Projectile Motion

This week for our lab the class furthered our knowledge of physics by studying projectile motion.  What is a projectile?  An object in motion with only the force of gravity that is influencing it.

 

How does one analyze projectiles?  For our class we went down to the gym and shot some hoops.  In the gym, we took videos of ourselves shooting (this is very accurate because one has to remember that a projectile will travel with a parabolic trajectory). 

 With the Vernier App we were able to plot our points in time (x and y coordinates seperately) and graph position over time with the velocity over time graphs.

With all of this information we were able to derive these equations

y=mx+b
y=acceleration
m=slop=velocity
x=time

Real Life application:

The best shooter of all time, Miami Heat guard Ray Allen, is an exceptionally talented athlete as well as physicist.  Allen understands the concept of projectile motion as he has made the most three pointers in NBA history and has a career free throw shooting percentage of 89.4%

Voltage

Lemon Lab:

Never in my wildest dreams did I think it was possible for a lemon to power a battery.  It turns out this is possible through voltage which is similar to that of a mountain.  Electrons go up and the protons go down the mountain creating charge!  This makes sense after taking the lemons and after sticking a penny and a nail inside the lemon we were able to see the scientifically beautiful results.  

The iPad is a staple in the education of an SI student nowadays.  This is possible through the lithium-ion polymer batteries that iPads use. These batteries have a long battery life because of their high power density. When charging the iPad battery, the voltage increases in the first two hours and stays constant for the final two hours. The iPad charges to 80% in very quick fashion which is why the voltage greatly increases for the first two hours. But when it reaches 80% the voltage is constant hence the large charging period.  The "mountain" is working a lot for the first two hours to charge the iPad and then works at a constant speed for the last two hours.  I have much more respect for the people at apple that develop this stuff!

http://www.apple.com/batteries/

Fan Cart Lab (Newton's Laws of Motion)

Big Question:
What is the relationship between Mass, Force, and Acceleration?

Introduction:
This week in physics we were able to learn about three very prevalent laws in our universe; Newton's laws of Motion!  To begin to understand this we needed to get some hands on experience, so Ms. Tye let us relax on a late Thursday afternoon and let us tackle some physics in the gym foyer!  We used some awesome hover cars that eliminated friction and combined this with some diagramming to help us realize why things happen the way they do.  Following that, in the second lab, we collided a fan cart with aluminum on the force probe.  After each of the five trials using a different mass, we used the wicked smart LoggerPro to calculate our slope which then equated acceleration. Once that was completed, we were able to derive the equation F=ma. 

Understanding this stuff
OK.  Now to really discern what this means we need to recap these three individual laws:

Newtons 1st Law of Motion: 
1. An object at rest or traveling at a constant speed will continue to do so, unless a net force acts on it.
2. An object moving at a constant speed or at rest has no net force acting on it.

Newtons 2nd Law of Motion:
-the amount that an object accelerates depends on the object's mass and the net force it experiences

Netwon's 3rd Law of Motion: 
Whenever two objects happen to interact, they each exert an equal but opposite force on the other.
The force that one object feels is the same type of force that the object feels, the same amount/magnitude of force that the other one feels, and the opposite direction of the force that the other object feels.
Example given in class: A mosquito crashes into a truck.  They exert equal but opposite force on each other.

Real World Connection:
A man that really understands Newton's Law of Motion is Cristiano Ronaldo.  Though I don't like him (he plays for Real Madrid and I like Barcelona, which is the biggest rivalry in soccer) I have to admit the man is a darn good physicist in his own right.  He understands how to strike the ball perfectly which prevents this amazing goal against Levante from becoming an NFL-esque field goal into the 15th row of the stands.  The strike of the ball itself incorporates the latter two of Newton's laws, while the dip into the back of the net is a perfect example of Newton's first law of Motion.  Enjoy!

Impulse Lab

Big Question:

What is the relationship between impulse, force, and time during a collision?

Intro:

In this week's lab we created a collision between an empty red cart into a force-probe with aluminum  attached to a ring stand with a heavier blue cart. We then deduced the velocity of the cart before and after the collision.  Finally came the determination of the impulse itself which by definition is a change in momentum. We did this to measure the relationship between impulse, force, and time during a collision since they are related to each other somehow.  Get ready to get your mind blown because there is some interesting stuff coming up!

Data:

Red Cart Velocity Before Collision:  -0.667 m/s
Red Cart Velocity After Collision: 0.609 m/s
Area of Force: -0.337 Impulse: J = -0.319

Comparing the area of the force vs time graph has showed us that it is roughly the same as impulse.  These two are equal and from there we were able to derive the equation J(impulse)= Force X time.

Big Ideas:

-Force and time are inversely related.  When force goes up time goes down and when time goes up force goes down.  

-In a collision the force is equal from both sides.  How can this be? Well in every situation where there is a collision the force exerted on an object is the same.  However what causes the great change in momentum is then the mass of the object, as the smaller object would have a much greater change in momentum and impact the overall impulse.

Real World Connection:

In soccer you must control the ball to win.  There are many times when the ball goes in the air and you must bring it down close to you.  How does one do this?  By applying the same physics laws as to that of airbags it is quite easy.  Stick your foot out until it makes contact with the ball and then remove your leg.  This will increase the time it takes to hit the ground, thus reducing the force.  Of course this is easier said than done, so I'll let FC Barcelona player Thiago demonstrate from this video I showed Ms. Tye in class last week.  

Collisions Lab

Collisions Lab
     Big Question:

       1. What is the difference between the amount of energy lost in an elastic Collision vs. inelastic Collision?

       2. What is a better conserved quantity- momentum or energy?

       Introduction:

This week for our lab a new concept was introduced!  It was pretty interesting and somewhat difficult, and it was collisions with momentum.  For the experiment we collided two carts in two different ways elastically and inelastically. We found the amount of energy that traveled in or out of the system as well as the tiny amount of momentum that went in or out of the system.  After determining the percent error we were able to determine which was better conserved, energy or momentum.

Data:  Attached is my group's consensual data as well as a snapshot of our computer screen when the experiment was performed

   Post Lab Analysis: 

   The whole point of this lab is to see which is better conserved, momentum or energy.  So we have to calculate the percent error of the two to determine that.  Otherwise there is no point in doing this whole experiment (though it is pretty fun/cool).  Here is the formula to calculate percent error:

{(Total Energy After - Total Energy Before) / Average of Total Energy Before and After} x 100

Here are pictures for each type of equation

Conclusion:

As these results blatantly show, momentum is WAYYYYYYYY more conserved than energy.  This is because energy can be lost from friction, or heat.  Momentum deals strictly with how far two colliding objects would go based on how fast they are going and their mass.  

Real World Connection:

Immediately when I think of collision I think of rugby.  My dad played rugby in college and almost went professional (until he had me, then he had to be a dad).  In rugby you see nothing but collisions as some of the best athletes in the world tackle each other with perfect form.  Attached is a cool video about the New Zealand All-Blacks pre-game ritual; the Haka

                                     

Rubber Band Launcher

Rubber Band Cart Launcher

Big Question:
How are energy and velocity related?

Key:
m = meters
v = velocity
J = Joules (Energy)
KE or K = kinetic energy
Us = elastic potential energy


Introduction:
In this week's lab we launched a glider from a rubber band using an air track, and used a sensor to measure the velocity. We changed the distance stretched of the rubber band for each trial our independent variable. There were five different distances we had to measure, ranging from 1-5 centimeters. We recorded the velocity of the cart in a table for graphing purposes and then repeated the process. 

Here is our data:

Afterwards, we took our data and put it on the Graphical Analysis App.  It formed this graph

Next Step:
We need to connect this to physics in some way and make an equation that fits our needs as well as our answer the questions to our post lab analysis
1. The mass of the Red cart is 0.38kg. How do you think the slope and the mass of the glider relate?

•  We figured out our slope was 0.216 v2/J which is approximately 1/2 mass of the Red cart.

2. Can you derive an equation using Energy (E), mass (m) and velocity (v2)?

•  y=mx+b is the main equation we are to derive this off of and so we incorporated in information we needed in our new equation. We figured that since the slope was half the mass in the first post-lab analysis question we need to show that in our new equation which came out to be: Energy=.50(m)(v2).

Big Idea:
     The big idea here is energy is always conserved.  How does that apply here?  Well all of the energy before we launched the cart was in the rubber band via potential elastic energy.  Once it was launched, the cart was in motion, and the rubber band was no longer influencing the energy this transferred over into kinetic energy!  Crazy, I know!


Real World Connection:
Being the fantasy nerd that I am, it was only fitting that my thought came to Legolas, from the Lord of the Rings trilogy.  He must have been an amazing physicist because he was so accurate with shooting a bow and arrow and used the equation E= .50(m)(v2) to his best ability in order to help destroy the One Ring in Middle Earth!

Rubber Band Lab

Big Questions:
1. How can we store energy to do work for us later?
2. How does the force it takes to stretch a rubber band depend on the amount by which you stretch it?

Intro:
This week in physics we see how energy is being stored.  This was achieved using a rubber band, a force probe,  and some air! We would loop the rubber band stretch it to a certain distance and recorded the amount of force necessary.  Following that, we looped it over double and repeated the process.  

Data:

Key for Variables:
m = meters (height)
N = newtons (force)
k = elastic constant
Fs = force needed to stretch
x = distance stretched
Us = elastic potential energy

Following that, the goup formed an equation! 

I missed the rest of the week, so derivation of the the equation is hard to explain, but by plugging the variables k, Fs, and x into y=mx+b we were able to form it and make it more relatable to physics.  Force belonged to the y-axis and distance was on the x-axis, so we knew that the y variable would become Fs and the x variable would  then correlate to x.  Slope come out to be 60 n/m.

Real world connection:
One major part of our childhood that most kids love playing with is the slingshot.  Such a simple yet super fun invention!  In order to hit something (or someone) with a slingshot you need to pull it back a certain distance.  This directly applies to the lab because in order to pull the slingback you had to apply a certain amount of force.