Unit 6 Reflection!

Work:
The first thing we talked about in this unit was about work! Work is the effort put n something that changes its energy. The equation for work is;

work = fd

It is really important to remember that the force and distance of the equation above have to be parallel! That mean that if someone is walking around (on a flat surface) carying a tray he is not doing any work on it. The distance the person is going is perpendicular to the force that is pushing the tray up. Now imagine that someone is walking up the stairs,  the distance now is parallel to the force, that in this case is the weight of the person. Remember that if you were to calculate the work done by the person climbing up the stairs you wold use the distance from the very top straight down, not the diagonal extension of the stairs! What matters in the stairs scenario is how far up from the ground you are, not how much distance you walked. Remember that if you are pushing against a wall, you are not doing work on the wall since its not moving, but you are doing work within yourself inside your body.

Power:

Power is a rate of  how fast work is being done! The equations for power is


Power = work/time

Imagine that there is a race up the stairs and both participants have the same weight (force is constant), which of the competitors would have more power? The one that won the race! The winer of the race would have more power because he would have done the same amount of work (since the distance and force are constant) in a shorter amount of time!

Potential Energy:

Pontial Energy is the energy of possition, is the energy stored in "readiness", the energy that has the potential of doing work. Because Potential Energy is the energy of possition, ther higher something is from the ground the more PE it has! The Equation for Potential Energy is:

PE = mgh

Kinetic Energy:

Kinetic Energy is the energy of movement! The faster something is moving the more kinetic energy it has. The equation for Kinetic Energy is

KE = 1/2mv2

Another important thing to remember about KE is that the change in kinetic energy is equal to work. Therefore...

 change in KE = fd

Work = 1/2 mv2

Conservation of Energy:

Conservation of Energy's simple deffinition is enegy in is equal to energy out! Based on that deffinition we can talk about the relationship between the kinetic energy and potential energy. Let's say that there is a person jumping from a rock to the sea, when the person is on the top of the rock and about to jump he has PE. When he jumps from the rock he loses height and therefore loses PE  (PE = mgh), but since we have established that energy in is equal to energy out, the energy can't be lost right? Right, the energy is being transformed from PE to KE. Now the person does not have as much height but it is a greater velocity therefore no energy is lost, it is only transfered.

The same idea applies to roller coasters, the same hill is always the highest one so that it accumulates enough energy to go through all the elevations. As the car goes down, the PE goes down but KE goes up. If added together at any part of the ride, the KE and PE of the car will equal the PE that the car had on the first hill.

Machines:

Machines can be understood by using the concept of conservation of energy. We said earlier that energy in = energy out and that change in KE = work. That means that the work in also equals the work out! A machine works by increasing the distance you put in in order to decrease the force (work = fd).  To decrease the force you have to exert, you will have to pull for a longer distance and the distance that the object will move will be smaller that the one you pulled. Regardless of how the distances turn out to be the work in wil always equal the work out.

Efficiency: 

In real life no machine works with 100% efficiency. There is always some energy that is transformed in something else, like in heat due to friction. The efficiency of a machine can be meassure by dividing the energy output by the energy input.

Reflection:

The first part of this unit was easy to understand. The concept of work seemed easy enough to understand. On the quizzes about work tough... I fell for every single one of the questions that asked how much work someone walking with their books is doing. No work, the  answer is no work! I found it hard not to be ready to plug in numbers that were given to me before analising if there was any work being done at all. When question asked for me to say what would happened to the work if the velocity was doubled I also got a little confused but after going over on of those questions with my teacher I now know what to do! The questions about the change in kinetic energy, when the velocity went from a number to another also tricked me. I made the mistake of calculating the difference in velocity first and using that number in the kinetic energy formular, while I learned that I should have calculated the kinetic energy of each individually, and then found the difference.  This energy was easy in theory but complicated in practice but after looking back to some quizzes I found out what mistakes I made and now know what not to do!

Second Day of Construction of the mousetrap car

Once again the construction of the car did not go as smoothly as we imagined... We drilled a whole and added the four eye-hooks and then tried to cut the axle out of the wood stick we bought. We planed on connecting everything with the zip ties, but that was the part that did not work as predicted. We all of the four wheels on the axle and placed one zip tie of each side of all the wheels. The wheels did not move out of place but they did not spin faster either. Mrs. Lawrence than suggested that we used tape instead of the zip ties, and that idea in fact was a lot more effective. My partner and I also observed that the wheels were not aligned, and that might also be the reason for the them to be unstable. We took everything apart and made sure that the axle were of the same length, and started to put the same amount of tape on each end of the wood stick so that the wheels are the same distance from the car. That was when our time was done!

First Day of Construction of the Mousetrap Car!

The first day of construction of the car did not go as me and my partner expected... We began by trying to get the wheels off the toy car we bought. The wheels did not seem to want to come out at all, and soon we found out that it was because the car was a remote controlled so it did not have an axle! That was a big disappointment because we planed on using the axle from the toy car on our mouse trap car. We were finally able to take the wheel off and decided to use the wood stick, we had bought for extending the lever of the mouse trap, as the axle. We drilled a whole on the four wheels so that they fit through the wood stick, and on the mouse trap so we could insert the eye hooks on the second construction day. Our first day of construction was not as easy as I expected it to be, but we ended up figuring out how to make it work! Looking forward for the second day of construction!

Mousetrap car!

Building a Mousetrap Car

My partner and I had no idea how to build a mousetrap car so we looked up some videos on the internet and found this tutorial that was really helpful on understanding what we had to do. One interesting thing about the mousetrap car on the video is that the frame is the mousetrap! My partner and I thought that might be a really good idea to not use a frame so the car would be lighter. We plan to follow the video but make a few adjustments. We are going to start with the eye-hooks and the wheels from toy car seemed to work pretty effectively. Extending the lever was also something we saw be done on every video about mousetraps so we plan to do that too. The one thing we did not like about the way the car from the video bellow was built was that the wheels could move from left to right and that can cause  the car to curve. To solve this problem we thought that we could maybe use zip ties on each side to keep the wheel from shifting without stopping them to turn. So our plan step by step is:

1. Buy eye-hooks, rubber bands, wood stick, two toy cars (with different sizes of wheels) and zip ties;
2. Unlock the mousetrap;
3. Lengthen the lever with the wood stick and attached with three zip ties;
4. Make a whole on the sides of the mousetrap with a pin and place the eye-hooks on the wholes;
5. Take the wheels out of the toy cars and put the larger wheels though the eye-hooks on the back side of the car and the small one in front;
6. Fix the wheels with a zip tie on each side of the wheels so that it wont move side to side and put the rubber bands around each tire;
7. Attach the string;
8. Win the race!!!

Unit 5 Reflection!

Tangential and Rotational Velocity:
We started the unit by learning about tangential velocity and rotational velocity. My class found out that rotational velocity is about the number of rotations over a time. When talking about rotational inertia we discovered that if, for example, two kids are playing on a merry-go-round regardless of their position their rotational velocity is the same! So, does that mean their tangential velocity is the same? No! Tangential velocity depends on how far away the body is from the axis of rotation. If the body is far away from the axis of rotation it needs to cover a greater distance per rotation therefore it has a greater tangential velocity, the opposite is true for an object close to the axis of rotation.

tangential speed ~ radial distance x rotational speed 

Rotational inertia:

Rotational inertia is the same as linear inertia but for rotating objects. Just like objects moving in a linear path, rotating objects do not want to stop doing what they are already doing. Rewriting Newton's first law we can say: 

An object rotating about an axis tends to remain rotating around an axis unless interfered with by some external force and an object not rotating wants to remain that way unless an outside force is applied. 

Rotational inertia depends on concentration of mass and how far is it from the axis of rotation. The furthest away the concentration of mass is from the center the greater it's rotational inertia is. I struggled to convince myself that the greater the rotational inertia the hardest it is to start rotating, I always wanted to say that it would start rotating sooner than an object with a small rotational inertia. The secret to understand this concept is always to remind yourself that the inertia is laziness and the lazier the object is the more reluctant it would be to start rotating!

The video above shows that because the hoop has it's concentration of mass away from the axis and the disk is solid (both have the same mass). The hoop has more rotational inertia and therefore is more reluctant to start rotating and therefore loses the race.

Torque:

http://microship.com/resources/resourcepix/cgdb-1.jpg
microship.com

After talking about rotational inertia we talked about torque which changes the rotation of things. It is important to know that torque is lever arm times the force (force = weight). The concept of torque is used to understand why some things are balanced and how to create a balanced system. The best example for this is a see-saw. If you have too people with different weights it is impossible to maintain the board balanced if they are both sited the same distance from the axis of rotation since for a system to be balanced there needs to be equal torques. To make the board balanced with different weights you need to increase the lever arm (lever arm = smallest distance from the axis of rotation, always perpendicular to force) of the person with the least weight so that the torques equal.  In practice the heaviest person of a see-saw needs to sit close to the center while the lightest one sits away from it as the Figure 1 shows.

Center of Mass/Weight and Stability:
Center of mass is the average position of all the mass that makes up the object. If the object is symmetrical the center of mass is at the geometrical center. Center of mass is called center of gravity when weight is involved. To balance an object one needs to hold it on the center of mass and that will support the entire object and thus it will be balanced. Stability has everything to do with center of gravity. If the center of balance of an object is directly above it's base it will have balance if it is not it is unbalanced. The concept of center of mass and stability explains why you lean forward when carrying a heavy backpack, you want to keep your center of mass over your feet so you can keep your balance. The boy in the picture above is not leaning forward and that is why he feels unbalanced. If he can shift his center of mass so that is over his feet maybe he can make in time for class!

http://staff.fcps.net/sms-news/archive/2006-07/vol1issue1/6th/backpack.JPG
staff.fcbps.net
Dylan Kimmel

Centripetal Force and Centrifugal "Force":
Centripetal force is a force directed towards the center. If you have a can and a sting that your swing above your head you can notice the effect of centrifugal force. Even though you may think that there is a force pulling the can out there is only the force of tension of the string pulling it to the center. When talking about centripetal force we used the spin cycle of the of a washing machine as an example. The fact that the clothes are drier after the spin cycle is explained because the water and clothes have the same tangential velocity the water can go through the wholes in the side because there is no external force stopping them from continuing moving in the straight line they want to keep following since it has inertia.  The sides of the washing machine provide a force of friction on the clothes that for that reason are pushed inward (centripetal force). It is possible to think that there is a centrifugal force on the clothes on the washing machine since they stay up against the washing machine walls but centrifugal force does not exist! The clothes seemed to be pushed outward because of the combination of the velocity of the clothes that is tangential to the circle with the friction force from the walls of the washing machine.

Conservation of Angular Momentum: 
Just like linear momentum angular momentum is also conserved. The fact that angular momentum is conserved   allows us to establish a relationship between it's two component: rotational inertia and rotational velocity. Angular momentum is rotational velocity times rotational inertia, since angular momentum is conserved they have a inversely proportional relation. The inversely proportional relation means, in other words, that if rotational inertia increases rotational velocity will decrease and the other way around. The ballerina on the video bellow is an example of conservation of angular momentum. The girl extends her leg and arms and that increases her rotational inertia (because her mass is farther away from the axis of rotation) and therefore decreases her rotational velocity  since angular momentum is conserved. The ballerina probably has no idea but the fact that she decreases her velocity after every turn allows her to be able to put her foot flat on the ground and regain balance to do another pirouette.

Reflection:
This unit was probably one of the trickiest on the sense that all the concepts seemed to overlap. When trying to answer homework questions it was sometimes difficult to understand which concept to use. After some practice it became easier to distinct what concept the question was actually asking about. I struggled understanding how the train wheels work, what helped me to understand this was reading about on the book again. After reading about it I figured out that it was all about different tangential velocities and that they cause the train to self correct along it's way.

Meter Stick Lab

The objective of this lab was to use a meter stick and a 100g lead weight to find the mass of the meter stick. My original plan was to find the lever arm of the meter stick with the weight and than calculate the torque by using the equation torque = lever arm x force. My plan did not work because I did not know that the force that had to be used for this equation was only the force of the lead weight and not the force of the lead weight plus the force of the meter stick as I previously thought. When me and my partner started to try different approaches to finding out the mass of the meter stick we both agree that the torque of the meter stick would equal the torque of the lead weight. (torque1 = torque 2 /  force x lever arm = force x lever arm) since the meter stick was balancing. From that point we started to try finding the numbers that had to be plug in to find the weight of the meter stick. We knew that force in this case would equal the weight of the meter stick and the other force would equal the weight of the lead weight.  We balanced the meter stick with the lead weight on the edge and found that the lever arm for the that side was 29 cm and assumed that the lever arm for the meter stick alone would be from the axis of rotation to the end of the stick (51 cm). Thinking we finally got the right result we wrote down the equation: 

           

This was not the right result! After struggling some more we noticed that the force could not be in grams therefore the force had to be converted to newtons. We used the formula w = mg and found out that the force was 0.98 Newtons. That was not our only mistake on the equation above. Miss Lawrence explained that the lever arm for the the meter stick was not 51 because that was not the measure from the center of mass of the meter stick to the axis of rotation. To find the correct lever arm we balanced the stick without the weight and than measured the distance between the distance from the axis of rotation of the system to the center of mass of the stick and we got 21.2 cm. Now that we had all the correct number we plug them all in the previous equation:

                

When I got to this result and converted from weight to mass (w = mg) and got 0.136 I though I got the wrong answer again since a meter stick could not be 0.136 grams. Ms. Lawrence than pointed out that my answer was not in grams but in Kg so it was actually 136g  which makes a lot more sense. 

Unit 4 reflection!

Unit 4 mainly talked about momentum and impulse. We stablished that momentum is inertia in motion and is equal to the mass times the velocity of the body (P = mv). The product of the force acting on an object and the time which acts its called impulse (J = f Δt). Impulse is also the result of change in momentum (J = ΔP). Momentum and impulse can explain a lot of everyday life situation. For example: why is it better for a karate fighter to exert a force for a short period of time when breaking a brick? The answer to that questions seems like it would be prety easy, but... in order two variables in an equation, the other variable needs to be proven constant. In the equation J = f Δt, in order to prove that time determines the force necessary to achieve a certain impulse, the impulse needs to be proven constant. To prove impulse is constant you need to state that regardless of the time, (continuing with the karate example) the hand of the fighter is moving and comes to a stop therefore since the mass is obviously the same and P = mv, the change in impulse is the same (ΔP = Pfinal - Pinitial). We stated before that J = ΔP therefore J is constant! To continue to answer the question, you should now state that J is also J = fΔt.  Because of the last equation is possible to afirm that the smallest the time of contact the greater the force will be in order to achieve the constant J. Since to break a brick you need the greatest force possible, the time of contact should be as small as possible.
Still don't understand? Try watching this explanation

  After learning about the relationship of momentum and impulse we talked about bouncing. 

To explain bouncing, my class watched a demonstration of two identical balls in direction of a wood block each. One of the ball sticks and the other one bounces. The question was which one of the balls will knock the wood block over? The answer to that question was the bouncing ball! The reason why the bouncing ball knocks the block over is because there is not only one force acting on that block. Because of Newton's third law, we know that for every action there is an equal and opposite direction therefore ball pushes block, block pushes ball in both cases. The bouncing ball not only causes that force, the ball will bounce on the block adding another force taht causes the block to fall over.

After talking about bouncing, we talked about concervation of momentum. Conservation of momentum is apliable when there is a system. Conservation of momentum is represented by the equation: 
P before = P after . When dealing with collisions conservation of momentum is verry helpful. We learned that ther are two different types of collisions:

Elastic collision:
A collision in which colliding objects rebound wothout lasting deformation or the generation of heat.

Inelastic Collisions:
A collision in wich colliding objects become distorted, generate heat, and possibly stick together.

We learned that because of the concept of collision and conservation of momentum is possible to find out many things about the colliding objects. If for example you know the masses and the velocity of the objects before the collision and they stick together, or one object is at rest, it only takes a few steps to find out  the velocity of those objects after the collision by using the conservation of law affirmation.

Reflection:
The hardest part of this unit was writing out a complete answer for a problem like the karate one. It became easier to remember to include all the information neeeded after we  answered homework questions on the board and got a chance to learn with each others mistake.