Unit 3

Newtons 3rd Law + Action and Reaction Pairs
   Newtons 3rd Law states that every action has an equal and opposite reaction. For instance if a book was sitting on a table, the book would be pushing down on the table and the table would be pushing up on the book. These are called action and reaction pairs. Another example is walking. As a person pushes the ground backwards with their foot, the earth pushes foreword.
Tug of War
   We can use our knowledge of Newtons 3rd Law and Action and Reaction pairs to win a game of tug of war. In tug of war, the amount each team pulls actually doesn't make a difference because of Newtons 3rd Law. What does matter is how hard each team pushes on the earth. If one team pushes back the earth with a force of 5 making the earth push back with an equal force, and the other team pushes the earth with a force of 10, the second team would win.
   We can also use our knowledge of Newtons 3rd Law and Action and Reaction pairs to understand how a horse and buggy move. Similar to the tug of war situation, whatever force the horse pulls foreword, the buggy will pull back in the opposite direction because of Newtons 3rd Law so what makes the buggy move is the horse pushing the ground harder than the buggy pushes the ground.
Forces in Perpendicular Directions
   A person is in a sled on a snowy hill. They slide down the hill. This happens because of forces that occur in perpendicular directions. The weight of the person on the sled is called F gravity. The perpendicular force to this is called F support. If we add up the vectors, we get a force that would bring the sled down the hill. If the F friction is greater than the force that makes the sled move, the sled would stay still. We can use these same ideas in relation to sail boats, currents, and other movements.
   A heavy box is being suspended by a rope which is attached to the ceiling however, one side is longer and has a smaller angle. When drawing in support vectors in either direction we can draw tension vectors. The longer the vector, the more tension there is.  
Momentum and Impulse
   Momentum, or p, is mass, or m, times velocity, or v. The equation for momentum is p=mv. So if a box was being pushed at a velocity of 10 and it had a mass of 5 its momentum would be 50. Impulse, or J, is how much force, or F, occurs over an amount of time, or t. The equation for impulse is J=Ft. We use impulse when talking about something changing momentum like stopping: going from moving to not moving. Continuing off of the box example, if the box stopped, it would go from 50 to 0 no matter how it stopped. This equation is J=change in momentum. If the box was stopped on a concrete wall versus a sponge wall, there would be very different outcomes. To deal with this type of situation we use the J=Ft equation. In this equation, Force is inversely proportional to time meaning if time is small, force is big and vice versa.  If the box stopped on a concrete wall it would be a very abrupt halt = a small amount of time = big force. If the box stopped on a sponge wall it would be a much gentler halt = long time = small force = less damage. This is the reason we have air bags in vehicles.  
Gravity and Tides
   The reason that tides occur is because of the moons pull on the earth. Tides on opposite sides of the earth are always the same. If you picture the globe, the left and right sides would have high tides and the top and bottom would have low tides or vice versa. This happens because of the difference in force felt by each side. For example, one side of the earth, lets call it side A, is adjacent to the moon and the other side of the earth, lets call it side B, is opposite to the first side. Side A would be a shorter distance away from the moon and because of the formula F=m1m2/d^2, it would have a large net force. Therefore, side B would be a larger distance away from the moon and have a smaller net force. The moon would also have a pull on the center of the earth which would be less than the force of side A, but greater than the force of side B. For example, the force of side A is 15, side B is 5 and the middle is 10. As stated earlier, the difference in force felt by each side is what makes opposing sides of the earth have equal tides. To find this difference, we subtract 10, the middle number from 15 and 5, each side. When doing this, we get 5 and -5. This means that we have a force of 5 pulling to the right and to the left. This creates a tidal bulge. Without a difference in force, we would get a net force of 0, creating no tides at all.  High and low tides alternate and occur about every 6 hours with each occurring 2 times a day.  High and low tides occur every 6 hours because of the time it takes the moon to orbit earth. There are also tides called spring tides and neap tides. Spring tides occur when the sun, earth, and moon are lined up either sun, moon, earth or sun, earth, moon. When this happens, there is either a full moon or a new moon and the tides are unusually high and unusually low. Neap tides occur when the sun, moon, and earth do not line up either sun, earth, and moon above or below the globe. When this happens there is a half moon and the difference between the tides are unusually low.
Conservation of Momentum
   Because of what we know from Newtons 3rd Law, momentum is always conserved. When playing pool, one ball hits the other resulting in the ball that was moving to stop and the ball that was still to move with the same speed as the first one originally moved. A ball could also crash into another cart resulting in them both moving together. 

Tides

This video is a time lapse of the Bay of Fundy's tides. Although this is an extreme case of high and low tides, it clearly shows the difference between high and low tides.
The reason that tides occur is because of the moons pull on the earth. Tides on opposite sides of the earth are always the same. If you picture the globe, the left and right sides would have high tides and the top and bottom would have low tides or vice versa. This happens because of the difference in force felt by each side. For example, one side of the earth, lets call it side A, is adjacent to the moon and the other side of the earth, lets call it side B, is opposite to the first side. Side A would be a shorter distance away from the moon and because of the formula F=m1m2/d^2, it would have a large net force. Therefore, side B would be a larger distance away from the moon and have a smaller net force. The moon would also have a pull on the center of the earth which would be less than the force of side A, but greater than the force of side B. For example, the force of side A is 15, side B is 5 and the middle is 10. As stated earlier, the difference in force felt by each side is what makes opposing sides of the earth have equal tides. To find this difference, we subtract 10, the middle number from 15 and 5, each side. When doing this, we get 5 and -5. This means that we have a force of 5 pulling to the right and to the left. This creates a tidal bulge. Without a difference in force, we would get a net force of 0, creating no tides at all.  High and low tides alternate and occur about every 6 hours with each occurring 2 times a day.  High and low tides occur every 6 hours because of the time it takes the moon to orbit earth. There are also tides called spring tides and neap tides. Spring tides occur when the sun, earth, and moon are lined up either sun, moon, earth or sun, earth, moon. When this happens, there is either a full moon or a new moon and the tides are unusually high and unusually low. Neap tides occur when the sun, moon, and earth do not line up either sun, earth, and moon above or below the globe. When this happens there is a half moon and the difference between the tides are unusually low.
In the summer, my family likes to visit our friends in Rhode Island. They own a house on the Sakonnet beach. Here is a link to a Sakonnet tide chart: http://ri.usharbors.com/monthly-tides/Rhode%20Island/Sakonnet . Right now, as I am writing this post at 8:50 pm, the beach is in-between high and low tides and turning into a high tide and experiencing neap tides. 

Newtons 3rd Law Resource

Despite the minimal animation, I think this video does a good job simply and clearly explaining Newtons 3rd Law. It helps to explain action and reaction pairs and clearly states the law. I found the bicycle example most helpful because it showed a real life application of the law.

Newtons Second Law Unit Summary

    In unit 2...

 We learned about three different types of free fall: free fall straight down, free fall thrown upward, free fall with projectile motion, and free fall straight down with air resistance.

     1) The simplest form of free fall would be, for example, a ball was dropped off of a building. In this situation, air resistance is negligible and the object is falling from rest. Free fall is when objects fall due to the acceleration of gravity only.
     Say you were on a hike. You come across a cliff. You want to know how far down the drop is. In order to do this, you could drop a rock off of the cliff and time how long it took to make the fall. In order to calculate the hight of this cliff, you need to know a formula: d=1/2gt^2. In this formula, g or the force of gravity, will theoretically always be 10 (but in the real world it is 9.8). Say it took the rock 8 seconds to fall. You would say d=1/2x10x8^2. If you solve this equation, you would find out that the distance, or hight of the cliff is 320m.
     If you want to know how fast the rock, or whatever object you drop from whatever hight is moving at a certain time, you need to know the equation: v=gt and remember that because the force of gravity is 10, our velocity will increase by 10m/s every second. So say you want to know how fast the object was moving after 5 seconds of falling. You would simply multiply 10 (gravity) by 5 (time) and you would get the velocity at that time. In this scenario, the velocity would be 50 m/s.

     2) You are watching a soccer game. The goalie catches the ball and decides to punt it down the field. She tosses the ball up, waits for it to come back down, and then kicks it. You can figure out how high the ball goes, how long it is in the air, and how fast it is moving at any time. As you can see in the picture, this speed will decrease by 10m/s every second so by drawing out what we know, we can figure out the aforementioned three things just by knowing the starting velocity or the time in the air.
     If we want to know high the ball was at the top of its path before it started to fall, we use our trusty d=1/2gt^2 formula. So in this case, we have figured out that the ball was in the air for 4 seconds before reaching the top of its path. If we plug that number in for t, we find that it reached a hight of 80m. Lets say we want to know the balls hight at 2 seconds. In order to find this, we need to find the total hight as we did before (pictured in green) and subtract this from the distance pictured in blue. This equals the orange hight, or the hight at 2 seconds. 

     3) Once the goalie kicks the ball, it is propelled foreword and shoots down the field. This is an example of projectile motion. The goalie kicks the ball 50m down the field at a 45 degree angle and the ball stays in the air for 4 seconds. You can figure out how hard she kicked the ball. As you can see in the picture, you can predict where the ball would be every second and how fast it would be going at each second. If we look at our picture, we can see that the ball was kicked at a vertical speed of 20m/s at 0seconds. Remember that its horizontal velocity is constant. In order to find it, we just plug our numbers into the formula: v=d/t. In order to figure out how fast the ball was actually moving at any given time, we draw out a picture like this:   The actual speed will be the hypotenuse. In order to solve for this, we just use the pythagorean theorem: a^2+b^2=c^2, or one of our special triangles: 3, 4, 5, or x, x, xsqrt2. Remember that the square root of 2 is 1.41. So we can find out that in order for the soccer ball to land 50m away, the goalie must kick the ball at about 22 m/s. We can figure out how long the ball will be in the air, how fast the ball will be at the top of its path, and how far away it will land. Remember that the vertical velocity is the main component. In summary, the big formulas to remember are: vertical: d=1/2gt^2, v=gt horizontal: d=vt, v=d/t.

     So lets say that for some strange reason, the goalie who is holding a ball sprouts wings and begins to fly foreword at a speed of 90m/s 125 meters above the ground. She wants to make a goal by dropping the ball into it. The ball has a constant vertical acceleration and a constant horizontal velocity. First lets find out how long the ball will be in the air by using d=1/2gt^2. We should get 5s. Remember we have to drop the ball very early because the ball is moving foreword at 90m/s and will continue to because of inertia. In order to find how far away to drop the ball in order to make a goal, we use the formula v=d/t and find out that horizontal distance is 450m. In order to find where the ball would be in the vertical direction each second, we use d=1/2gt^2. In order to see the actual estimated path, just find where the horizontal and vertical would meet up.

      4)In this unit we also learned about Newtons Second Law. The law states that acceleration is directly proportional to force and inversely proportional to mass. This statement can also be written as a formula: a=F/m or a=Fx1/m. This means that if acceleration increases, force would increase or if acceleration decreased, force would decrease also. This also means that if acceleration increases, mass decreases or if acceleration decreased, mass would increase. In the real world, Newtons Second Law can be seen in a person pushing a box. If the box was light (or had a small mass) it would be easier to move, or accelerate and if the box was heavy (or had a large mass) it would be more difficult to move or accelerate. If you had a box and pushed it just a little bit (with a small amount of force) it would not accelerate quickly. If you pushed the same box with a lot of force it would accelerate quickly.

     5) We did a lab to demonstrate these concepts and illustrate how acceleration depends on force and mass. In this lab, we had a cart on a track with a string attached. The string ran over a pulley to a hanging weight below. In this example, the hanging weight applied the force that caused the acceleration. We needed to find all of the components in our formula: a=F/m. In this case, the acceleration is basically how fast the cart goes. To find the mass, we added up the masses of the cart and hanger to find the total mass of the system. To find the force, we found the weight of the hanger by using the formula w=mg (weight equals mass times force of gravity) and kept this constant throughout the experiment. In .10 kg increments we added more masses onto the cart therefore changing the the total mass of the system. We found that as the mass of the cart increased, the acceleration decreased. In our next part of the experiment, we kept the total mass constant, but moved around the weights from the cart to the hanger one at a time. We found that as the force of the cart increased the acceleration increased.

     6) In this unit we also learned about skydiving. Skydiving is like free fall, but weight matters, and air resistance is a large factor. As a person jumps out of a plane, they are pulled down by the F-weight (which is found using the formula w=mg) and they accelerate towards earth. F-air (the force of air resistance) acts in the opposite direction and increases as the person gains speed. This is because acceleration is directly proportional to force. In this situation the force is air resistance and acceleration is how fast their velocity is increasing. F-air increases until it becomes equal to the constant F-weight. This is called terminal velocity. In terminal velocity, the net force is 0 which means the person is no longer accelerating (although they continue to move downward) and is in equilibrium. Once the person opens their parachute, the F-air becomes much greater than before, the person is no longer in equilibrium, and the speed of the person slows down. Because the speed is decreasing, air resistance decreases also because they are directly proportional. These two factors continue to decrease until F-air is equal to F-weight again. This is the second terminal velocity. In the second terminal velocity, the speed is slower than in the first and the air resistance is larger than in the first. The person continues to fall toward the ground at this much slower speed and can safely land on the ground. VIDEO HERE!!
     
 F-air and F-weight are important parts of falling things besides sky diving.
     If you dropped a crumpled piece of paper and a flat piece of paper, although they are the same weight, the crumpled paper would land first. This is because of surface area. The crumpled piece of paper has a small surface area, so it would have to accelerate longer in order to reach terminal velocity and get its F-air to equal its F-weight. The flat piece of paper has a large surface area, so it would not have to accelerate long to reach terminal velocity and have an equal F-air and F-weight.

     If you dropped a lead ball and a ping pong ball, although they have the same surface area, they would land at different times. This is because they have different weights. The lead ball has to accelerate for much longer in order to reach terminal velocity and get equal F-weight and F-air and the ping pong ball doesn't have to accelerate long to reach terminal velocity with equal F-weight and F-air.

     It was interesting to learn how physics plays a role in a wide range of things as simple as tossing a ball into the air, as common as playing sports, and as exiting as skydiving.

Unit #1 Summary

In this unit I learned...

1) about inertia. No object will move on its own accord. However, If an object starts moving and there is no outside force to prevent this movement such as friction, gravity, ect. it would keep moving forever and it requires the same amount of energy to stop something and to start something. This all means that objects are 'lazy' and like to stay where they are. In a nut shell, inertia is the fact that no object moves on it's own accord.
   Newton's First Law supports the idea of inertia by stating that all objects at rest stay at rest and all objects in motion will stay in motion unless acted on by an outside force.
   We learned about these concepts in many ways. In one lesson, we watched a cart that had a ball in it move. At some point, the ball was popped up and out of the cart, and although the cart was moving foreword and the ball was launched up, the ball landed back in the cart. This occurred because both the ball and the cart were moving foreword. When the all was popped up, it continued to move foreword because as Newtons law states, objects in motion stay in motion, and it landed back in the cart. This same exact concept can be seen in many different everyday ways including the quick removal of a table cloth out from under dishes when the dishes stay in place (objects at rest stay at rest), as well as a coffee cup spilling or falling when a vehicle stops or starts (objects in motion stay at motion), and many more.  
        

2) When we rode the hovercraft, we learned about inertia and Newton's First Law but we also learned about equilibrium and net force. Net force is the total forces being put on an object that makes the object move. For example, if one person is pushing a box with a force of 5 newtons to the right, and someone joins them and pushes the box the box to the right with a force of 13 newtons, the net force would be 5+13, or 18n. However if someone was pushing a box to the right with a force of 5 newtons, and someone else is pushing the box to the left with a force of 13 newtons the net force would be 13-5, or 8.

Equilibrium is when the net force adds up to zero newtons. This can mean that the aforementioned box is stationary or that it is moving at a constant velocity. If it is moving at a constant velocity of 15, for example, the friction pushing against the box would be 15. Since equilibrium requires a net force of zero and 15-15=0, the box would be in equilibrium.

3) If we wanted to know how fast this illusive box is traveling, we would need to find the speed or the velocity. Speed is simply the measure of the distance an object travels in a designated amount of time.   Physicists usually measure speed in meters per second or m/s. Velocity is the same as speed, except it requires a specific direction. For example, you could say that as a race car rounds the track it increases its speed but you could not say that as a race car rounds the track it increases its velocity. Velocity is represented with arrows called vectors that represent magnitude and direction. The three ways to change velocity are changing direction, speeding up, or slowing down.

The equation for constant velocity if we want to know how fast an object is moving is v = d/t. The equation for constant velocity if we want to know how far an object moved  is d=vt.

Here is a video my classmates and I made about velocity:
4) If we want to know how fast an object is picking up speed, we need to know about acceleration. Acceleration is simply a change of speed like slowing down or speeding up. If a car is moving at a speed of 4m/s and in the next second it is moving at a speed of 8m/s, and in the next second the car is moving at a speed of 12m/s the car has accelerated by 4m/s^2 every second. This means that the car has constant acceleration. If a car is moving at 2m/s one second, 6m/s the next second, and 13m/s the third, the car has accelerated by 4m/s ^2 the first second, 7m/s^2 the second second. Because the car is not speeding up at the same rate, but increasing the rate in which it is speeding up, the car has increasing acceleration. If a car is moving at 10m/s the first second, 18m/s the second, and 25 m/s the third, the car has accelerated by 8m/s^2 the first second ,7m/s^2 the second, and 5m/s^2 the third. Although the car is still increasing its speed, it is increasing its speed slower.

 

The acceleration equation is change in v/time.
The equation for constant acceleration if you want to know how fast something is going is v=at.
The equation for constant acceleration if you want to know how far something is going is d=1/2at^2.
5) Here is a graph that represents constant velocity:

In order to use this graph to solve a problem, the first step is to turn the y=mx equation into words. In this case y=4x would turn into d=4•t. This looks like the formula d=vt. When these two equations are compared, we can see that 4 and v are the only things that are not the same. This means that 4 is the slope. You can now use this information to plug into equations that correspond with the question you are being asked.
Here is a graph that represents constant acceleration:

In this case, because we are dealing with acceleration, time is squared so that we have a straight line. We now go through the same steps as above. We will find that our equation looks like d=1/2at^2.

Today we Rode Hovercrafts!

Today we rode hovercrafts! Riding on a hovercraft is interesting because once it starts going, it stays at that speed; it never slows down or speeds up unless stopped. It is different than riding on a sled or a skateboard because, unlike a sled or skateboard, it is not slowed down by friction. Riding the hovercraft helped to further understand inertia, net force, and equilibrium.
Inertia can be clearly seen in the hovercraft because when the craft was at rest it stayed in rest and when it was in motion it stayed in motion. What a lazy lout!
We could see net force when the hovercraft was stopped. The force of my classmates stopping the craft was greater than the speed of the hovercraft.
We also learned about equilibrium which happened once the hovercraft had accelerated and started moving because it was not slowing down or speeding up.
Based on this lab, acceleration depends on how hard the hovercraft is pushed and how heavy the person riding it is. The weight of the person riding the craft also makes them harder to stop because mass plays a large roll in inertia. You can find further explanation of this concept in the video I posted recently.
The hovercraft had constant velocity after it had been pushed and before it was stopped. Once it had accelerated, it stayed at the same speed because of Newton's First Law, and the lack of friction.

Here's me on the hovercraft!

Inertia!

Newtons First Law of inertia states that all objects at rest stay at rest and all objects in motion stay in motion unless acted on by an outside force.
This video is a helpful illustration of the law (and a super cool trick that will make you lots of friends). The egg stays in place and falls into the cup because the outside force of the hand hits the plate, not the egg, and there is minimal friction on the egg because of the toilet paper roll. The egg, because it is at rest, stays at rest even when the plate is taken out from underneath it thanks to the law of inertia!

Physics Goals

        This year in physics, I expect to learn how everything we know about works from the coversion of energy involved in eating, to the physics behind kicking a soccer ball and the movement of running, to the science behind spaceships. I think that studying physiscs is important so that we understand our world and why it functions. In adition to this, I am wondering how space travel and exploration works as well as the physics behind planets, nebuals, galaxies, and other space related bodies and concepts.

        I think that problem solving is recognizing a problem and finding a solution through innovation and thoughtful thinking and reasoning. I hope to be able to hone my problem solving skills this year and use them to do well on quizzes and tests as well as participate and do well in class. 

        In this class I hope to become a learner, exceed beyond being a student, and become a committed knower. To become a learner I want to try to learn because I want to learn and try to enjoy what I am learning not just trying to get a good grade. I will be willing to learn and improve my learning and study habits. This will all hopefully help me to comprehend, versus complete, and know, versus remember. I hope that this will all translate into a fun filled year full of learning adventures.