Rubber Band Cart Launcher

Big Question:

How are energy and velocity related?

 ~ This week we launched a red air glider using a rubber band. With the "Photogate" sensor, we were able to measure the velocity when it went through the gate. We varied the distances at which the rubber band was pulled: .01 m, .02 m, .03 m, .04 m, and .05 m.

 ~ From this data, we can see that as the velocity goes up, the energy goes up also. Then we graphed our data with the Energy (J) on the y-axis and velocity squared on the x-axis.

 ~ With this graph, we were able to derive an equation relating mass, velocity, and energy with the equation of a line: y=mx+b. After finding our slope (.2), we saw that it was half the mass of our red cart (.4). Then we substituted "E" (energy) for y, 1/2 m for m, and velocity squared for x, E=1/2mv^2. 

Speed of a Slingshot

 ~ In this picture, the distance at which this person pull back the sling, the faster the rock will go towards the apple. Right now, there is potential energy in the sling and it will be transferred to the rock when the person lets go of the sling.

Rubber Band Lab

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

 ~ This week we performed a lab where we measured the amount of force needed to stretch the rubber band a certain distance. With the electronic force probe, we pulled the rubber band for a variety of distances. At first we measured the force needed to stretch a single-banded rubber band. Then we double-banded it and repeated the steps.

     Single-banded Rubber Band Data:

     0.01 m: 0.538 N
     0.02 m: 1.341 N
     0.03 m: 1.710 N
     0.04 m: 2.693 N
     0.05 m: 3.372 N

     Elastic Constant: 70.85 N/m

     Double-banded Rubber Band Data:

     0.01 m: 3.835 N
     0.02 m: 6.375 N
     0.03 m: 8.605 N
     0.04 m: 11.313 N
     0.05 m: 12.782 N

     Elastic Constant: 223.675 N/m

 ~ We see that as the distance of the stretch increased, the amount of force needed increased as well. Also, as we stretch the rubber band, it has potential energy. We acquired the elastic constant by graphing our data. By drawing the best-fit line through the points, we can find the slope (elastic constant). We can derive two equations from this: Fs=kx (Hooke's Law) and Us=1/2kx squared. Us=1/2kx squared is the equation for elastic potential energy.

      We got Fs=kx from the y=mx+b. We substitued Fs (force) for y and the slope k (elastic constant) for m.

      The second equation is acquired from the equation for the area of the triangle. The equation of the area is A=1/2b•h. We substitued Us for A, x (distance) for b, kx (force) for h.

Slingshots

     

To use a slingshot, you must pull the sling back as far as you can to get maximum distance and speed. By pulling it back, there is potential energy. It is then transferred to the object in the sling when you release it.

Pyramid Lab

Big Question: Is the product of force and distance universally conserved (a constant in systems other than pulleys)?

 ~ This week we performed a lab where we pulled a car up a ramp at different angles. We hooked the electronic force probe to the car and pulled. We measured the amount of force it took.

       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

 ~ Two of the results show how work is conserved, but the last trial threw us off. We performed Trial #3 multiple times, but came up with the same product of force and distance. It must have been human error that gave us the wrong data. We might have pulled too hard or too little, or we were not able to get a clear measurement on the force because our hands may have been shaking.

Truck Ramps: 

This truck ramp us used to pull up and push down heavy objects. The ramp allows these people to perform this action with less force, but not less work. Work is a constant and will stay the same. The ramp uses less force but requires more distance. If they were not to use a ramp, the force will increase and the distance will decrease. 

Simple Machines: They Make Life Easier

 ~ For this week's lab we studied simple machines. In class, we built a pulley, and tt may have looked easy at first, but it was more complicated than we thought. Using the pulley, we attached the electronic force probe to one end and a 0.2 kilogram brass object to the other and pulled. We did this many times adjusting the speed we pulled at, the length of string we used, and trying to adjust the amount of force we used. One of the goals was to use only 0.5 N of force to lift up the brass object 10 centimeters. It took quite a lot of tries to achieve it, but we were able to do it.

              Trade-Off

 ~ With simple machines, we have found ways to use less force in our everyday lives. BUT, there is always that trade-off. Force and distance are inversely proportional meaning that when force goes up, distance goes down and vice versa. Without a pulley, it took 2 N to lift up the 0.2 kg brass object 10 cm. With the pulley, it took about 1 N to lift up the 0.2 kg brass object 10 centimeters. But we had to increase the length of the string to do this and it was 20 centimeters. We can see that the distance doubled. So we can see "that you really can't have something for nothing."

BIG QUESTIONS:

1. How can force be manipulated using a simple machine?

2. What do you observe regarding the relationship between force and distance in a simple machine? 

          

         -Using a simple machine, we can decrease the amount of force we use. But there is always a trade off. To use less force, you must increase the distance you use. This is shown with the data that we came up with. 

Without pulley: 2 N and 10 cm to lift it up 10 cm

With pulley: 1 N and 20 cm to lift it up 10 cm

The equation we got is A=fd.

       Elevators and Pulleys

Elevators and Pulleys

This link shows us how many people use a simple machine everyday: the pulley for an elevator. 

Mass and Force: How do they relate?

 ~ Last week, we performed a lab that showed how the force needed to lift an object was affected by its mass. Using both the spring-gauge and the electronic force probe, we hung brass objects of different masses on the hooks of both tools. The benefit of using two measuring devices is that you can make sure that the measurement is accurate. The spring-gauge is a good tool to use, but the electronic force probe allows us to get more accurate measurements. With the data that was found, we noticed that more mass means more force needed. We recorded our data then we used a whiteboard to create a graph:

 ~ This graph not only shows the data; it gives us important information such as the equation relating mass to force. Using two points on the graph, we found the slope of the line: 10.1. With the equation of the line y=mx+b, we substituted f (force) for y, 10 (slope) for m, and m (mass) for x to come up with the equation f=10m. 10 Newtons/kilogram has been determined to be the gravitational constant (g) on Earth. The equation then becomes f=mg. 

With this lab, I learned that more force is needed on an object with more mass. I also learned how to find an equation using the graph by substituting for x and y and finding the slope of the line. Finding the slope, we came up with the gravitational constant on Earth which is 10 Newtons/kilogram. The gravitational constant on other planets and moons may not be the same however. Our weight on different planets may differ than our weight on Earth, but our mass will always stay the same regardless of where you are. I learned that mass does not change because it is the amount of matter in an object. That amount does not change based on location and is not affected by gravity. 

          ~Tennis Ball vs. Medicine Ball

 ~ As you can see, tennis balls are much easier to lift than the medicine ball. The tennis balls are light and most likely have less mass than the medicine ball. There is not much effort into picking up a tennis ball and you can pick many tennis balls at a time. The medicine ball, however, requires much more effort. The man in the second picture is having a tough time picking it up. He is putting a lot of force into picking up the medicine ball that has more mass than the tennis ball. The kids are using force to pick up the tennis balls but not as much as the man because the tennis balls have less mass. These two pictures demonstrate how the amount of force needed is affected by the amount of mass.