KOH Final Report

Our car lost to Austin Zhu's car.

Unfortunately, when our car was released, it went sideways instead of forwards and up the ramp. We were easily defeated because our car never made it up the hill in the first place, and the competing car did. When we collided, the opposing care was already over the top of the ramp, and just further proved how badly our car was running. Their velocity was much greater than ours because we lost energy to colliding with the side of the ramp, and our displacement was not in the right direction, while theirs was much greater.

The mass of our car was a good one, solidly built but light enough to pick up speed. Our problem was that the wheels were not very sturdy, and when they broke, the car ran the wrong way. Our mass was also less than that of our opponent's, and that affected us when they collided with our smaller car by doing more damage to our car, because the force of the opponents on us was much greater than our force on them due to mass differences. The friction on our wheels was sufficient, in fact superior to our opponents, who used duct tape while we used rubber bands. This didn't help us, however, because all the nice friction we had just propelled us into the wall better. The momentum of our car was also useless because all the momentum that was supposed to be driven into the opponent got driven into the wall, making our car lose energy and ultimately fail to make it up the ramp.

I was very disappointed in this result because I had worked very hard to screw the wheels of the car into the axles, and the wheels ended up breaking anyways. The wheels were our downfall, and I honestly am sad that the project crashed and burned the way it did.

Energy Equations Lab

Rebecca, Joe, Alondra

Elastic Interaction Energy

VM: As the displacement increases, the force of the spring increases proportionally.

MM: Fs = 0.1(N/cm)(deltaX) - 0.02N

Slope: For every 1 cm of displacement, there is 0.1 Newtons of force.

Y-int: When there is no displacement, there should be no force. The intercept is close enough to 0 to be negligible.

General Equation:

Fs = k(displacement)

       k = the "spring constant" or the "stretchiness" of the spring
This equation is called Hooke's Law, saying that the stretch of the spring is proportional to the force of the spring. Springs that follow this law are called "Hookean springs"
The slope physically represents how stretchy the spring is. For instance, the spring inside a pen is not very tightly wound, so t has a relatively low spring constant. The springs inside a car have to have a very high spring constant in order to perform at maximum capacity and safety.

Area represents the elastic energy. The equation, when integrated, gives us the energy of the spring in joules. In order to find this equation, we calculated the area by calculating the area of a triangle.
Area = 1/2 bh
Ee = 1/2(deltaX)(Fs)
Fs = k(deltaX), therefore:
Ee = 1/2 k(deltaX)^2
The units are joules because Energy = N/m x m^2, meaning that Energy = N x m, which we call joules.

Gravitational/Kinetic Interaction

The area under the graph of the gravitational interaction represents the gravitational energy. Its equation, as derived form the area equation of length x width, or Eg = Fa(deltaX), Fa is equal to the force of gravity, which is equivalent to the mass of the object times the gravitational field. Therefore: Eg = mgh   (with h being the height, equivalent to the displacement.)

The area under the graph of the kinetic interaction represents the kinetic energy. Its equation, as derived from the area equation of length x width, or Ek = Fa(deltaX), Fa is equal to the mass times the acceleration because the object is accelerating in a positive direction. The displacement is also equal to half the acceleration times the time squared. In the case of acceleration, we can plug in velocity over time for all of the "a" variables, and the time cancels out, leaving the final equation:
Ek = 1/2 mv^2

KOH Eval

I modified my car from the original plans by using sliders instead of wooden wheels, which were screwed in rather than attached via hot glue. The body was plastic, not wood, and the frame wasn't a block, but rather a set of shingles to support the rat trap. Unfortunately, my car did not go up the ramp. It moved, but only slightly because as I was winding it one of the wheels came loose. This made it impossible for the car to move because the force of the rat trap went into the axle rather than the wheel, and there was no friction between the wheel and the ground to propel the car forward. I think in terms of what went wrong, the wooden axle was too thin and split under the pressure of the screw. I will definitely make further modifications, maybe even construct a whole new car in order to make sure this one doesn't fall apart when I need it most.

Famous Physics Experiments

Experiment 1:
Galileo demonstrated that objects, no matter their mass, fall at the same rate by dropping two balls of different masses from the Leaning Tower of Pisa. They fell at the same time and therefore proved his hypothesis correct and disproved Aristotle's theory of gravity, which was the commonly held belief that an object's rate of freefall was dependent on its mass.
Galileo's experiment was validated by the moon landing, where astronauts demonstrated a feather and a hammer falling at the same rate because of no air resistance.

Experiment 2: Hooke's Law
Robert Hooke discovered the law of elasticity by attaching weights to a spring and measuring how the force and the "stretch" were related. He discovered that they were directly proportional, and that the amount of force applied to the spring was linearly related to the extension of the spring. Not all springs exhibit this, but those that do are called "Hookean" springs.

KOH Justification

Rebecca Harvey Block 6

Materials:

• 30 cm string (2 cents at Ace Hardware)
• 2 straws (about 4 cents total at Ace)
• Hot glue (2 dollars at Ace)
• Mousetrap (5 dollars on Amazon)
• Wooden square (4 dollars at Ace)
• Small screws (2 dollars at Ace)
• Bottle caps (about 5 cents)
• Large cardboard tube (2 dollars at Ace)
• Styrofoam board (4 dollars at Ace)
• Pencil (about 15 cents at Office Max)
• Pack of rubber bands (about 30 cents for 20 bands at Ace)

Diagrams:

* I accidentally put the inches symbol instead of centimeters for the dimensions

Statement:

The dimensions of the car I designed are 12 cm wide by 20 cm long. The car is very basic and made basically out of a wooden body, mousetrap to power it, two axles, four wheels, and a taller wooden barrier in the front. Rubber bands line the cardboard wheels to create a rubber traction and to increase the friction between the wheels and the ramp when it is in motion, thereby making sure the car moves forward rather than sliding backwards after the initial acceleration due to the energy released by the mouse trap.

The design of this car allows for heaviness over speed, because the mousetrap will provide enough energy for the car to get up the ramp, and the mass will ensure that the car, when colliding with another car, will have the same force exerted on it by the other car (Newton's Third Law) but will be less affected and more stable in the event of a head-on collision. Also, since the car isn’t very tall, the car’s center of gravity is low and can withstand the force of a collision without flipping over.

Finally, the car's increased mass will also increase the normal force of the ramp on the car, in order to compensate for the larger force of gravity. This increased normal force also increases the force of friction, thereby giving the car more traction and having it lose less energy as it goes up the ramp. However, we don't want the car to be too heavy, other wise the acceleration would decrease according to our sum of the forces equation. Because mass and acceleration are inversely related, we have to make sure that as we increase the mass of the car to increase its chances of surviving collision and also increasing the friction, we have to not overdo it so hat the acceleration becomes too little and the car never moves in the first place.

ok! test test test!

Newton's Second Law

Block 6, Rebecca Harvey, Blossom Wong, Anthony R
make sure you publish!!
Pre-Lab: In the pre-lab demo, Ms. Freudenberg pulled Erin down the hall with constant force, and Erin dropped sugar packets at a constant rate. This showed greater distance between the packets as she got faster. This shows that a constant pull will create constant acceleration. Ms. Freudenberg then pulled with a greater constant force. This equaled a greater acceleration, showing that the the strength of the constant pull and the acceleration are directly related. Ms. Freudenberg then pulled both Erin and Shannah at the same time with a constant force, and the acceleration was smaller. This shows that acceleration and mass are indirectly related.

Purpose: In our lab, our purpose was to find how the force of the pull affected the acceleration. In order to do this, our independent variable was the force of the pull, our dependent variable was the acceleration, and the variable we held constant was the mass. and what else?

Procedure:

1. Set up a motion sensor on one end of a table.
2. Place cart wheel side up in front of motion sensor. Attach spring scale onto cart.
3. Place two 500g weights (constant mass) on top of cart to create constant friction. 
4. Pull spring scale at 4 Newtons constantly for first trial. Account for a force of friction of 3.5, and calculate acceleration from slope of the graph of motion sensor.
5. Pull spring at 6 Newtons constantly for second trial. Calculate acceleration keeping friction in mind.
6. Pull spring scale at 8 Newtons constantly. Calculate acceleration keeping friction in mind.
7. Pull spring scale at 10 Newtons constantly. Calculate acceleration keeping friction in mind.

Graph:

Verbal Model: As the force of pull increases, the acceleration increases proportionally.I think you variable was actually net force right - didn't you subtract off the fricition?

Math model: Acceleration = 0.614 m/s/s/N (Force of the Pull) - 0.057 m/s/s

Slope: The slope is an indication of how the force of the pull affect the acceleration. As the force of the pull increases by 1 N, the Acceleration increases by 0.6 m/s/s. The slope is representing the mass as a constant, except because the force affects the acceleration, the slope is actually the reciprocal of the mass.

Y-Intercept: close enough to zero to be negligible. Should be zero because when there is no net force pull, there is no acceleration.

The slope of the graph is equal to the reciprocal of the mass, which in our case is kept constant. Its equation is 1/kg. The y-intercept is a representation of the acceleration when there is no force of pull. The equation showing the relationship between acceleration, mass, and net force is:

Fnet = ma

This was derived from a force vs. acceleration graph which gave us:

Fp = ma + Ff
Fp - Ff = ma

The force of friction subtracted from the force of the pull is equal to the net force, which gave us our equation. This means that the force is directly proportionate to both the mass and acceleration, while mass and acceleration are inversely related.

For instance, the harder I push my brother on his bike, the more he accelerates, because the more force I apply, the acceleration directly increases. However, when I push my sister on her bike, she is much heavier than my brother, so the heavier she is, the less acceleration there is with the same pushing force. This is because mass and acceleration are indirectly related, with more mass equaling less acceleration and less mass equaling more acceleration.

Some sources of error include our immense force of friction because of the cart being on its back, which was difficult to measure and accurately account for. The angle of the spring scale measuring the force might have affected the data, as well as motion detector malfunctions; sometimes the cart was out of range of the sensor and that might have messed up the data. In the data itself, we might have included some data that was not related because we cropped only a certain portion of data on the screen. and how did you end up accounting for the friction?  That is an important part of the story!

Some suggestions include not placing the cart on its back but rather using the wheels to get rid of the friction as a factor in the lab. We could fix the angle of the spring scale as well, by using a protractor to make sure the angle is 90 degrees.

feedback?

Newton's Third Law

Block 6 Rebecca Harvey, Aleksi Arostegui
By: Rebecca Harvey

In this lab, we tested Newton's Third Law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.

Part 1: Two Sensors and a Rubber Band

In this part of the lab, we used two force sensors with a rubber band between them and pulled. We first had one partner pull and one hold steady, then switched roles. After that, we both pulled at the same time. We recorded our data as follows. 

In this graph, Alek pulled on the sensor while I held still. 

In this graph, I pulled the sensor and Alek held still. 

In this graph, we both pulled at the same time.











Part 2: Scales and Rolling Chairs

In this part, we sat in rolling chars and pressed two scales against each other. First, we pushed each other and read the scales, which were both at 10 N. Alek started rolling backwards because the wheels on his chair had less friction with the ground than mine. Then, we had a third person push us together, and both scales in that case read 20 N.






Part 3: Collisions

In this part, we had a cart with a sensor on it moving towards another sensor. We rolled the cart slowly at first, the with more force. Both sensors read the same amount of force no matter how hard we did it.








Part 4: Colliding Carts with Rings

In this part, there were two videos of two carts bouncing off of each other using stretchy rings as buffers. In both videos, the rings bent exactly the same amount. In the first one, where both carts had nothing on them, both carts hit each other and bounced back with the same force, with both rings at the same degree of bendiness. In the second one, one of the carts was weighed down with a books. The rings still bent at the same angle, but the heavier cart moved backward less that the unladen cart did. This shows that while the forces were equal when the carts collided, the force was more effective in moving the lighter cart.

Summary: In all these different experiments, we learned that the forces of two objects interacting are always equal, no matter whether they are moving, at rest, pushed, pulled, or anything in between. As long as two objects are touching, the force between them is the saem.

Friction Lab

Block 6, Rebecca Harvey and Aleksi Arostegui
By: Rebecca Harvey

In this lab, we set up a sled with which we attached a force sensor. We would add different weights to the sled, and then pull the whole contraption and determine the force of that pull. Since the force of the pull is equal to the force of friction when the object is moving at a constant velocity, we could then measure the friction. We then flipped the sled, and used the side that had negligible friction for our second trial.good!

Setup:

Trial 1: (rubber - more friction)

Normal Force (N)	Force of Friction (N)
0.7	0.49 N
1.2	0.68 N
1.7	0.91 N
2.2	1.26 N
2.7	1.61 N

Analysis: 

Verbal Model: As the normal force increases, the force of friction increases proportionally.

Math Model: Force of Friction = 0.56 (N/N)(Normal Force) + 0.03 N

Slope: For every 1 Newton of Normal Force, the Force of Friction increases by 0.56 N.

Y-Intercept: Close enough to 0 to be negligible. When there is no normal force, then the surfaces are not touching and there can be no friction between them.good

Trial 2: (Felt - less friction)

Normal Force (N)	Force of Friction (N)
0.7	0.05
1.2	0.12
1.7	0.18
2.2	0.27
2.7	0.35

Analysis:

Verbal model: As the normal force increases, the force of friction increases proportionally

Math Model: Force of Friction = 0.15 (N/N)(Normal Force) + 0.06 N

Slope: For every 1 Newton of normal force, the force of friction increases by 0.15 N.

Y-Intercept: Close enough to be negligible. When there is no movement, there is no friction. true but that's not why here, it was moving...

Conclusion:

Everyone in the class had the same y-intercepts on their graphs, 0, because when there is no normal force, the surfaces are not touching and therefore have no friction between them. The class data was very similar in that the slopes were all close to the same value, about 0.2 for the felt side of the sled. The rubber side of the sled had more variation in slope, from 0.5 to 0.7, because the rubber has more friction than the felt, which meant a larger slope in general, but because of this greater amount of friction, it was more difficult to pull the sled at a constant speed, therefore some groups had different data than other due to varying pulls.good

The slope is, physically, the friction relationship between two individual surfaces. This is known as the coefficient of friction (mu). This coefficient varies between different surface relationships, but is always the same between the two surfaces. For instance, concrete on copper is always the same as concrete on copper, but never the same as concrete on lead. excellentWe tested only two of these relationships: table vs. rubber and table vs. felt.

The way to calculate the force of friction is this equation: Ff = mu (FN)

The people wearing identical shoes could have different amounts of friction because they could have different masses and therefore the normal force of the ground pushing them up is different. This affects the force of friction by increasing or decreasing the normal force.yes

The people wearing different shoes could have the same amount of friction because in the equation, a smaller normal force with a greater coefficient of friction could balance out to be equal to a larger normal force with a smaller coefficient of friction. yesThe coefficients must be different because the shoes are different and the surfaces would therefore be different, but varying masses of the people could balance out the normal forces. Therefore, we can conclude that the force of friction is dependent on surface (coefficient of friction - relationship between surfaces) and the force of the surfaces pressed together (normal force).

Some sources of error include not pulling the sled at a constant speed, and irregularities in the table's surface (not being completely flat, having divots and scratches that increase friction). Next time, we could use a buggy to pull the sled, because it would move at a more constant rate than my hand.

Another factor that could affect the friction would be having the normal force pushing sideways rather than directly opposite form the force of gravity. This could be using a ramp instead of a flat table, and changing the angle of the slant of it. In the experiment, we could test how this affected both the direction and the force of friction. The controlled variables would have to be the same surfaces, the same mass of the sled, and a constant pull. This is really still testing the Fn, but changing the Fn in a different way (you will see when we do angles)

This lab worked, in that we understood mainly what to do and the whiteboarding process was quick and easy. I think the only thing I have to complain about is that we weren't sure what units to use. If that had been specified form the beginning it would have saved some trouble. Ok!  :) Nice job.