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.  

Pyramid Lab

The BIG Question?

        - Is the product of force and distance universally conserved, which means a constant in systems other than pulleys?
     

     In Physics class this week we wanted to see if energy (in the SI unit Joules) was universally conserved.  Three books were stacked on a table and then a ramp was placed at an angle on the books.  Then a cart was placed on the ramp which was 750g.  The cart was manually pulled up the ramp and we used an electronic force probe to measure the force required to pull it up.  Here are our results

       Trial #1
          Force: .25 N
          Distance: 1.33 m
          Work: .3325 J

       Trial #2
          Force: .50 N
          Distance: .7 m
          Work: .35 J

       Trial #3
          Force: .4 N
          Distance: 1.6 m
          Work: .64 J
The first two results were consistent with our hypothesis but our third trial was very random and different.  After trying multiple times we got the same answer.  This is just down to human error and the fact that we are a bunch of sleep deprived high school students who can't focus for more than ten seconds at a time.  

From this lab, we were able to see that energy is conserved, and we discovered the relationship between its two factors.

The relationship with Force and Distance is inverse.

• When the force goes UP, the distance goes DOWN
• When the distance goes UP, the force goes DOWN.

Real Life Connection:

For those people in our world who have to use a wheelchair ramp, they are putting in the same work as those who use the stairs.  Those who take the stairs cover less distance but use more force to get themselves up.  Those in wheelchairs inversely then cover more distance but use less force.  

The Pulley Lab

The Big Question

• What pattern do you observe regarding the relationship between force and distance in a simple machine?
• How can force be manipulated using a simple machine?

Introduction:

     This week in Physics class we performed a lab that demonstrated the relationship between mass  and the amount of force needed to hold it in place.  This was done using "simple machines" (a clever title since making one was actually very difficult).  We were asked to find how many Newtons were needed to lift .2 kg 10cm in the air without the pulley system.  Then we were asked to do the same thing but with the pulley system.  Each method was supposed to use a certain amount of force.  Without the system took 2 N whereas with it should take about 1.0, and for the challenge .5 N.  Attached are the groups results 

Results: How can force be manipulated using a simple machine?
     Since politics have been my focus for the week, I'm going to answer the big question with an government analogy: the relationship between the mass of an object and the amount of force needed to keep it in place is similar to our system of government, with checks and balances.  The less amount of force needed meant you needed to pull on the string more since you can't receive anything for free in a trade off.  

What pattern do you observe regarding the relationship between force and distance in a simple machine?
     The relationship between the two is inverse.  When the force goes up the distance decreases and when the force goes down the distance increases.

New Key Terms:
     (J) for Joules which is the unit for energy.  J= D(distance)xF(force) which is always constant.  

Real Life Example:
Soccer players are the athletes that use natural simple machines the most; the patella

Without this "pulley" the knee joint isn't demolished and the thigh muscles are able to lift the lower leg.  Thanks to this pulley, society is able to enjoy the best sport in the world; soccer.

Mass-Force Lab

• In the first lab of the 2012-2013 school year we were instructed to measure the force from a brass weight.  There multiple brass weights, each with a particular mass.  For the first set of weighing we used a manual probe, and following that was an electric probe.  Once the data was collected, our group formed a graph using the formula y=mx+b to create the line.  The process was repeated, but rather this time with an electric probe.  With both types it was difficult to get an exact measurement because of human error. 
• Once the information was recorded and substituted for variables, we had to figure out what this meant.  After plugging in numbers into the formula the slope was 10 so y=10x+b.  But, there were still three other variables to solve.  X and Y were subbed out for mass and force respectively since they related to the lab.  That left us with B.  After discussing with the group we came to the conclusion that B wasn't necessary because the line passed through the origin.  Compiling all that info together we were able to discover that the gravitational constant on earth is 10 N/kg.  Final Conclusions: an increase of mass means an increase in force, gravitational constant on Earth is 10 N/kg
• Connection to the Real World: This concept is applied in the sport of boxing.  In boxing players are divided up by their weight in order to make the game fair.  For example, 6'4, 220 pound Muhammad Ali would not fight 5'6, 135 pound Manny Pacquiao because Ali produces much more force than the smaller Pacquiao due to his weight.