Unit 3 Summary - Blog Post

Unit 3 Summary

A) In this unit I learned about...

• Newton's 3rd Law / Action and Reaction Pairs
• Tug of war / horse and buggy reactions
• Forces in perpendicular directions
• Gravity and Tides
• Momentum and impulse-momentum relationships
• Conservation of Momentum

There is a lot to say about each of these topics, but I will hopefully be able to explain each one in a simplified way and make it easier to understand.

Newton's 3rd Law / Action and Reaction Pairs

Newton's 3rd Law states that, "For every action, there is an equal and opposite reaction." This means that every time a force is applied to an object, and equal and opposite force is applied to the opposite side of it. When talking about Newton's 3rd Law, you have to mention action and reaction pairs to fully understand the concept. But BE CAREFUL, a lot of people get tripped up on the difference between action/reaction pairs and simply just two forces being equal and opposite. An example easily demonstrates the difference. 

Example of an equal and opposite action/reaction pair:

A girl, weighing 5N, is standing on the earth. The earth is also pushing up on this girl with 5N of force. This, therefore, creates a net force of 0N because the girl's force cancels out the earth's force (and vice versa). This is an example of an action and reaction pair. 

Example of an equal and opposite NON-action/reaction pair:

This same girl, still weighing 5N is now standing on top of a table. The force of the girl pushing down on the earth is still the same as before, but now the force of the table must also be taken into account. The earth will now be pushing up on the girl and the table. The force will remain equal and opposite, but this reaction does not create an action/reaction pair. (The action/reaction pairs would be between the girl and the table and the table and the earth.) 

Horse and Buggy & Tug of War (another example of action/reaction pairs)

The horse and buggy reaction and a game of tug of war are both easy examples to further prove Newton's 3rd Law. 

Horse and buggy- First of all, there is the force of the horse pulling on the buggy and the buggy pulling back on the horse. This creates an action and reaction pair and the forces and both equal and opposite. Then there is the horse pushing the ground back and the ground pushing the horse forward. This is also an action & reaction pair of equal and opposite forces. The last set of action and reaction pairs is between the buggy pushing the earth forward and the earth pushing the buggy backwards. There is one thing you have to remember about the horse/ground reaction and the buggy/ground reaction. In order for the buggy to be moving (which in this case, let's say that it is), the arrows that you draw between the horse and the ground when making a diagram must be bigger than the set of arrows between the buggy and the ground.

Tug Of War- You may be surprised to know that when you are in a tug-of-war, the winner is really not determined by who is stronger, it is more so who exerts the greater force on the ground. This means that whichever side of the rope has the bigger action/reaction pair, will win the war. 

Forces in Perpendicular Directions

Forces in perpendicular directions is basically all to do with lines and vectors. We show the amount of force exerted on a object with these vectors and that is how we can tell where the most force is being applied. 

Example:

Box A is sliding down a ramp that is not so steep, while box B is sliding down a very steep ramp. You must show the force of gravity on each box (with lines that are equal in length) pulling down on the box, and then the supporting force pulling up on the box. To find out how fast the box is actually moving down the ramp, you can draw dotted lines parallel to the opposite line and then you will be able to see that the acceleration vector will be much longer in Box B sliding down the steeper ramp. 

Gravity & Tides

Gravity and tides was a very interesting topic, and probably my favorite, throughout Unit 3. I think that I liked it so much because it really made sense and was relevant to my everyday life. To understand tides, you first need to understand gravity. Gravity equals 6.67 x 10 to the negative 11th power (a very very small number) is a force that pulls an object towards it, like the earth's pull on us. Everything with mass attracts all other things to it making f ~ m. Although, as you move farther away from that object, the force becomes less and less strong making f ~ 1/m as well. The Universal Gravitational Law is F=Gm1m2/d2. 

Example:

Planet A has a mass of 8x10 to the 30th kg, and planet B with a mass of 6x10 to the 15th kg. The two planets are a distance of 4x10 to the 22nd m. What is the force between them?

To solve this problem you have to sub in the two masses multiplied by gravity, divided by and the distance (squared) and you will be able to calculate the force.

Gravity is the main reason why we have tides. To understand tides you must know why a tidal bulge occurs on opposite sides of the earth and what a Spring and a Neap tide is. 

FUN FACT: Between every high-tide and low-tide, 6 hours pass. Therefore, it takes a full 12 hours to reach another high-tide!

• Tides have to do with the earth, moon, and sun. The gravitational pull of all three of these create our tides, although the most important is the moon. The moon has a gravitational pull on the earth causing the water on the surface of the earth to actually rise and move towards the moon. The rising and falling of the water are what we call our tides. This creates a tidal bulge around the surface of the earth. The bulge will be the same size on the opposite sides of the earth. It may seem like the side closest to the moon should have a higher tide than the side farthest away from the moon, but this is not the case. The side closest to the moon rises because there is a strong force on it, but the side farther away from the moon also rises because it is so much farther away therefore with much less force acting upon it. 

• Spring Tide occurs when the gravitational pull of the moon and the sun are combined. This creates very high high-tides and very low low-tides. There can be either a full moon or a new moon during Spring tides. 
• A Neap Tide occurs when the force of the sun and the moon are perpendicular to one another, cancelling each other out. Neap tides have a much smaller difference between high and low tides. Neap tides occur during quarter moons. 

Conservation of Momentum

Any moving object has a momentum (p=mv). In every single case, the total momentum before and after an explosion or collision will be equal to each other. An example of this would be with a canon and a cannon ball. The cannon can only push the cannon ball as far as strong as the cannon ball can push back (equal and opposite). This can be expressed in the formula ∆p=ptotal before-ptotal after. We know this because momentum is conserved in this kind of reaction, making the net external impulse = 0N. BUT WAIT, what's impulse? Well, impulse is the force upon something and how long that force is applied. It is what causes and is equal to a change in momentum (∆p=m∆v). 

• Another good example to mention is the bug crashing into a windshield. You would guess at a glance that the difference in size proportions would make there be no change in momentum for the car (since it is so much bigger than the bug), however that is not the case. Something can only be pushed as hard as it can be pushed back.

• In some special cases, such as explosions where both objects are initially at rest, one object will move forward with a positive velocity while the other moves backwards with a negative velocity. It may seem as if the ptotal before and ptotal after could not possible equal each other. Although, when you add the + velocity and the - velocity, you will find that they will cancel each other out to equal zero like before the explosion. 

Momentum & Impulse-Momentum Relationships

I think that it is important that I explain a little bit more thoroughly how momentum compares to impulse in real life situations. We already know that momentum = mass x velocity, and we also know that the total change in momentum before a reaction = the final momentum - the initial momentum. Therefore, we can conclude that the ∆p will be the same regardless of how it is actually stopped. All that matters is that we know that the object goes from moving to not moving in a certain amount of time. The ∆p = J. The only difference is that the units chance from kgm/s to Ns. We learned one very important example of this in order to prepare for the test. 

Example:

Explain why someone who jumps off of a cliff into the snow would not get as badly injured (if injured at all) as someone who jumped off a cliff and landed on an icy surface. 

1. First, I would reference the p=mv formula: The person will go from moving to not moving regardless of what surface they hit. 
2. ∆p=pfinal-pinitial: The change in momentum will always be the same, regardless of what surface stops it. All that matters is that it will go from moving to not moving over a specific period of time.
3. ∆p=J: The change in p is the same as the impulse as long as you change the units. They are the same regardless of what surface brings the person to a stop.
4. J= F•∆ t: Since J remains the same, the snow will increase the time to stop. When there is more time to stop, the force will become less and less. With less force, there is less of a chance that you will get injured.

THEREFORE:

With snow: J= F • ∆ t (less injury)

Without snow/on ice: J= F • ∆ t (more injury)

One last thing to know!

In some collisions, we have created things in order to catch or succumb to an object rather than have it bounce off. This happens with a bulletproof vest for a police officer and why cars don't have rubber bumpers anymore. In both of these cases, bouncing will occur. Bouncing is not good and has actually caused more injury than it has justice for us. When there is bouncing (bullet bouncing off of vest/cars bouncing off of each other in a crash) it creates double the force. There is 2 ∆p's, 2 J's and 2 forces. This is why our bulletproof vests work the way they do and cars do not have rubber bumpers. 

B) This unit connects with our everyday lives better than any other unit we have had so far. Every example we dealt with, (whether it was pool balls hitting off of each other, hanging a picture, or getting in a car crash), the event is an everyday occurrence. I think that this factor helps especially when trying to understand Unit 3 as a whole. I hope this blog post has cleared up some confusing topics for you and good luck on your next assignment regarding this information! 

Tides

1a) The earth will experience 2 high tides and 2 low tides in one day. It takes 6 hours to go from a high-tide to a low-tide, and 12 hours to get back to the high-tide. This is all because of the moon and the sun. The moon makes one full rotation around the earth each day. This means that it is in line with the sun and the earth two times, and it is at a 90º angle to the sun two times. This placement of the moon creates our tides.

b) There is a difference in force felt by each side of the earth. The side closer to the sun will experience a much stronger force, while the side opposite from the sun will experience a much smaller force. Still, the tides will be the same on each opposing side of the earth.

c) The tides are still the same on each side of the earth even though they have different forces. At a high-tide the earths ocean are being pulled on strongly on one side, and on the other there is a much smaller pull. Therefore, one side will rise because of the strong force upon it and the other side will rise because there is little force on it which counter-acts the stronger pull.

d) A Spring tide occurs when the gradational pull of the moon and the sun are combined. This creates very high high-tides and very low low-tides. There can be either a full moon or a new moon during Spring tides. A Neap tide occurs when the sun and moon forces are perpendicular to one another, cancelling each other out. Neap tides result in a smaller difference between high-tides and low-tides. Neap tides occur during quarter moons.

2a) At roughly 7:30 on Friday evening (14th) Nassau is experiencing a low tide.

b) About a week ago (5th, 6th, 7th) Nassau would have been experiencing Spring tides because there was a full moon. Now however, Nassau is somewhere in between because there is a half moon. When it reaches a quarter, it will be experiencing Neap tides. 

Newton's 3rd Law

This youtube video on Newton's 3rd Law was really helpful for me to gain a better understanding of the concepts and ideas that we covered in class. Newton's 3rd Law states that "For every action, there is an equal and opposite reaction." The visual effects in this video were most helpful to me. Being able to actually see the action and reaction when the tennis ball hit the earth was really helpful. Every time we talk about Newton's 3rd Law, we have to remember that the earth does move when we put our own forces on it, it is just so marginal that we do not notice. Although, in this video, the ground would sink down when the ball hit it and rise up when the ball left it. The slight exaggeration helped me to gain a more confident understanding of Newton's 3rd Law. 

                                 Unit Summary Blog Post 

Part A)

In this unit I learned about …

Newton’s Second Law

Newton’s Second Law is easily stated as a= F/m. When you break this down, we can see that force is directly proportional to acceleration (F~a) which means that that when the force increases or decreases, acceleration does the same. The second part states that acceleration is inversely proportional to mass (a~1/m) which means that as the acceleration increases or decreases, the mass does the opposite. *Also, if you ever need to find the weight of an object, use the formula w=mg.

Example:

If one person is providing 100N of force to an object and the acceleration is 2m/s2, what is the new acceleration of your force increased to 200N?

a=F/m

2m/s2=100/m

m=50

a=200/50

a=4m/s2

Free Fall Straight Down (with no air resistance)

Free fall is when an object is falling through the air with no air resistance. This means that the only force working on the object is gravity. Gravity is technically equal to 9.8m/s2, but for simpler purposes we mainly used 10m/s2 in class. The acceleration of an object in free fall is always a constant 10m/s2. There are two formulas to calculate the vertical free fall of an object. The formula for calculating distance is d=1/2gt2 and the formula for calculating velocity is v=gt. Below is a podcast that Mark and I created to help us to understand free fall better.

Example: 

If I fell off of my balcony, and it took me 5 seconds to land in the pool below, how high was my balcony and how fast was I falling just before I hit the pool?

d=1/2gt2

d=1/2g(5)2

d=1/2g(25)

d=5(25)

d=125m

And if you were trying to calculate the velocity at which I was falling:

v=gt

v=10(5)

v=50m/s

Free Fall At an Angle (with no air resistance)

Free fall at an angle is very similar to regular free fall, except now we have a constant horizontal velocity. Free falling at an angle could be anything from a plane dropping a package below as it continues to fly, to a person running straight off of a cliff. *An important thing to keep in mind is that even when that package is released from the plane or the man finally reaches the edge of the cliff, the horizontal velocity does not change. Meaning that when the package hits the ground, it would still be directly below the plane regardless of where it was released.

Example:

You throw a ball off of a cliff that is 80m high with an initial horizontal velocity of 5m/s. Calculate the time that the ball spent in the air and how far away from the cliff it landed.

d=1/2gt2

80=1/210(t2)

80=5(t2)

80/5=t2

16=t2

t=4 seconds

What is the diagonal velocity (hypotenuse of the special right triangle)?

a2+b2=c2

(5)2+(10)2=c2

25+100=c2

square root of 125 = 11.18m

Throwing Things Straight Up (Free Fall)

When throwing an object straight up into the air (neglecting air resistance) we can be sure that the acceleration will always be 10m/s2. The object will have an initial velocity of whatever force you throw it up with and continues to decrease by 10m/s until the velocity reaches 0m/s and the ball is at the top of its path. Once the ball reaches the top of its path, it will begin to free fall back down. This portion of the free fall is no different from just dropping an object from the same height. 

Example: 

A ball is thrown straight up with an initial speed of 40m/s. How long does it take for the ball to reach the top of its path? = 4 seconds

How long is the ball in the air? = 8 seconds

How high was the ball at the top of its path? 

d=1/2gt2 

d=1/2g(4)2

d=5(16)

d=80m

How high was the ball at 2 seconds?

d=1/2gt2

d=1/2g(2)2

d=5(4)

d=20m

80-20

distance at 2 seconds= 60m

Throwing Things Up At An Angle 

When throwing things up at an angle (projectile motion) we must remember the two different sets of formulas.

Horizontal-

d=vt

v=d/t

Vertical-

d=1/2gt2

v=gt

Example:

A man throws a ball with an initial velocity of 100m/s, and the ball is in the air for 10 seconds. Using the 1, 1, 1√2 triangle, (there is also a 3,4,5 triangle) we can see that the actual velocity of the ball is 100√2, which = 141m/s. 

The veritcal distance of the ball-

d=1/2gt2

d=1/2g(10)2

d=5(100)

d=500m

The horizontal distance of the ball-

d=vt

d=100(10)

d=1000m

Falling Through Air WITH Air Resistance (Skydiving)

Finally, air resistance comes into play when we are talking about skydiving. When you jump out of a plane and begin to fall down to the earth, there are two forces to be aware of. Your downward force is called F-weight. As you fall, you are gaining speed, meaning that your your F-weight is increasing, even though your acceleration is decreasing. Since your speed is increasing downwards, this causes your upward force to increase as well. This upward force is called F-air. In the first stages of the fall, your F-weight is much greater than your F-air. Velocity is directly proportional to air resistance, resulting in the increase of F-air until you reach your first terminal velocity. At terminal velocity, your velocity is remaining constant while your acceleration is at 0m/s2.

Opening the parachute:

When you first open the parachute, your magnitude automatically increases in the upward direction. Although, as you continue to fall, your magnitude decreases in the upwards direction until your F-weight and F-air equal out again and you reach your second terminal velocity. This terminal velocity is similar to the first but it is much, much slower.

*Remember* that net force and acceleration are directly proportional to each other. Also, keep in mind that the forces of air resistance are equal and opposite to weight.

Part B)

This all connects to our everyday lives without us noticing. Tossing a ball to your friend during afternoon activities or even just accidentally dropping your phone are all actions that can be better understood with physics. Each of the examples I gave above were real life ways of looking at free fall and newton's second law. I hope that they help you to gain a less complex understanding of unit 2!

Physicist Reflection

1. What type of learner were you in this unit? What specific behaviours/actions led you to your selection?

- I came into this unit wanting to be a committed knower and I think that I unfortunately became more of a received knower. I was genuinely excited to learn more about physics, even though it came with the connotation of being difficult. When we began the unit with such simple and easy to understand ideas, I was tricked into thinking I understood all of it when in reality, I didn’t. I wasn’t able to be a committed knower and take my learning to the next level because I was trying hard to catch up and learn what I was having difficulty comprehending. 

2. What was the hardest thing for you to grasp? How did you overcome the challenge?

- The hardest concept for me to grasp was the idea that acceleration does not only mean speeding up and that it can also be slowing down or changing direction. Also, the idea of constant acceleration and velocity confused me for a while. I overcame this challenge by going over multiple practice problems and labs we did on acceleration and velocity. It was helpful for me to write out the problems from previous worksheets with no answers and solve them again. 

3.   How did you study throughout this unit? Did this work for you and/or do you want/need to adjust your techniques?

-Throughout this unit I did a lot of sample questions and quizzing myself with my own notes. I think it would have been much for helpful if I had spaced out my studying intervals. A lot of the time I would attempt to learn a lot of information in a short period of time, when I should have been doing small amounts each night. My study techniques did not work out for me as well as I would have liked for them to and I plan on making those adjustments for the next units. 

4.   How did you take advantage of the opportunities to learn during class? What about ou of class opportunities? 

- In class I took notes and tried my best to record answers and ideas that I thought may come up later in class or on a test. Outside of the classroom, like in labs and while I studied, I always tried my best to do so actively. If we were pulling a piece of paper out from a bottle, I tried to keep in mind why this is happening and how it relates to physics and my everyday life rather than just trying to complete the task. 

5.   How do you predict you did on the unit test? Were you able to demonstrate your understanding of the concepts on the test? What did you learn from taking the test that you want to remember for future units?

- I think that I did relatively okay on the unit test. I know that I could have done better, but I think that it is a fair and honest evaluation of my knowledge for this unit. The only thing that I think is unfair is that each multiple choice question was worth 3 points, so if I got 3 wrong I got something like a 60% on that section. I found this frustrating and wish each one had been worth only one point but I suppose this helped me learn that I should try to use all of these concepts in different situations to get a more well-rounded understand of them for future units. 

6. What did you learn from my feedback during this unit? What are you hoping to get better at in the next unit?

- I learned that Ms. Lawrence is not trying to trick us. She is trying to help us do well in her class and if we put in the effort, we will do well. So, for the next unit I am really aiming towards trying harder and putting more time into my homework and out of class studying. 

7. What did you get better at during this unit? What are you hoping to get better at in the next unit?

- I got better at using mathematical formulas and switching around what I am trying to solve for. In the next unit, I would like to get better at taking notes and actively participating in every class. 

8. What effort grade would you give yourself for your efforts during this unit? What specific behaviours are you basing this score on? 

- I think that I would give myself a 3 effort grade for this unit. I made an effort to understand everything, but I know that I could have done more. I think that I deserve a 3 because I came into conference period multiple times when I felt unsure about the previous night’s homework or when I felt like I hadn’t been paying enough attention to the class time. 

9. Is there anything else you would like me to know about your experience or approach to the class? What questions do you have at this time?

- The only thing I want to make sure that you know is that I know that I have the potential to do much better in this class and I am ready to be much more determined and focused on setting and reaching goals for myself. 

What Did I Learn In This Unit? 

In this unit I learned about inertia, Newton’s 1st Law, net force, equilibrium, velocity, acceleration, and how to graph the equation of a straight line. At first glance this may seem like a lot of confusing concepts although, if they are all fully explained, they are very easy to comprehend. I will give a brief summary of each topic.

• Inertia: Inertia is properly defined as, “a tendency to do nothing or to remain unchanged”. An example of this is if you are trying to re-arrange the furniture in your room. It can be extremely difficult to get your desk from one side of the room to the other because it wants to remain unchanged and continue to do nothing. This is inertia.

• Newton’s 1st Law: Newton’s 1st Law states that, “things want to keep doing what they are already doing.” This law actually has a direct connection to inertia. Now we have realised that things do not only want to continue doing nothing, they also do not want to stop doing something once they begin. And example of this is kicking a rock. It may take some effort at first but once it begins to move, the rock will only stop eventually because of an outside force such as air, the ground, or an obstacle. 

• Net force: Net force is the total force placed on an object. Net force is measured in Newtons (N). Do not get confused with net force and mass. Mass is a measure of inertia which is measured in kg. If a man is pushing a box to the right with a force of 5N to the right, and a woman is pushing the same box with a force of 6N to the left, the net force on the box ends up being 1N.

• Equilibrium: Equilibrium is the point in which opposing forces become balanced. Take the same box as in the previous example. If the mad continues to push the box with 5N of force, and the woman now also pushes the box with 5N of force, the net force on the box will be 0N, creating equilibrium. When an object is at equilibrium it can either be moving at a constant rate, or remain in the same place.

• Velocity: Velocity is the rate at which an object is moving. For my podcast I actually explained velocity in less than 3 minutes. I think that Alexander da’ Costa and I did a pretty good job summarising velocity there. You can watch out video below . 

• Acceleration: Acceleration can be any of three things. Speeding up, slowing down, or changing direction. This can be very confusing as acceleration has always been grouped with the increase of speed, however that is not the case. The formula for acceleration is a=∆v/t (change in velocity / time). There are two more formulas that we are using for constant acceleration. These are the how fast equation which is v=at and the how far equation which is d=1/2at². If you remember these three formulas, calculating acceleration and other things based off of constant acceleration becomes very simple. 

• Graphing the equation of a straight line: Graphing an equation was one of the hardest things for me to do in this unit but now, I think I finally understand it. It is easiest for me if I look at the equation of the line in words/symbols instead of solely numbers.

An example of this would be 

y=4x + .002

If we put this into words we get 

Distance=.002(time²) 

A sample problem : A car increased its speed from 10m/s to 40m/s over 10 seconds...

What was the acceleration of the car?: 
a=∆v/t

a=30/10
a=3m/s²

If the car continues to accelerate at this rate, how fast would it be going after 10 seconds?:

v=at

v=3(10)
v=30m/s

If the car continues to accelerate at this rate, how far would it be after 10 seconds?:
d=1/2a(t²)
d=1/2(3)(10²)
d=1/2(1.5)(100)
d=1/2(150)
d=75m

Overall, every concept we learned in this unit is extremely relevant and important to our everyday lives. Think about it, almost everyone gets into a car on a daily basis (unless you are a boarder at Asheville School) but excluding us, a car is a daily mean of transportation. Understanding Newton's First Law and Inertia would have been really helpful in the beginnings of construction and manual labor. On the very first day of class, Ms. Lawrence told us that we would not be learning anything this year that was not 100% relevant to our lives, and she has kept that promise so far.