties, but we persevered. I have completed all of my blog posts on time and have featured the required criteria. I feel that I have been very persistent throughout my work, and I engage and ask questions in class. I am learning to take the information we've previously learned and connect it to new information, like the relationships between force and momentum, etc. My goal for the next unit is to complete all of my homework to its fullest and on time, along with coming into conference period more often when I am confused on a topic.

Connections

This unit was interesting, because we learned about many things that apply to everyday life, like the forces between every single object. I also learned why we have tides, something pretty important to people who live at the beach. Additionally, I learned about the physics of certain safety precautions, like airbags in cars and stretchy ropes/chord for climbing. All go these things connect to various recreational activities which impact us every day.