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.

Tides Resource

http://www.youtube.com/watch?v=YS6IqnvnOak

<iframe width="560" height="315" src="//www.youtube.com/embed/YS6IqnvnOak" frameborder="0" allowfullscreen></iframe>

This video by Hewitt-Drew-It discusses the gravitational force of the moon on bodies of water. He also addresses the moons orbit around the earth and how it affects tides, along with neap tides and spring tides. He leaves us with a question about tides during certain times of the day: "Suppose you go to the beach to dig clams at the time of an extra low tide. Is it reasonable to assume that in about six hours, the hight tide that follows will be extra high?"

Unit 2 Explanation

In this unit I learned about...

Newton's Second Law
Newton's first law states: force is proportional to acceleration and inversely proportional to mass (a=f/m). This means that the more force applied to an object, the more it will accelerate. It also means that as mass increases, acceleration decreases. The equation w = mg (weight equals mass times gravity) tells us how much force is needed to move a particular object. Gravity is equal to 9.8N, but we use 10N to simplify our equations. This means that if we know the mass of something we can also calculate its weight. If an object has a mass of 8kg, then w = (8)(10), w = 80N.

Falling Through the Air with Air Resistance (Skydiving)
fair: force of air resistance
fweight: force of weight (w = mg)
fnet: fweight - fair
When someone first jumps out of an airplane, their velocity is at its lowest point (0 m/s), while their acceleration is at its highest point. When falling, an object's speed increases, and its air resistance increases as well, so speed and air resistance are proportional. This causes its fnet to decrease. Since force is proportional to acceleration, acceleration will decrease as well. Eventually your fair will become equal to your fweight, which means that your fnet will be 0N, so your acceleration will be 0 m/s/s. All of this means that your are at equilibrium (constant/terminal velocity). At this time, velocity is at its highest point, while fnet and acceleration are at their lowest points.

Free Fall - Falling Straight Down
Free fall is when an object falls due to the force of gravity alone. There is no air resistance in free fall, and gravity is the only force acting on the object. This means that the acceleration is always 9.8 m/s/s (10 m/s/s) in free fall, because acceleration is proportional to force, and gravity is the only force present in free fall.

Example: A ball is dropped from a cliff and takes 3 seconds to hit the ground. How far did the ball fall and how fast was it moving when it hit the ground?
To solve for distance...
We use the equation: d = 1/2 at/t
acceleration = gravity, so: d = 1/2 gt/t
plug in what you know: d = 1/2 (10)(3)(3)
solve for distance: d = 1/2 (10)(9)
                                 = 1/2 (90)
                                 = 45 m (don't forget your units!)
To solve for velocity...
We use the equation: v = at
acceleration = gravity, so: v = gt
plug in what you know: v = (10)(3)
                                       v = 30 m/s (units are essential!)

Using these equations, we can calculate the distance and velocity of an object in free fall at any time interval

Throwing Things Straight Up (Free Fall)
So what's the difference between objects being thrown up and an object being dropped? When thrown up, an object has an initial velocity. Our equations d = gt/t and v = gt won't work for objects being thrown up, because these equations assume that the object is starting from rest.

The following images depict (A) free fall, (B) throwing things straight up, and (C) throwing things at an angle (which I will discuss later).

                                            (A)                (B)                                (C)

Remember, as mentioned earlier, the only force present in free fall is gravity (10N) so an object's acceleration is 10 m/s/s. This same rule applies to an object being thrown straight upwards, except the object is decelerating by 10 m/s/s rather than accelerating. The object will continue to decelerate until its velocity is 0 m/s/. When the object's velocity equals 0, then it has reached the top of its path. At this point, it will begin to fall down and accelerate by 10 m/s/s until it again reaches its initial velocity. Picture (B) illustrates what I have just said. Let's practice what we've just learned:

Let's say the ball in picture (B) has an initial velocity of 40 m/s at 0s (initial velocity will always start at 0 seconds). What will its velocity be at 2s?
You may be thinking you need an equation to solve this problem, but you don't! Since the object is being thrown up, it is decelerating by 10m/s every second. In order to find the velocity of this object, we only need to subtract 10m/s for every second that the object decelerates. That means the velocity of the object at 2s is 20m/s.

When the ball is coming back down, the velocities will mirror the velocities on the way up. This means that the velocity at 6s will also be 20m/s, because the object has a constant acceleration of 10m/s/s.

All of this is reiterated in my group's podcast:

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

Falling at an Angle (Free Fall)
Falling at an angle is a type of projectile motion. This means that, along with an increasing vertical velocity, an object also has a constant horizontal velocity. With objects falling at an angle, we must remember that vertical distance determines the time an object is in the air. Falling at an angle is illustrated by a box being dropped out of an airplane and reaching a target below.

In free fall, once this box is dropped it has a constant acceleration of 10m/s/s (g). Let's say it is 125 m off of the ground. How long is the package going to be in the air? Remember time is determined by vertical distance. We can solve for time by using the distance equation:
d = 1/2 gt^2
125 = 1/2 (10)(t^2)
125 = (5) (t^2)
25 = t^2
5s = t

How much farther back from the target must the plane drop the box? This is just a different way of saying, what is the horizontal distance from the target? Let's say the package is moving at 90 m/s in the horizontal direction. We can use the velocity equation to solve for distance:
v = d/t
90 = d/5

450m = d

Throwing Things Up at an Angle (Free Fall)
This is another type of projectile motion. Just as when an object is thrown straight upward, objects thrown up at an angle have an initial velocity. In addition, they also have a constant horizontal velocity (like things falling at an angle). This type of motion is depicted in image (C).

                                            (A)                  (B)                          (C)
To find the resultant velocities of the horizontal and vertical velocities at a given time interval, we use the equation a^2 + b^2 = c^2
We use the same equations used for things falling at an angle to find distance and time.


My problem solving skills, effort, and learning...

In this unit I was diligent throughout my work. I participated in class, and completed my homework to the best of my ability, although sometimes my workload prohibited me from doing it fully. In group activities I happily gave and received help on certain subjects. 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, never hesitating to ask questions in class and during conference period. I am learning to take the information we've learned in class and apply it to more difficult problems, as well as work effectively within a group to accomplish challenging assignments. My goal for the next unit is to complete all of my homework to its fullest and continue engaging in class.

Connections...

It is useful for me to know about falling at an angle, because pilots must know about this when dropping relief packages. I could also use what I learned about falling straight down to calculate how far a jump might be and whether or not it would be safe.

Free Fall Resource

<iframe width="560" height="315" src="//www.youtube.com/embed/j1TOMsUG4Tk" frameborder="0" allowfullscreen></iframe>
http://www.youtube.com/watch?v=j1TOMsUG4T

The video begins with a definition of free fall. He explains that the only force on an object in free fall is gravity (10N), so the object's acceleration is 10 m/s/s. He then tells us the initial speed of the object is 0 m/s. He uses a speedometer and and odometer to tell us the velocity and distance of the object at each time interval. Later, he explains his data using equations, including the equations for acceleration (a = Δv/ Δt), distance (d = 1/2gt², and velocity (v = gt).

Newton's Second Law Resource

<iframe width="560" height="315" src="//www.youtube.com/embed/nJTKiS444BQ" frameborder="0" allowfullscreen></iframe>

http://www.youtube.com/watch?v=nJTKiS444BQ

This video describes Newton's Second law by giving an example of a kicker on a football team. It tells us how the equation f=ma can be applies to kicking a football, and what exactly is happening when the kicker applies force to the ball.

Unit 1 Review

In this unit I learned about...

Newton's First Law/ Inertia
Newton's First Law states: An object at rest stays at rest and an object in motion stays in motion unless acted upon by an outside force. This means that if I threw a ball, and no forces were present to stop that ball, it would continue on in the direction I threw it for eternity, or until something blocked its path. In other words, object are lazy. Inertia is how hard it is for something to start and stop. The most important thing to remember, is that INERTIA IS NOT A FORCE, it is a principal. After learning about Newton's first law and inertia, I now understand why certain objects do and do not move, and how this is possible. The following video I created with my group illustrates these properties:

<iframe width="420" height="315" src="//www.youtube.com/embed/GaqeAwDBJMY" frameborder="0" allowfullscreen></iframe>

Net Force and Equilibrium
Net force is the overall force (push or pull) acting on an object, and is measured in Newtons (N). Equilibrium occurs anytime the net force on an object is 0 N. This happens when something is moving at constant velocity or is at rest. When forces are pushing an object in the same direction, then those forces are added together to find the net force on the object. When they are pushing an object in opposite directions, the forces are subtracted to find the net force. If an object is not at equilibrium, there is a force causing it to speed up or slow down (accelerate). You cannot tell the motion of an object when it is at equilibrium, because it could be moving or it could be at rest.

Speed and Velocity
Speed and velocity are often misused in everyday language. Speed refers to how fast an object is moving. Velocity also refers to how fast an object is moving, but it refers to the direction in which an object is moving as well. This means that when an object changes direction, its velocity changes too. In physics, speed and velocity are measured in m/s (meters per second). When solving problems, vectors are given to illustrate said problems. Vectors are shown as arrows and are used to represent the greatness and direction of the velocity of the object in the problem. The formula for velocity is: v = d/t (velocity equals distance over time). It was useful for me to understand speed and velocity, because they apply to everyday movements.

Acceleration
Acceleration is a change in velocity (speed or direction). When the velocity of an object is constant, then an object is not accelerating. The formula for acceleration is: a = Δv/t (acceleration = change in velocity over time). Acceleration is measured in m/s2 (meters per second squared). By learning aboutacceleration, I now understand what is happening when an object changes direction or speed and how I can predict the movement of the object.

Equation of the Line

The equation of the line is y = mx + b. Y represents the units in the y axis. M represents the slope (change in y over change in x). X represents the units on the x axis. B represents where the line crosses the y axis. In physics, the equation of the line can be used to solve the distance equation (d = 1/2 at2). The x represents time squared, the y represents distance, and the m represents 1/2 the acceleration. The b is disregarded. 

Formulas
v = at (accleration)
a = Δv/t (accleration)
d = 1/2 at2 (distance = 1/2 acceleration squared)
v = d/t (constant velocity)

Difficulties
What I have found difficult about what I have studied is the concept that even though something's acceleration may be decreasing, it is still changing velocity. This simply means that isn't getting faster as quickly as it was before. Initially this concept confused me, but after discussing it in class, I now understand why it is possible for an object's velocity to be increasing as its acceleration is decreasing. 

Problem-Solving, Effort, and Learning
I switched into this class two weeks into unit 1. At first, I was a bit confused, but after doing all of my makeup work and watching all of the video lessons Mrs. Lawrence created, I feel like I understand what we have been learning. I have completed all of my makeup assignments, homework, and blog posts on time and in an orderly fashion. I have also come into conference period when I did not understand certain concepts. I have mastered the formulas used in this unit and feel ready to face any challenging problems that may arise on the upcoming test. I also feel that I am able to effectively communicate the concepts learned in this unit through words and equations. Working in groups was helpful for me to gage my understanding of this first unit compared to my classmates. We were able to help one another on difficult conceptual questions, and to realize where the gaps were in our knowledge of what we had learned so far. 

Goals
My goal for the next unit is to maintain my promptness of assignments, turning things in when they are do. I also hope to come into conference period when I need help from Mrs. Lawrence in order to master the material that is being taught. 

Constant Velocity Vs. Constant Acceleration

The main purpose of this lab was to compare constant velocity and constant acceleration, as well as to learn about the equation of a line and how to use it in physics. Constant velocity is when an object is moving at a constant speed. We can tell when something is at constant velocity when it is evenly spaced apart at different time intervals. Constant acceleration is when an object is constantly speeding up. We can tell if something is at constant velocity when the space between it and its last position at a given time interval becomes larger. In this lab, we placed a marble on a flat surface and marked its position at every half second to study constant velocity. We also placed a marble on a ramp and marked its position at every half second to study constant acceleration. When the marble was at constant velocity, it continued at the same speed during the entire experiment. When it was at constant acceleration, it consistently sped up. The formula for constant velocity is: v = d/t. The formula for constant acceleration is: a = △v/t. The line in a graph for constant velocity is straight, while the line in a graph for constant acceleration curves upwards. We used the graph to tell if the marble was undergoing constant velocity or constant acceleration. We used the equation of the line to find the acceleration, velocity, and distance in an equation by translating it into physics terms.In this lab, I learned the equation of a line, how to translate that into physics terms, and how to make a graph in excel, all of which will help me in future labs.