Rubber Band Cart Launcher

     In this week's lab, we were asked to determine the relationship between energy and velocity. To do so, we detained the velocity of our red glider cart, using the electronic force probe. We stretched the rubber band to a distance of .01 m, .02 m, .03 m, .04 m, and .05 m. According to the electronic force probe, we documented the velocity of the cart at each distance. We did two trials for each distance and then found the average velocity, the average velocity squared, and we noted the energy measured in joules from our experiment last week. We used our graphical analysis app to determine the graph of our data, using the average velocity squared as the x-axis and the energy as the y-axis. Our graph is shown in the image below:

Using two points on our graph, we found the slope to be 1/2. We converted our y= mx+ b formula into Energy= 1/2 mass x velocity squared.  With K as the elastic constant and Us as the potential energy, we were able to determine that Us = 1/2 k x squared.

We determined that energy in a system always stays the same and that energy and velocity are directly related, and if energy increases velocity must increase. If velocity increases, so will energy.

Real World Connection:

http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/shawna_sastamoinen/Velocity&Kinetic.htm

A rollar coaster can demonstrate the relationship between velocity and energy because if the mass is constant, and the velocity is increased, the kinetic energy must also increase. The article linked above clearly demonstrates this principle as well.

Rubber Band Lab

In this week's lab, we figured out if the force it takes to stretch a rubber band depends on the amount by which you stretch it. To solve this, we stretched a rubber band to different lengths of .01cm, .02 cm, .03 cm, .04 cm, and .05 cm with the electronic force probe. With one rubber band loop, we measured the following:

.01 m = .4 N

.02 m = 1 N

.03 m = 1.9 N

.04 m = 2.7 N

.05 m  = 3.2 N

We repeated the process with a double rubber band loop and got the following data:

.01 m = 1.6 N

.02 m = 2.2 N

.03 m = 5.5 N

.04 m = 5.6 N

.05 m  = 6 N

We notice that when we stretched the band farther, the force increased. Then, we graphed our data using a best fit line. We were given Fs as the force needed to stretch the band, K as the elastic constant, and X as the distance pulled. We discovered the equation Fs=KX, also known as Hooke's Law. Our graph is shown below:

We measured our energy, area, in the shape of a triangle. Area was represented by Us, the elastic potential energy. Using the standard equation of the triangle, our equation became Us = 1/2 ( base x height). With X as the base, Fs as the height, and using K as the constant, our equation turned into Us = 1/2 (K) (Xsquared). We discovered that distance and force are directly proportional, when one increases so does the other. Here is a picture of our white board:

Real World Connection:

An example of the effects of force and distance is a slingshot. The more force used to pull back, the greater distance it will reach. Therefore, the g reater distance you would like to reach, the more force needed as well. This use of force and distance is a great example of elastic potential energy. Below is an image of a slingshot you could use:

Pyramid Lab

In this week's lab, we tested the relationship between force and distance to see if energy is universally conserved as a constant of systems other than pulleys. To experiment this, we placed three books on a ramp with a car at the bottom of the ramp being pulled up by an electronic force probe. In our first trial, it took .1 Newtons to pull the 250 g car up a ramp of 166 cm. so 1.66 meters (.1 Newtons) = .166 Joules.

In our second trial, it took .12 Newtons of force to pull the car up a shortened ramp of 132 cm. so .132 meters (.12 Newtons) = .158 Joules. Below is a picture of our ramp:

More force, Less distance = Same energy

Less force, More distance = Same energy

We continued to adjust the measurement of the ramp and add mass to our car, but we ultimately came to the conclusion that despite the measurement of force and distance, the amount of work or energy will always stay the same. Whether there is more force and less distance or less force and more distance, they same amount of energy is always conserved. In conclusion, the product of force and distance is universally conserved because the amount of energy remains the same always.

Real World Connection:

In the real world, skate ramps are built in the same structure as the ramp we built for our car. Ramps in our everyday lives are simple machines which reduce force, with the trade-off being distance, however, the amount of work, or energy, used is the same.

The Pulley Lab

• In our Pulley Lab, we manipulated force using a simple machine. First, Ms. Tye demonstrated how to lift .1 meters of string with 2 Newtons, without a pulley. Our group was challenged to create our own pulley and once it was finally built, we successfully reached 1.3 Newtons with 20 cm. of string and 0.5 Newtons using 48 cm. of string. Here is an image of the data we graphed, using a bar graph:

•   We concluded from our graph that the less force you use, the more distance you have to pull. Force and distance relate inversely. As force increases, distance decreases and as distance increases, force decreases. We also recognized that force x distance = area, or 1/2 (force) = 2 (distance). From our post-lab discussion, we discovered this measure of area is energy, measured in Joules (J) and that work is energy transferred by applying a force over a distance and that Work (J) = Force (N) x Distance (m). But no matter what the measure of force and distance is, the energy is always the same.

• Real World Connection:
  
  

  

  
  -http://www2.hesston.edu/Physics/Volleyball/paper.htm
  -In volleyball, at the rate the volleyball is hit, you need to absorb the ball and use less force if you want to get it farther and complete the pass. This is clearly demonstrated in the article above.