Tides

If you've ever been to the beach, I'm sure you've noticed how the water is high up on the shore at some parts of the day and it is very low at other points of the day. These are called high and low tides and they are caused by the moon and the sun and their position in relation to the Earth. Force is inversely proportional to distance squared, so the closer the moon is to a point on the Earth, the stronger the force between them will be. Likewise, with different points of water on the Earth, closer blobs of water to the moon will have a greater force on them than blobs of water on the other side of the Earth. This causes a bulge in the Earth's water; it has an ovular shape which allows for high tides to occur twice a day and low tides to occur twice a day across the globe, happening on opposite ends of the world at the same time. At different times of the year, the position of the moon in relation to the sun causes what are called spring tides (very high high-tides and very low low-tides) or neap tides (tides that are not as great in difference). Although I just gave a very brief summary of this relationship, the video below explains it quite well. Adam Hart-Davis uses food to demonstrate the moon's movement, the Earth's movement, and their effect on the Earth's tides. The visuals are very helpful. He could have included more detail about the process but I think this video gives a very good, simple explanation of tides.

Unit 2 Blog Summary

Part A: What I Learned

In this unit, I learned about Newton's 2nd Law, skydiving, free fall, throwing objects straight up, throwing objects up at an angle, and falling at an angle.

Newton's 2nd law states that  acceleration is directly proportional to force and inversely proportional to mass. We completed a lab to demonstrate this relationship. In conclusion, we found that as mass increases, acceleration will decrease, and if force increases, acceleration will increase in the same ratio.
You can write Newton's 2nd law using symbols...
a~F
a~ 1/m
or as an equation....
acceleration= net force/ mass
a= f(net)/m
An object's weight can be the force acting on the object. Weight is equal to the mass of an object times gravity (w=mg). If you know the mass of an object, you can find the weight or force on the object as gravity is always 9.8 m/s^2 (or 10m/s^2 for simple calculations).

Above is an illustration of the experiment we performed in the lab, including labels of acceleration and force. If you add mass into the picture, depending on where it is placed (on the hanging weight or the cart), either the force and acceleration will increase or they will both decrease.

When you go skydiving, air resistance plays a large role in your fall through the air. As you fall, your speed increases which in turn causes your air resistance to increase. Conversely, as your speed decreases, your air resistance decreases as well. Air resistance is affected by two things: speed, and surface area.

To start at the beginning, when you first step out of a plane, your velocity is at 0m/s, which is its lowest point during the entire fall. In this same moment, acceleration and net force are at their highest points of the fall. This is because at t=0 seconds, you have not yet begun moving at speed, thus you have no velocity. However, your acceleration will decrease as you build up more air resistance. Keep in mind, you are still falling faster and faster (velocity increases), but you are gaining speed at a decreasing rate (acceleration decreases). Your net force is at its highest point at t=0 seconds as well, not only because acceleration is directly proportional to force, but also because your air resistance builds up to equal your weight (aka the force of gravity which is pulling you down). When you have no air resistance, your weight is the only force acting on your body. As the opposing force of air resistance builds, the net force decreases until it reaches 0 Newtons (the point when air resistance = your f weight). This point when the two forces are equal is also the time in your fall when your velocity has reached the fastest it can possibly be- this is called terminal velocity. When you are in terminal velocity, f net = 0, velocity is constant, and acceleration = 0 m/s^2. It is a total reversal from t=0s because velocity is at its highest point in terminal velocity while acceleration and net force are at their lowest points.

So that covers the falling part. But to skydive, there comes a point when you need a parachute. If you fell without a parachute, hitting the ground at terminal velocity would be very painful! 

When you are falling and have reached terminal velocity, this is the point when you open your parachute. Immediately, your surface area is increased by the chute which increases the air resistance. The air resistance will be greater than the force of your weight, and since it is a force pulling you in the upward direction, your acceleration will be upward. This also causes the net force to be negative (it will no longer equal zero; at this point you are no longer in terminal velocity). As you slow down again and air resistance decreases, you reach a second terminal velocity. In this second terminal velocity, the acceleration and net force are both 0 again (equal to the first terminal velocity) and the air resistance will also be equal to the air resistance in the first terminal velocity as it has to equal the force of your weight for the net force to equal zero. The only thing that is different in the second terminal velocity is the velocity itself- it will still be constant but it will be much slower and safer in the second terminal velocity. From here you safely fall to the ground and the parachute has done its job.

When you fall straight down in free fall, another concept I learned in this unit, this means you are falling without any forces acting on you except for gravity. When you skydive, you are not in free fall. One cool thing about free fall is that mass does not matter. If you dropped a coin and a feather at the same time in a vacuum without air resistance, they would hit the bottom at the same time. This is because the only force acting on the objects is the force of gravity which is determined by an object's weight. You might be thinking, "I thought weight didn't matter?" You're wrong. Mass and weight are not the same thing. Weight is the mass of an object times gravity (w=mg). So, if you are finding the acceleration of an object, you use a=f net / mass; in free fall the f net = weight, so you can change the equation to say a= mg/m (acceleration is equal to mass times gravity divided by mass). Mass divided by itself equals one, so you can cancel out the m's. This leaves the equation as a=g (acceleration = gravity = 9.8m/s^2). So no matter what the mass of an object is, when an object is in free fall, it will always have the same acceleration. Here is a video to demonstrate:

You can use the distance equation (d=1/2gt^2) to find how far an object fell in free fall, substituting gravity for acceleration. You can also use V=gt to find how fast the object was moving when it hit the ground.

In free fall, you can (obviously) fall straight down, But you can also throw things up.

The picture above illustrates the path a ball will take. In reality, it would fall straight up and straight down, but for the sake of the drawing, the ball is shown a little displaced from this path. As the ball travels upward, it is propelled by the initial velocity with which it is thrown while gravity is acting on the ball in the opposite direction (down), causing it to slow down as it reaches the top of its path. Since the ball is in free fall, its acceleration is 10 m/s^2 during the entire time in the air. In this particular drawing, the ball is thrown up with an initial velocity of 30 m/s and its speed decreases by 10m/s each second it falls up. When the ball is at the top of its path, it has a velocity of 0m/s, but the acceleration of the ball will still be 10m/s^2. The ball then falls back toward the earth with an increasing velocity because velocity and gravity will be in the same direction again.
Just from this picture you can tell a lot about the situation. You know the balls initial velocity as well as its velocity at each point along its journey. You know the hang time of the ball (total time in the air) is 6 seconds. To find how high the ball got, you can use the distance formula. However, this formula does not account for velocity in the upward direction, so you can only plug in values from the ball's downward fall. For example:
d=(1/2)gt^2
=(1/2) (10) (3)^2
= 1/2 (90)
d= 45 m
To find how far the ball is from the ground at any given second of the fall, you would use the value found for the total distance as shown just above. Then you would count the number of seconds from the top of the path down to the second you are finding the distance for and use that number of seconds as the t value in the distance formula. Once a distance is found, subtract it from the total distance and you will have the distance from the ground at that second.

After I learned about falling in free fall and throwing things straight up in free fall, I learned about things falling at an angle in free fall and things being thrown up at an angle in free fall.

When an object falls at an angle, the vertical acceleration is constant (9.8m/s^2) and the horizontal velocity is constant (the initial velocity the object is thrown with is the velocity that the object will have in the horizontal direction for the entire fall). The vertical velocity continues to increase as the object falls, so the path it takes to the ground will be curved, or parabolic. To find the vertical distance you can use the same distance equation we are familiar with (d=(1/2)gt^2) and you can use v=gt to find the vertical velocity at a given second. You could use either of these equations to find the time of the object's fall. The time the object falls is the same vertically and horizontally; t is one variable that will remain the same in any equations for vertical or horizontal values, besides g. The time of the object's fall is determined by the vertical distance, or the height from which the object falls, which is why the distance formula is so useful and is only used for vertical values. To find the horizontal distance, velocity, or the time of the fall, we can use the equation v=d/t. Problems like this can be applied to an object being dropped from a plane or something being thrown off a cliff. 
It is also important to note that we use the vertical and horizontal velocities in our equations but we do not use the actual velocity of the object.
To find the actual velocity, we must know the vertical and horizontal velocities. When they are put together they make two sides of a box, through which a vector can be drawn diagonally to show the actual velocity of the object. In my physics class, we use either a 45 degree angle or a 3, 4, 5 triangle to find this value. The picture below is an example of how this is drawn. 

We use this triangle system to find the actual velocity for objects thrown up at an angle as well. An example of this would be hitting a home-run in a baseball game. To find the horizontal velocity and distance, we again use the v=d/t equation. For vertical distance and velocity in this situation, we use d=1/2gt^2 and v=gt because these objects are still in free fall. We treat the vertical equations that use g in the same way we treat them in problems of objects being thrown straight up. They can only be used with values from the fall downward. The vertical height determines the hang time of the ball so these equations are really useful. If the vertical velocity of the object was 1m/s and the horizontal velocity was 1m/s, the actual velocity would be 1.41 (the square root of 2) at a 45 degree angle. If both velocities were 10m/s, the actual velocity would be 14.1 m/s, and if they were 100m/s, the actual velocity would be 141 m/s.
When an object is thrown up at an angle, vertical velocity decreases on the way up- at its highest point, the object has a vertical velocity of 0m/s. The horizontal velocity, however, is constant. If an object is thrown with a horizontal velocity of 10 m/s, it will still move horizontally at 10m/s at the top of its path when the vertical velocity is 0m/s. Since it keeps moving horizontally, it has a curved path. On the fall back to the ground, the vertical velocity will increase at a constant acceleration of 10m/s^2.


What I found difficult about this unit was the concept of skydiving with air resistance. At first, I just couldn't wrap my mind around the fact that you speed up so you have more air resistance and then once you open your parachute your air resistance will increase, but as speed decreases the air resistance decreases as well. After some practice and looking at tons of examples and diagrams, it makes a lot more sense now. The transition to falling with air resistance to falling in free fall was weird at first because I kept expecting the objects to reach a terminal velocity but I think I have gotten the hang of that concept now, too. Again, I made the lightbulb click with visual examples and just really breaking the concept down.


This unit, I think I had more effort in class but I could have put more effort into my work outside of class. I need to make more time for myself to not only get my work done but also to do it well. I do think, conversely, that the time I put into doing problems paid off. I always took the time to finish the problems and think through them which really helped me to be active and present in class. When we went over concepts and certain problems in class, I had already spent a lot of time on them and mostly understood them in my own way, so it was nice to be able to use class as a solidifier. I am getting to be very confident in physics- I feel like I really understand what is going on and I do not question everything I do. This comes from making sure I understand everything on my own time and then moving on in class, adding onto the information learned.


My goals for the next unit are to spend more time on my work outside of class and to finish my podcast early. I have found that the podcast gets really stressful when I have other work to do and my group starts finding less and less time to meet. Hopefully we can utilize the preceding weekend more efficiently int he next unit. I also want to have a very deep, holistic knowledge of the next unit. I think it would be a very bad time to start only half processing the information and I want to keep working hard all semester (all year, too, but I am thinking short-term until winter break).



Part B: Connections

I can connect this unit to soccer. I play right back, and one of my best assets in the game is my ability to clear the ball. This is similar to throwing things up at an angle; I use my foot to lift the ball and kick it across the field, in an arc through the air. I had usually just focused on my form for this, making sure I transferred my body weight over the ball and followed through my kick with my leg and foot pointed. I would love to find the actual velocity necessary to get the ball where I want it to be and then use this to find the horizontal velocity I need to swing my leg with to get this kind of power. I know that I will now start trying to kick the ball at a 45 degree angle to see if that gives it a smoother arc at all. It would also be really interesting to feel what different velocities feel like. For example, how hard will I need to swing my leg to hit a ball at 30m/s? And how will this feel on my leg? Is this an easy velocity to reach or would I need to really kick with power?

My group this unit made a podcast about things falling at an angle.


I can't wait to learn the next unit! Yay physics!

Freefall

I think we're all familiar with Tom Petty's song, "Free Fallin'," but we usually don't think of freefall as a physics concept. Free fall occurs when an object falls due to the effect of gravity only. When in free fall, an object has a constant acceleration of 10 m/s per second (which is the force of gravity). In free fall, there is no air resistance and weight does not matter. The video below explains free fall pretty thoroughly, including the example of Felix Baumgartner who set the world record for the longest free fall.

I think that video explains the concept of free fall really well, but I am including this second video which is a demonstration of free fall- the experiment is conducted with a feather and a coin in a vacuum. My physics teacher conducted this experiment in class and I was really excited to find an easy-to-follow video of the same experiment.



I hope this clears up free fall for you!

Newton's 2nd Law of Motion

In this video, Newton's 2nd Law of Motion is demonstrated in several different ways; first the video shows the effects of mass on acceleration in space as compared to on Earth. Several different examples follow this as the video moves on to explain the effects of force on acceleration, specifically the force of friction.
I think it is super cool how Newton's 2nd Law is shown in space and it is helpful as we can take gravity out of the equation and just focus on the relationship between force, acceleration, and mass. According to Newton's 2nd Law, acceleration is directly proportional to force and inversely proportional to mass. This means that acceleration will increase as force increase, while it will decrease when the mass of the object increases.
The relationship between mass and acceleration is very clearly demonstrated in the first part of the video. I think the later parts of this video are less clear in their explanation of force in relation to acceleration. However, this is still a helpful and unique resource. I hope this broadens your understanding of Newton's 2nd Law! Enjoy!

Unit 1 Reflection

In this unit, I learned about many concepts of physics. 

I learned about Newton's 1st Law, which states that an object in motion tends to stay in motion, while an object at rest will stay at rest, unless acted upon by an outside force. Inertia, or the "laziness" of an object, is the property of an object to follow Newton's 1st Law. The more mass an object has, the more inertia it has.(You can even describe mass as a measure of inertia). Applying the concept of inertia and Newton's Law to everyday life: if a table is set with dishes and such, and the tablecloth is pulled out from underneath the settings, the dishes will remain on the table. This is because both the tablecloth and the place settings are at rest. When you pull the tablecloth, you are exerting force on it which causes it to no longer be at rest. The dishes, however, have not been acted upon by an outside force. Thus, in accordance with Newton's 1st Law, the table settings will remain at rest; the tablecloth is pulled cleanly from the table while the dishes remain in their original spots.

I just mentioned force and how they can change an object's motion. Force, measured in Newtons, is defined as a push or a pull- a pretty broad definition if you ask me. To make things simpler for discussion's sake, we measure the net force of objects. Net Force is the total force acting on an object. 
For example, in the drawing below, a box is being pushed with a force of 50 Newtons. Assuming there are no other forces acting on the box at this moment, the box would have a net force of 50N.

However, in the next image, two opposing forces are pushing on the box. The force from the left is pushing with 100N, while the force from the right is pushing with 50N. As these are opposing forces, you must subtract them to find the net force. 100-50=50, so the net force= 50N.

If these opposing forces were equal to each other, the box would be at equilibrium. Equilibrium occurs anytime the net force adds up to 0 Newtons. It occurs when an object is 1) moving at constant velocity or 2) at rest.

This brings me to the next lesson: velocity. Many people think of velocity as the speed of an object. This is only partially accurate. While "speed" describes how fast an object is moving, "velocity" describes the speed of an object, as well as the direction in which the object is moving. The equation of velocity is: V = d/t (Velocity is equal to distance over time). Velocity is measure in meters per second (m/s) and measures the distance covered in a certain amount of time, as shown by the equation.
If the direction of movement changes, the velocity changes. Thus to be moving at constant velocity, an object must maintain both constant speed and direction. An object is moving at constant velocity when it is at equilibrium (or at rest).

A common mistake is confusing velocity to be the same thing as acceleration. Acceleration describes the rate at which an object is changing speed. Its equation is: A= change in velocity/time interval. Acceleration is measured in meters per seconds squared (m/s^2). For an object to be accelerating, it needs to experience a change in velocity, which can occur one of three ways: 1) changing direction, 2) speeding up, or 3) slowing down. Acceleration can be increasing, decreasing, or constant, depending on the surface upon which the object is moving. If an object has constant acceleration, it cannot simultaneously have constant velocity. An object falling straight down will always have an acceleration of 10 m/s^2, meaning the object increases its speed by 10 m/s per each second.


To calculate how fast an object is moving, you can use the equation: V= at, which shows that velocity is equal to acceleration times time. 

To calculate how far an object has moved, use the equation: d= 1/2at^2, which indicates that the distance an object has traveled is equal to one half of the object's acceleration multiplied by the time it has been moving, squared. Both of these equations describe a relationship between acceleration and velocity, as do the three charts shown below.

The final lesson of the unit was about graphs and applying their equations to physics. The equation of a straight line is y= mx + b. This line, when graphed with time (squared) on the x-axis and distance on the y-axis, can be translated into the equation for distance (d= 1/2at^2). The slope (m) would stand for ½ acceleration, x would correlate with time, and the b is irrelevant from here on out. Using that information, you can visually represent data of an object’s distance traveled by graphing it. Also, you can translate this equation into the “how fast” equation. Since m= ½ a, to find a (in V = at), you would multiply whatever value you’ve found for m by 2. You already would know the value for time, so you could then use the information from the graph to find not only the distance traveled by an object in a specified amount of time, but also how fast the object traveled this distance.

What I found difficult about what I have studied is connecting the topics of acceleration and velocity and then translating this connection into graph-able data. At first I was so determined to understand the difference between acceleration and velocity that I compartmentalized the two concepts in my mind. Really, they cannot be completely separated if you want to fully understand each concept. I overcame this by working out different problems using the equations involving velocity and acceleration and studying over the explanations of each. The light bulb really clicked when I could put into words that “velocity measures the direction and speed of an object and acceleration measures how fast the speed of said object is changing; acceleration is defined as the change in velocity over a given time.” This really makes sense to me, as both concepts involve speed and can be linked in that way. Also, the graphs we worked with this unit were very intimidating to me at first glance. I am not the most computer savvy person and often find myself completely overwhelmed by tasks involving Excel. These graphs, however, made more sense as our class got more comfortable working with them. It helps that I have been working with plotting data on a graph in my math classes for several years now. Going over the correlation between the equations for the graph and the corresponding physics equations clarified the entire process for me; now I understand why I am putting which value on which axis.

I started this unit off very strong, in my opinion. I took detailed notes and gave myself ample time to complete each assignment with full understanding of the material. As my workload increased, this diligence lost some of its initial luster. I continued to work hard though; my homework has consistently been completed on time (save for one instance in which I had only 30 minutes of study hall along with a packed Thursday night schedule), my lab work done with care and elaboration, and blog postings finished promptly and with extensive explanation. Over the course of the year I hope to become more creative in my work and less “cut and dry.” This is definitely an area with room for improvement. My confidence in physics has grown so much already and I enjoy being able to discuss a concept with self-assurance. Not only do I understand the concepts but I am able to apply the concepts to examples we are given in class, etc. When it comes to solving different problems, my skills are varied. I consider writing to be my strongest asset in school. Thus, short answer problems are very easy for me as I find them logical; when I can write out the process it makes more sense. However, the shorter math problems that involve a conceptual formula make sense to me as well and I think I am generally rather good at these. I have a lot of trouble when it comes to “problem solving” questions in which harder math is needed as well as the application of several concepts at once. This is something I need to work on and would like to get better at as these types of questions will show up in my future math and science courses.

My goal for the next unit is to study more frequently by redoing problems I do not understand or have gotten wrong in the past, as well as doing harder level problems of concepts I do understand just to challenge myself and make sure I have taken my knowledge to the next level. I also have a goal to come to conference period at least once a week in the future as a way to make sure I have all my questions answered and every point is clarified. I think these extra steps will boost my grade as well as my confidence in the material.

In the fall, I run cross-country. I love running and spend a lot of my time outside of the season running and learning about the sport. Physics relates to running; I have thought about my acceleration time and time again as I tackle large hills or sprint down the final stretch of track. I enjoy playing soccer just as much, if not more, than I enjoy running. It is not soccer season yet, but 90% of the time soccer is on my mind in one way or another. Going over physics concepts has made me reflect on my game a lot in the past few weeks. For example, the force with which I kick a ball will need to be greater than the force of friction from the field or the air resistance the ball will meet if I were to chip it through the air. Additionally, the velocity with which I kick the ball will influence how far the ball travels and how fast it does so. I cannot wait until soccer season so I can apply these new concepts out on the field. I am also very excited to learn more about the physics involved sports (mostly soccer, but other sports as well, like running, football, and tennis) and why they work the way they do. Who knew athletics and science worked together so well?!

Below is a podcast I made with  group about making graphs and how to use them efficiently. Enjoy!

Speed, Distance, and Time: Experimenting With Acceleration And Velocity

Constant velocity occurs when an object is moving at the same speed and in the same direction; constant acceleration occurs when an object is changing speed at a constant rate. If an object is traveling at an increasing acceleration, its velocity will increase as well. Likewise, if that object is traveling at a decreasing acceleration, its velocity will also be decreasing. An object, however, cannot have both constant acceleration and constant velocity at the same time.

Along with two other members of a group, I conducted a lab experiment about constant acceleration and velocity. In this lab, we rolled a marble across a tabletop and marked the distance it traveled every 0.5 seconds using chalk. We consistently measured this amount of time using a metronome.  We used a flat surface to measure constant velocity, whereas we created a ramp to measure constant acceleration.  The purpose of this lab was to demonstrate the difference between constant velocity and constant acceleration as well as to support our lessons on these traits with data we found ourselves. Our intent was to collect data that we could present as concrete information on a graph.

The markings of the marble’s progressive movements at a constant velocity were equidistant from each other, as expected for an object, which, by definition, is theoretically covering the same amount of distance in a set time interval. Conversely, the markings we made to measure the progress of the marble moving with a constant acceleration grew increasingly further apart from each other as the marble’s journey continued. This is due to the fact that and object moving with a constant acceleration will continue to gain speed at a set rate until its acceleration changes due to the slope of the surface upon which the object moves or until it is acted upon by an outside force. We measured the distance from the starting line of the marble’s trek to each line (each of which were marked 0.5 seconds after the last) and used this information to create x and y points so we could graph our data.

The formula used for constant velocity is V=d/t (velocity is equal to distance over time) and the formula for constant acceleration is d=(1/2)at^2 (distance equals one half of acceleration times time squared).

The graphed line of constant velocity was a straight line whereas constant acceleration formed a slight curve along the graph (we graphed it as a straight line for viewing purposes although the points graphed did not exactly match up with the trend line). The graphs were used to support our data by visually demonstrating the relationship between distance and time in the equations for constant velocity and acceleration. In the velocity graph, distance was shown as values on the y-axis while time was shown along the x-axis. As time increased, distance followed suit, demonstrating a consistently straight line on the graph; this displayed the marble’s constant velocity. In the graph of the marble’s acceleration, distance was again on the y-axis, but the x-axis showed values of time squared as opposed to time. Again, each of these values increased contiguously to show that constant acceleration depended on distance covered in increasingly fast time increments. These graphs supported out demonstrations of the concepts as well as our data collected.

This lab was informative in several ways. I realized in the process of marking of the marble’s movement that more often than not an experiment will need to be repeated for accurate results; in the future I will be prepared for a lab to require time. Things do not always work perfectly on the first try. In future labs I will repeat the careful notation of equations and units as it helped me immensely in my calculations during this experiment. And lastly, I learned from this lab that the experiments we conduct are not simply arbitrary activities- they do in fact relate to our studies of physics and I should work harder in the future to apply my knowledge to the lab as I am conducting the experiment.

Velocity and Acceleration

Acceleration: Calculating the acceleration of a Porshe


The video I posted above is an explanation of acceleration kindly provided by Khan Academy. Acceleration is the change in velocity over a given time interval; or you could say that acceleration is  how fast an object is changing speed. Acceleration is measured in units of meters per second squared (m/s^2). This video really goes through the steps of how to calculate the acceleration of an object and I think it is a great resource to clear up any confusion about acceleration. It is especially helpful to be able to see the instructor writing out his work on the problem with his explanation matched up in the background; this makes it easy to follow along.



After that explanation of acceleration you may be wondering, what is velocity anyway? Velocity is both the speed and the direction of an object. Velocity is measured in units of meters per second (m/s). Constant velocity can only be achieved if an object is moving at the same speed as well as moving in the same direction; for example, a runner sprinting at the same speed in a straight line would be moving at a constant velocity. The second video I have included is less serious; it is an animated little jingle about the difference between speed and velocity. While velocity measures both an object's speed and direction, speed only measures how fast something is going. I think this video showed a lot of cute examples of objects moving with constant or changing speed and velocity and presented it in a fun manner.

So, just a quick recap:

• velocity (not to be confused with speed) is an object's speed and direction 
• acceleration is the change in an object's velocity over time