Fan Cart Lab

Purpose: The purpose of this lab was to answer the Big Question, "What is the relationship between mass, force and acceleration?"We answered this question throughout our let when we tested the acceleration of each fan cart mass.

How?: In this lab, we started by measuring the mass of fan cart (300 g). Then we recored the acceleration of the fan cart without any added mass, and recorded our data in the Time vs. Velocity graph by measuring the slope. We then repeated this many times, each time with a different mass. We started to notice that the slope of the line in our graph changed each time.

Graph: These two graphs represent the different accelerations of the fan cart. The first one, represents the fan cart's initial  acceleration without any added mass (300 g). The second graph is the fan cart's acceleration with the greatest amount of mass added (1300 g).

Conclusion: Based on our data, we concluded that there is an inverse relationship between acceleration and mass. As mass increases, acceleration decreases, and vice versa. The equation used to represent this would be F=m • a
This lab is related to Newton;s Second Law of Motion.

Real World: This lab relates to pushing a shopping cart at the grocery store. When you first walk in to the grocery store and grab an empty cart, it is easy to push because there is nothing inside. The force you exert would make the cart accelerate faster because of its low mass. However, after you are done shopping, the cart becomes harder to push because you have put many items inside. If you exert the same amount of force onto the full cart as you did to the empty cart, it would accelerate slower because of its higher mass.

Hover Disk--Interaction Diagrams

Purpose: The purpose of this lab was to test motion without the force of friction. We used a hover disk because it floats on a pocket of air, essentially allowing it to glide on a frictionless surface. We used Newton's 3 Laws to answer the Big Question, "What gives rise to a change in motion?" This lab focused on the different forces being applied to an object--force pairs. This lab is summed up in Newton's Third Law.

How?: In this lab, the object we applied force to was the hover disc. First, we turned on the hover disc (removing friction) and pushed it across the floor to the other person. Then we repeated this with the hover disc off, which added the element of friction. After completing these motions, we looked at the interaction diagrams and filled in arrows to each object which represented the type of force being used.

Conclusion--Interaction Diagrams: As you can see in the two diagrams below, the Force of Gravity (pink) and Normal Force (purple) are ALWAYS present between the earth, the two people, and the hover disc. The Normal Force is only present between the person and the hover disc when they are in contact. Also, notice that once the hover disc was turned off, the Force of Friction (blue) is now added between the hover disc and the earth.

Real World: An example of this lab would be comparing ice skating to walking. When we walk, the Force of Friction is present between us and the ground (hover disc off). This force enables us to keep a steady pace and firm footing on the ground, because without it, we would glide on forever instead of walking. However, ice skating is a little different. Since ice skaters are on blades as well as a slick ice surface, there is less friction between the person and the ice, enabling them to glide smoothly over the surface.

Impulse

Purpose: In this lab, we explored the new concept of impulse, and used our data to answer the Big Question, "What is the relationship between impulse, force and time?" This lab is connected to our previous collision lab, and we found impulse by going off of our knowledge of momentum.

How?: We started this lab the exact same way we started the last one, except on one side of the track we had a Logger Pro to record the car's velocity and a Force Probe Ring of the other side. We measured the car's velocity before and after the collision, and also measured the area of the dip in the "Force vs. Time" graph.

Graph: We used the velocity we collected to help us calculate momentum, "P".
We needed to find the momentum before and after the collision to find impulse, "J".
Impulse=ΔP
J=Pf - Pi

Conclusion: The area of the dip in our "Force vs. Time" graph was about -0.3613.
Our calculated impulse was -0.301. The impulse is about equal to the area. This is an example of Newton's Third Law of Motion--"For every action, there is an equal and opposite reaction." The concept of impulse is the relationship between force, time and momentum.

Real World: This lab relates to the popular middle school game, "Wall Ball." When a kid hits the ball against the wall, it comes back to the other player with an equal amount of force and momentum.

Collision Lab

Purpose: In this lab we focused on momentum. We answered the Big Question, "What is a better conserved quantity-momentum or energy?" by colliding the red and blue cars together. We learned about the conservation of energy in inelastic and elastic collisions.

How?: Elastic Collision: In an elastic collision, the two cars do NOT stick together. We set up both cars on opposite ends of the track then pushed the red car into the blue one. Once they collided, they rolled in opposite directions, and the sensors set up of each end of the track recorded the velocity of the cars. We used the graphs on the computer to calculate the velocity before and after the collision.
Inelastic Collision: In this collision the two cars stick together after colliding. We approached this the same way we did with the first collision. We pushed the red car into the blue car, and after they collided both cars stared moving in the initial direction of the red car.

Conclusion: After, we calculated the percent difference of momentum and kinetic energy.
 Pa-Pb ÷ (Pa+Pb)/2    or     KEa-KEb ÷ (KEa+KEb)/2
Momentum is better conserved because more energy is leaving the system during the equation.

Real World: This collisions lab reminded me of playing pool--an example of an elastic equation. When someone shoots the cue ball, it travels and as soon as it collides with another ball, it stops and the other ball travels in its place.

Rubber Band Cart Launcher

Purpose: In this lab, we were introduced to the new concept of velocity. From the data collected, we not only were able to observe the relationship between energy and velocity, but we were also able to observe energy transfer.

How?: First, we set up the sensor gate, which calculated the velocity of the glider. Then we connected the sensor to the LabQuest, which recorded the data. We then turned on the air for the air track, this enabled our glider to slide smoothy across the track with no resistance. We pulled the rubber band back the given distances (1cm,2cm,3cm,4cm,5cm) with the glider in it. When we released the rubber band, the glider passed through the sensor which recorded the average velocity. We then plugged our results into the data table given on the website. We used this table to compare the velocity to the energy results we calculated in last week's lab.

Graph:  After observing our data, we plugged our Velocity as well as Energy results into the data table on the Vernier Graphical Analysis App. This app used our data and created a liner graph and also created a best fit line.

*We then found the slope of the line which was about .2. 
*Derived from "y=mx+b" we used the energy equation E=(slope)(V^)+0----->E=0.2v^
*We then needed to find the constant. We used the equation (Slope)=c(mass)   ("c" being constant.)
*We were given the mass of thecart...0.4kg
* (Slope)=c(mass)  

   0.2=c(0.4kg)

      c=1/2

*From all the equations, we were able to derive the equation for Kinetic Energy

K=1/2mv^

*Slope=1/2m  ("m" being the mass of the object)

The Real World: This lab can also be related to archery in the real world. In the youtube video I posted below, the concept of energy transfer is discussed. When you pull back the arrow, you have potential energy and as soon as you let go, it is converted into kinetic energy. 

http://www.youtube.com/watch?v=b1D6v3kZrHM

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