Rubber Band Cart Launcher Lab

Rubber Band Cart Launcher Lab

Purpose: The purpose of this lab was to determine the relationship between energy and velocity.

Procedure: We attached our single banded rubber band to the air track, launched our glider with the rubber band, and our velocity was measured by the Photogate Censor. Each time we did this we increased the distance we pulled the rubber band back by .01 meters, and for each distance we launched the glider twice for more accuracy. We used five different distances, with our final distance being .05 meters, so we had a total of ten launches.

Data: Stretched distance, trial 1 and trial 2 velocities, average velocity, squared velocity, and energy

From this we came to the conclusion that energy and velocity are directly proportionate. Each time we increased our energy/(distance), our velocity increased as well.

We then plotted our points putting velocity(m/s)^2 on the x-axis, and energy(J) on the y-axis. This meant that our Independent Variable(IV) is the velocity or the glider, and the Dependent Variable(DV) is the energy used to launch the glider. Using the Graphical Analysis App we used a best fit line to interpret our data and came up with a slope of .258. 

LOL Chart: We discovered a different way to interpret our data and the transfer of energy by using a LOL chart. When you pull back the rubber band, the energy in the rubber band becomes potential energy, when you release( using the rubber band and the glider), the energy becomes kinetic energy, allowing the glider to move. 

Equation Time!

Because of glider was .4kg and our slope was about .2kg we were able to determine that the slope of our line was half the mass of the cart. Using a best fit line to evaluate our data, we modeled our linear equation off of y=mx+b(but b=0 so it cancelled out).

Kinetic Energy Equation:

K=1/2mv^2

• K= Kinetic Energy
• m=mass
• v=velocity squared

Real World Connection!

One real world connection doesn't involve any machines at all, just you and a ball. I have played softball for many years and have been taught to use correct form by all of the coaches I have played for, and over the years this has allowed me to increase the speed and distance I can throw the ball. What I have learned that the further you pull your arm back, the faster and farther the ball will go, so when you increase the distance, you increase the energy you out behind the ball, therefore increasing it's velocity too.

Rubber Band Lab

Rubber Band Lab

Purpose:We used the relationship of force and distance to measure spring potential(stored) energy of the rubber band.

Procedure: We attached a force probe to a single looped rubber band  and pulled the rubber band back by increments of .01 meters each time, holding our force probe for ten seconds at each distance. We did this a total of 5 times and took the mean of the force each time. We then completed this same exact procedure using a double banded rubber band.

 Data: for Single and Double Banded Rubber Bands:

From this we came to the conclusion that force and distance are directly proportionate. The further distance you go, the more force you need to get it there.

We then plotted our points, putting distance(m) on the x-axis and force(N) on the y-axis. This means that our Independent Variable(IV) is the distance the rubber band was stretched(m), and the Dependent Variable(DV) is the amount of force stored. We used a best fit line to interpret our data and came up with a slope of 57.143N/m for the single banded rubber band, and a slope of 280.5N/m for our double banded rubber band.

Because we were using a line, we modeled our equation off of y=mx+b and got the equation for spring force: Fs=kx

• Fs= Spring Force(N)
• k=Spring Constant(m) --> depends on object
• x=stretched distance

To find the Spring Potential Energy we used points on the line to create triangles, and from these triangles we used the equation A=1/2bh(area of a triangle) to derive the equation for Spring Potential Energy: Us=1/2kx^2

• Us=Spring Potential Energy
• k=spring constant--> depends on the object
• x^2=stretched distance

Connection to the Real World: 

Bow and Arrow

Slingshot:

Both the bow and arrow and the slingshot are perfect examples of spring force and potential energy!

• the farther you bull back on the band of either one, the more force it requires(distance and force=proportionate)
• the farther back you pull, the more energy you have stored
• the more force you pull back, the further the distance
• the more energy you have stored the more kinetic energy you will create upon release

Mass vs. Force Lab

Mass vs. Force

The Lab we did involved mass and force. We took several different brass masses and weighed them with the force probe. After we weighed each mass we recorded our data in a table. The general pattern we first realized was when we weighed a mass that was either 100 or 200 grams, which we then converted into .1 and .2 kilograms, on the force probe it would measure to be that first number in newtons, like 1 or 2. We couldn't tell too much from this though so we graphed our information, putting mass on the x-axis and force on the y-axis. After we plotted our points we drew a straight line that we thought best represented the dots. Then we found the slope of the line using the equation by picking two points on the graph and using the rise over run formula, and our answer came out to be 10 newtons of force for every 1 kilogram of mass. We then discovered the equation for Force of Gravity which is F=gm.

You can relate this lab to real life with anything that includes a relationship between mass and force. One of the main examples can be any type of sports. Just like you need a certain amount of force to hold up the brass mass, in the sports of basketball, if you want the ball to go in the hoop, you need to put a certain amount of force to get it there. Certain balls are heavier and lighter than others, so in order to get the ball to the hoop you need to apply different amounts of force. This also applies to on of my favorite sports, softball. When it comes to throwing the ball anywhere, you need to put a certain amount of force behind your throw to get in there. Sometimes after a rainy day, the balls get soaked in water and become heavier, and now because they are heavier, you need to put more force behind the ball to get it to go that same distance.Or even something as simple as holding your bags of groceries; the heavier the bag is, the more force you need to hold it up.

Pyramid Lab

Pyramid Lab

Overview of the lab:

In this lab we measured the inversely proportional relationship between force and distance, just as we did with our Pulley Lab, except this time with a ramp. We started out with a .08 meter ramp and a cart that weighed a total of .5 kg, which remained constant throughout the lab. For our first trial the cart went 1.5 meters and in took .120 Newtons of force. For our next trial the cart went a total of 1.0 meters and this took .414 Newtons of force. And for our last trial the cart traveled a total of 0.5 meter and this took .619 Newtons of Force. So we were able to come to the conclusion that each time we increased the slant of our ramp, it took more force to lift the cart.

*Data Collected/ Recorded in the Lab*

Trial #1:

                                                    

Trial #2

Trial #3

                     

Final Table:

Conclusions:

We observed that each time we increased the slant of our ramp, it took more force to lift the cart. The most important things we learned this week were that W=fd (work=force times distance), that work is measured in Joules (J), and most importantly, Work is universally conserved. No matter what the inversely proportional relationship is between force and distance, work will always remain the same.

Connection to the Real World:

This relationship between work, distance, and force holds true anytime you are either walking or running up a hill. When you run up short and steep hills you use more force than when you run up long hills with a gradual incline, but in each case you are are you the same amount of energy, or work, to get to the top of the hill. Aside from humans, this relationship also applies to mechanical machines, such as cars. When you go up short and steep hills you have to apply more force to the gas as opposed to going up a long, slightly steep hill where you don't have to apply as much force. Either way to you are using the same amount of energy in the long run.

Pulley Lab

  Pulley Lab

In this lab, we used a two-string pulley to determine the relationship between force and distance. We used the model at the front of the class to help build our pulley. When the pulley was built successfully we tried to balance the 100 and 200 gram brass masses. After we completed this we attached an electronic force probe in place of our 100 gram brass mass. We then pulled the electronic force probe enough to lift our 200 gram(2 Newton) brass mass 5 centimeters. Then we measured how many centimeters of string we used to do this and came up with the answer of 11 centimeters. We did this again in a more fluid motion and the data was recorded on our electronic force probe, and then we averaged out the data and our mean came out to be 1.159. So our results were that it took 1.159 Newtons of force to go .11 meters. Also with using the models at the front of the class we were able to determine force and distance are inversely proportional, the more force you use the less distance you have to go, and the less force you use the more distance you have to go.

This relationship between force and distance can be found in several different situations in our world. This relationship comes into play sometimes when people have to lift heavy objects into apartments that aren't on the first floor. An example of this is what you see a lot of times on commercials when movers are using the pulley system to life couches, pianos, furniture, etc. into windows. Also in certain weight lifting machines at the gym, the more force you use the less distance you have to pull to lift the weight, and vice versa.A couple of examples of  modern day pulley systems are an elevator and a well.