Rubber Band Lab

Purpose: The purpose of this lab was to observe the spring/elastic potential energy by measuring the amount of force it takes to stretch a rubber band. Through our data, we discovered the "displacement from equilibrium" or the amount of stretch. Our data helped us answer the Big Question, "How does the force it takes to stretch a rubber band depend on the AMOUNT by which you stretch it?"

How?: To test our big questions, we started with a rubber band at equilibrium. We used the force probe to stretch the rubber band a given distance (1cm, 2cm, 3cm, 4cm, 5cm). After we stretched the rubber band to the given distance and holding it steady for at least 10 seconds, we used the LabQuest to average the measure of force it took to hold the rubber band steady. We recorded our data. 

Graph: To determine the amount of force used in each trial, we used the equation F=kx 
K=spring constant x=displacement from equilibrium

However, F=kx was only one equation we covered. After finding this equation, we had to find the area of each triangle (A=1/2bh). Finding the area of each triangle meant that we were finding the Energy of each trial (spring potential energy). 

To find "Spring potential energy" we went from  A=1/2bh ----> Us=1/2(x)(Fs)

Since Fs=kx--------> Us=1/2(x)(kx)

with 2 "x"s---------> Us=1/2kx^

Real World: Spring potential energy can be seen in many aspects of everyday life. For example, a diving board. Imagine standing on the board--you are at equilibrium. However, after you jump off you are displacing it from equilibrium. The amount of energy can be determined by calculating the amount of force it takes to displace the diving board and the spring constant of the board.

Pyramid

Purpose: The purpose of this lab was to observe the relationship between force and distance as they relate to the larger concept of "work." By manipulating distance (changing the height of the ramp) we were able to observe how force and work changed. This eventually helped us answer the Big Question, ""Is the product of foce and distance universally conserved?"

How?: To start, our group set up a ramp across our table; one end resting on the table and the other supported by a stack of books. Starting at the lower end, we used the hook connected to our LabQuest2 to pull our 750g car up the ramp. We repeated this action 3 times; however, each time we adjusted the stack of books to make our ramp steeper. 

Conclusion:  By examining our data table, my group was able to conclude that force and distance are inversely proportional, meaning that if we decrease distance, force increases and vice versa. This also means that work stays the same, and is yes, universally conserved.

The Real World: For homework, we investigated how hidden ramps may solve the mystery to pyramid construction. Ramps may have allowed Egyptians to construct such massive structures made of millions of stone blocks. Below is a link that helps explain the mystery and use behind these ramps.  http://www.archaeology.org/0705/etc/pyramid.html

Also, ramps are seen in many aspects of our everyday life. They reduce the amount of force
we use, making our lives a whole lot easier.

Pulley

Purpose: The purpose of this lab was to observe the relationship between force and distance using the simple machines we built in class. My table and I built 3 pulleys (one string, two string, and four string) in an effort to compare the a length of string and the amount of force used to lift a brass mass. 


How?: Before we could begin gathering data, our group had to assemble our 3 pulleys. First, we assembled our one string pulley which allowed us to lift a 200 gram (g) mass 10 centimeters (cm) from the table, only using one Newton (N) of force. Then we measured the length of string we had to pull in order to raise the mass--we measured 20 cm. We then built a two string and 4 string pulley, and did the same experiment; however, this time we raised the mass 5 cm and measured how many Newtons required to hold it steady. 

Graph: After collecting the data, we determined that there is an inverse relationship between force and distance. This means that when we increase the amount of string used, there is a decrease in the amount of force needed and vice versa. By adding more wheels to the pulley, there is an increase in the number of strings, which in turn decreased the amount of force needed to lift the mass. 

To graph our data, we plotted Force in Newtons and Distance in Meters and from there, connected our point to our axis, making a rectangle which we colored in.

Real World: Attached is a link that explains the pulley system used in elevators. With equal loads on each side of the "sheave" in an elevator, it only takes a little bit of force to tip the balance one way or the other. The system is just like a see-saw in a park.

http://science.howstuffworks.com/transport/engines-equipment/elevator3.htm

Mass vs. Force

Purpose: The purpose of this lab was to discover the most accurate relationship between mass and force; in other words, how many Newtons (N) does it take to support a certain amount of kilograms (kg). By finding this relationship, we were able to discern and graph the best fit line.

How?:To start off the experiment, we were given various brass masses and a force probe. By keeping my arm at a constant steady height, my group hung a brass mass from the force probe. We were able to make a data table by recording the brass mass in grams and kilograms (1 g = 0.001 kg), and by recording the amount of force, in Newtons, needed to support the mass. We used a variety of masses and through our calculations we started noticing trends. By observing our trends we concluded that there was a direct relationship of 1- 10 between mass and force. For every one kilogram (1 kg), ten Newtons (10 N) were needed to support it.

Graph:With the trend established and our data table complete, our group was ready to graph our data. With mass in kilograms on the x-axis, and force in Newtons on the y-axis, our group was able to graph the best fit line for our data. By looking at our best fit line we determined the slope and used the equation y=mx+b. 

*m= slope. Δy over Δx, which in this case is 10

*b= y-intercept (where the line crosses the y-axis) which in this case is 0

After plugging in all our values we get the equation......y=10x therefore, F=10N/kg(m)+b

Note: The new equation is similar to y=mx+b where 10N/kg represents slope and "b" represents the y-intercept; however, F in this new equation is equal to force and "m"represents mass. 

The Real World: Below, I posted a couple videos that talk about the difference between mass and weight, two concepts that are commonly mistaken. Mass refers to the amount of matter in an object, but weight is a force. Weight is the "gravitational attraction that the object feels toward the Earth." When asked the question, why is it difficult to push a car? The most common response would be, "because it is heavy." Heaviness is used to describe weight, or a gravitational pull. But because the car is being pushed on a flat surface, the force of gravity does not oppose the motion. I feel that these two videos are relevant to our lab not only because we literally used brass "masses," but because when we hung the masses to the force probe, the amount of forced used is equivalent to the gravity acting on the object. 

http://www.youtube.com/watch?v=_Z0X0yE8Ioc

http://www.youtube.com/watch?v=1whMAIGNq7E