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.