Alison's Blog

Formula Confusion

bulkleya — Mon, 15 Feb 2010 18:39:28 +0000

As we venture further into the study of collisions, I am trying to tie everything together as much as possible before the end of the trimester. From the very beginning of projectile motion study to the current studies of collisions, physics of sports has been quite the adventure and most certainly a very interesting, enlightening class.

Recently we are trying to wrap up collision lab 2. In collision lab 2, we essentially push a red and blue car together gently with ideal circumstances and tried to see a pattern that it was creating. Then as we learned of the standard pattern, we put on weights on the different cars to try and compare the pattern to other circumstances.

Trying to reach a formula already known, my group and I tried to see where the formula “m1v1+m2v2=(m1+m2)(v1+v2) > (momentum 1+ momentum 2)/ (m1+m2) originated from with the data we collected from collision lab 2. With our masses, velocities, and changes in impulse and momentum, we tried to fit numbers together to see what made sense and what could be logically connected to the formula previously stated above.

What we did notice is as mass increases, momentum increases. The blue car velocity always was constant before, regardless of mass difference. The change in both of the red and blue cars velocities fluctuated, which frustrated us. We tried to understand as to what exactly was going on, but our data was not giving us any helpful hints.

Looking at the data now, I am trying to understand the patterns in a different environment and still cannot come up with a definite answer. Though, the formula works with the data we are given: I am just not sure as to how we can come up with that formula based off of the data we found. Because all of these labs will have different data (human error, ways of execution, etc.) I think that it will be difficult to try and see a pattern with such a various array of numbers.

Hopefully by the end of this week we can discover the real meaning as to what is going on here.

Impulse, Momentum, and Collisions

bulkleya — Tue, 02 Feb 2010 20:17:22 +0000

Momentum is the inertia- (I remember that word from a previous chapter… it means the inability to move)- of motion. The mass of an object DOES matter! Mass of that object times its velocity will indeed get you momentum. The larger amount of momentum, the larger the mass or speed… or both! If momentum changes, velocity or mass changed. How LONG an object is having force applied is quite important- a continual force is accelerating, yet once released in an ideal world, the velocity will be constant. But in the real world, the object will slow down due to friction and internal energy.

What’s up with impulse? An impulse is HOW LONG THE CHANGE OCCURS. Impulse is force multiplied by the change in time. Impact of an object is different than the impulse of an object. The longer the impact time reduces the force of the impact and decreases the resulting deceleration. Impact force= impact time. F0r example, if you drop an object on different surface areas the impact will react differently onto which the surface it has dropped. If I drop a glass ball on carpet, the impact will be far less than if I drop that same glass ball on concrete. The impulses are always greater when the object is bouncing.

In class today we learned that speed and velocity cannot be used interchangeably within a discussion. Within our collision lab (when two objects interact strongly but briefly). In our collision lab we are focusing on velocity only and are learning about impulse which I previously mentioned. We discussed how momentum and impulse were related and derived an equation that related to the mass and velocity at which the cart was traveling. Impulse is the change in momentum and what we will be looking at in the next few days is the conservation of momentum just like energy can also be conserved. The collision lab made me realize that the slope of the line in which I plotted from our class data that one (its linear, so that means there is a direct relationship between change in time and force) and two is it quite close to the mass of the cart. The reason it is not exact is that there is always the chance for human error or that the was a spring on the cart. Lastly, within the force vs. change in time graph the displacement underneath our trend line is the impulse which, as I mentioned before, clearly relates to momentum.

Slowly but surely…

bulkleya — Wed, 27 Jan 2010 01:50:38 +0000

Monday and Tuesday during class, we discussed the answers to my questions that I asked in my previous post. Monday tied most of what I was confused about together, this mainly being…

You need to put the correct units into your equations and the correct axis titles on each axis!

Adding the R-squared value onto your graph will give you a more accurate representation on what trend line exactly fits your specific graph.

The lower the slope, the greater the stiffness of the spring. The higher the slope, the lesser the stiffness of the spring.

Energy that is put into certain objects and exerted from those objects are moved into the gravitational field- from mass to the spring, for example. That’s also where the energy comes from- gravity.

The way that energy of the spring relates to the change of the length of the spring is by the following equation: 1/2 K (constant) x (change in length) squared

So, we had to graph ENERGY versus CHANGE IN STRETCH OF SPRING. This would tell us what was up with this relationship- and it turns out that it was growing. The longer the change in stretch, the more energy the spring has. It exhibits a power relationship. Our specific spring had a constant of .3179x to the 1.8064. This means that our spring exhibited a constant of the previous- and if we really needed to, we could see as to how much energy was being exerted within a certain length of the spring!

Today, we learned another equation for kinetic energy… 1/2 mass times velocity (speed) squared. This makes sense because KINETIC energy is energy capable of movement… capable of doing work. Therefore, MASS must have something to do with the way kinetic energy is calculated- a feather and brick are going to have different kinetic energies… they cannot possibly be the same because the brick is far more heavy than the feather. As for velocity (speed), this also must be factored into kinetic energy- it is the energy of movement.

We also talked about, in terms of work and kinetic energy, that…

If someone was carrying a ton of bricks at one height, it would not, in the terms of physics, be considered work.

If I drop a pencil, the point where it exhibits the highest amount of kinetic energy is at the point where it barely touches the floor (because this is at the point where the pencil is at it’s fastest). At this same point in time, the pencil has the smallest amount of potential energy. Yet the millisecond it hits the floor, the roles quickly reverse.

Energy Labs and Exploration of New Material

bulkleya — Sun, 24 Jan 2010 19:41:52 +0000

This week we focused our studies on energy. Some questions I initially had were:

1. What forms of kinetic energy are there? In which I got the general response of thermal energy (and sound energy, however this energy is quickly transformed into heat, thus making the overall energy categorized into thermal). This is also in response to the question Where does energy go?- which we concluded was into forms of heat and sound, or in a broader aspect, into the gravitational field. Energy, however, cannot be recycled, so we must have a constant input into the initial source of where energy comes from.

2. How can we represent energy on paper? We learned how to represent and track an object’s energy path by pie charts of energy- each step having a different chart to represent the stage it is at.

3. What formulas or relationships can we conclude from energy? Our main equation that we derived this week was (change of energy)=(mass)(gravity)(change in height.) This represents the amount of energy travelled into the gravitational field.

A Summary of Energy Labs:

1. Energy Lab 1 allowed us to explore the relationship between height and the energy of the spring within the car. How high did the car travel based off of different degree measures of the ramp? We learned that the car travelled the same height due to the fact that the energy remained constant and did not change.

2. Energy Lab 2 allowed us to measure how much force we needed to put into reaching the height that we concluded from Lab 1, and then see how long that distance was and what the relationship was between force and distance. We learned that the relationship is demonstrated within the exponential decay: the longer the distance (the elongated version of the ramp) to match the initial height, the lesser the force. The shorter the distance (the steeper the ramp), the greater the force.

3. Energy Lab 3 measured the stretch of the spring and force exerted based off of different weights. From there, we did Energy Lab 4, in which we measured the initial drop and stretch of the spring. What were the two relationships? When we graphed this, we saw a linear pattern. These two variables are directly related.

Yet, we have not quite discussed exactly what the relationship is between these two variables, so it is hard for me to fully understand and piece all of this together. What I do understand is that if there is a constant, our rules will be followed in an ideal world- for example, the energy of the spring was constant, so the height did not change in the first lab. In the second lab, we discovered that with the greater the angle (lesser the distance to match the height we learned of in the first lab), there will be more force. But with lesser the angle, there will be lesser force but a great distance. This definitely makes sense to me. In the third lab, we learned of the linear relationship with force versus stretch, and finally in the fourth the direct and linear relationship with change in stretch and weight.

Now my questions mainly are,

What does this all mean exactly? How can we make these bits of knowledge into a coherent, logical understanding? What are the relationships between all of these variables, and how can they affect one another in certain circumstances? Hopefully I will discover these answers by the end of this week!

Why use a ramp when moving?

bulkleya — Tue, 12 Jan 2010 01:09:59 +0000

Using a ramp allows you to lessen your amount of force over a particular amount of distance. Instead of lifting the heavy object and placing it in the truck, the ramp allows you to exert less force over a greater amount of distance. Like running, although the faster runner with the longer strides will cover more distance in a certain amount of time, the slower runner will be able to conserve more energy and, in the long run, will cover a greater amount of distance. The same concept applies to the usage of the ramp. Although the ramp may take “longer” to put an object inside the truck, the ramp will alleviate the pain of lifting and placing. With gravity, the object is fighting back to be placed back onto the ground. With the ramp, you and gravity can work together to accomplish the task with lesser force, hence, giving you an advantage to conserve energy.

11.5-11.7 Response

bulkleya — Fri, 08 Jan 2010 01:07:49 +0000

How is rotational motion similar to and different from linear motion? What is the rotational analogue to mass, and why?

Rotational motion, by definition. is the act of around turning, spinning, or orbiting an axis or center. In contrast, linear motion is straight and direct motion.

Similarities: Rotational motion and linear motion are both positive directions… you cannot move in a negative direction when in the act of any sort of motion. In Mechanics I, we learned about the displacement of an object, which both of these motions exhibit. We also can use the concept of velocity to decide exactly how we can measure these types of motion. We also can use acceleration and deceleration to see how quickly the change occurs.

Differences: Obviously these types of motion move in a different direction. While one rotates, the other strictly travels in a direct, straight path.

The rotational analogue to mass is inertia and torque, or a twisting force that tends to cause rotation. The reason is that gravity pulls the object to the center of the earth, creating a path that allows the object to have rotational movement. Inertia is an objects inability to move unless some force is acted upon it; hence, torque. Torque is also influenced by the angle at which it is and the connection of at which force is applied.

Reflection on Unit 1 and What’s to Come

bulkleya — Tue, 05 Jan 2010 19:58:59 +0000

1. From the past unit, I learned more in depth on projectile motion. Projectile motion introduced the concept of how horizontally the object’s motion would stay constant, while the vertical motion would decrease. This makes sense because if you think of an object in the air, like a tennis ball, the ball would be traveling constantly further, while gravity acts on the ball’s vertical motion. Thus, the graph would show a parabolic motion, or separately, a straight line for the horizontal and diagonal (down) for the vertical. We also learned a little about pressure and altitude within our web quest. We learned that the higher the pressure, the the more likely the “room” or “container” will explode, or simply it shows that the molecules within the container fill to the containers capacity, resulting in high pressure. Boyle’s law was introduced: pressure and volume are are inversely parallel. Pressure changes as air changes, and the higher an altitude, the higher the volume and lower the pressure. We also learned about the affects of heat and the way that an object moves while cold and hot. When hot, the molecules tend to move quicker and result in a frantic frenzy. Yet while cold, molecules act stiff, motionless, and are far apart from each other, as opposed to heated molecules. Finally, we talked about air resistance and how it affects the real world and the “ideal” situations we have based our observations and experiments on. Finally, we reinforced our learning on motion maps, velocity graphs, position graphs, and other diagrams that helped show and demonstrate our understanding. Furthermore, from this concept and idea I applied this to my final project, which I did with Erin Ginsburg. We took the circumstances of an ideal world and applied it to modern-day concepts, or in our case, future-day concepts, by comparing and contrasting basketball on earth and on the moon. Gravity played an immense role in our project and affected our results for “moon-ball.” We took ideal and realistic circumstances and eventually ended with rules and the future plans for basketball on the moon. Not only did our project show what we learned, but it was also rewarding to see what came of it.

2. To be honest, projectile motion seemed awfully difficult before the breakdown of horizontal and vertical motion. I thought of air resistance before thinking in simplistic terms: yet once I conquered the horizontal and vertical breakdown of the motion, I then incorporated the air resistance, or “friction” into the equation. Projectile motion was more simple and easier to see once I broke it down into parts. Once I discovered the way that projectile motion works, I then fully understood it by applying it to concepts that I already knew more about. For example, soccer and tennis are common American sports: therefore, the projectile motion model fit perfectly to these ideas. Then once on Logger Pro, I began to see exactly what projectile motion was about: and finally, that was when everything began to click for me. So as I applied something new to something I already knew, it helped me fully understand exactly what it is that was being taught.

3. Although the text book is a helpful guide unto learning the basics of physics and the actual definitions, what truly helps me is to actually relate the matter to something that I know well of, like soccer or tennis. When we get more in depth into the physics of sports, I will probably apply the concepts to my favorite sport, pole vaulting. This definitely will help me fully, fully understand what exactly I am learning. THEN I will be able to understand exactly what it is that we are learning.

4. Sometimes I get frustrated with problems that I do not understand, and simply give up and wait in class to discover the answer. From now on, I will read more in depth and really try to understand how to do the problem and what formulas or ways I can use to work it out. To improve how I learn, I can relate the concept to real life and then make connections that will help me understand even more. As I move into the next unit, however, I will really try to learn how I can understand in other ways instead of relying on what I already know so I can understand the concept and not rely on an example for understanding.

How does spin affect projectile motion (an object in mid-air?)

bulkleya — Wed, 09 Dec 2009 02:15:50 +0000

Before the lesson: To me, it depends on the way that the object is spinning. If an object is spinning:

Downwards: The object will have a tendency and will move quicker towards the ground, since gravity is being worked into the ball’s movement even more.

Upwards: The object will have the tendency and will work towards more moving higher, since the ball’s spin gives the ball an extra energy boost.

Right or Left: The ball will be lenient more towards the side it is spinning: in example, if the ball is spinning to the right, the ball will be inclined to move more to the right.

After (a part of) the lesson:

The pressure on one side of the ball is higher than the other, resulting in the ball being pulled towards a certain side and moving a certain way.

What we learned today…

bulkleya — Wed, 02 Dec 2009 23:56:56 +0000

We learned that the size and surface area of an object affect its traveling velocities and accelerations. Since there is more air resistance with surface area, the object travels slower in result. For example, we used a balled-up piece of paper- this had more surface area and less mass than the tennis ball. In result, it travelled slower than the tennis ball, which didn’t have what our class liked to call “air crevices.” Therefore, the surface area of the ball does indeed play a part in its travel. As for the size; usually, the bigger the slower, the smaller the faster. Mass/ weight-wise: the heavier the faster, the lighter the slower. Unlike previous labs and experiments, air resistance is now taken into account for an object’s travel. Air resistance is otherwise known as friction; or something that is slowing an object down. We also learned that an object can reach a terminal velocity; for example, when you sky dive, there is indeed a point where you can no longer accelerate: this is called terminal velocity. It means you are going at a constant speed at this point because the air resistance hinders you from traveling at a faster rate. Therefore, there is such a thing as an amount of speed that is the apex or pinnacle of an object (or person’s) flight.

Post board meeting (Youtube Projectile Motion Lab)

bulkleya — Wed, 02 Dec 2009 00:11:18 +0000

Worksheet wise: Initially, a diagram will have a vector of “force applied” because the racket hits the ball with force- yet as the ball travels, there is only, ideally, one force acting upon it: gravity. (We haven’t really talked about the factor of air molecules.) Therefore, there really is only one diagram to represent the projectile motion of the ball, because the horizontal and vertical action works simultaneously.

Youtube wise: Basically, what I mentioned above. We also discussed the ways in which an object would travel from one side of something (say, a river) to another with or without a current, given that is it the same distance to travel, since that velocity would not affect the object’s travel time. Also, we talked about how you can think of projectile motion as separate entities (horizontal and vertical) but in reality, they are occurring at the same time: therefore, there is one graph for the continuous motion and one graph for the instantaneous motion.