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.

Gravity Lab

Block 6, Group 1: Rebecca Harvey and Chelsea Chow

Summary: For the Force Lab, we set up a tool that measured the amount of force being pulled on it We then hooked different weights to it and let them hang, letting gravity act on them. We measured the force of gravity acting on different weights, and recorded our data. For the Picket Fence Free Fall, we set up a timer and a picket fence that would set the timer off at different intervals as it fell. We then let the picket fence free fall, and measured how much it sped up as it fell. We created position and velocity graphs to show how gravity affected the picket fence in free fall.

Graphs:

Verbal Model: As the mass increases, the force increases proportionally.

Math Model: Force = 9.71(N/kg)(Mass) + 0.03N

Slope: For every kilogram added, about 9.71 N of force is added.

Y-intercept: Should be 0, close enough as to be negligible. When the mass is zero, the force is zero.

Velocity Graph
Verbal Model: As time increases, the velocity increases proportionally.
Math Model: V = 9.78(m/s/s)(T) + 0.69(m/s)
Slope: Represents the acceleration due to gravity. For every 1 second, velocity increases by about 9.78(m/s).
Y-intercept: Should be 0, pretty close. When time is zero, the velocity is zero.

Slope Comparison: The slopes are very similar, in fact almost exactly the same, because they are both talking about the force of gravity and how it affects objects.

Acceleration: The slope of the velocity graph is the acceleration due to gravity, as represented by the letter g. This value is known to be about 9.8 m/s/s close to the surface of the earth, where we are now. On the moon, it would be about 1/6 of the value because the moon's value is much less, whereas on Jupiter the value would be a lot higher because Jupiter's gravity is much more forceful than on earth.

N = (kilogram) x (m/s/s)
Got this from rearranging the equation of the slope in Newtons per kilograms being equal to m/s/s.
Force (of gravity) = m(g)
Slope = 9.8 N/kg
Got this from rearranging the equation of setting the slopes of the graphs equal to each other.

Newton's First Law
Case 1: In this experiment, gravity acted on the weight by pulling downwards, but the force of the hook is pulling it up, and the two forces are equal and counteracting each other.
Balanced forces = no motion
Case 3: In this experiment, the only force acting on the picket fence is the force of gravity.
Unbalanced forces = changing motion

Gravity in Space: Yes
Weight = force of gravity
"Weightlessness" = no force of gravity -- not possible because the earth is still pulling
We can feel weightless when surroundings change (drop ride, when surroundings are also in free fall)
Free fall - falling with g = 9.8 m/s/s
Orbit - an object moving fast enough that it is in constant free fall around another, larger object

This lab worked well because we knew what to do, and were able to extrapolate the lesson without getting extremely confused. Getting the same slope in both graphs really helped with understanding the force of gravity. I think you demonstrating the lab, at least the practical part of it beforehand, really helped me understand what we were doing.good!  even I can learn!  :)

Marble Rolling into Buggy

Block 6 Group: Alek, Alex, Blossom
We found the average velocity of the marble over  second, which was 69 cm per second. We used this average velocity to determine the final velocity, which was 138 cm per second. We then plugged this into an equation for the acceleration of the marble, which turned out to be the same. We plugged these variables into the equation to find displacements. All we needed was the time. This was determined by plugging the velocity and displacement of the buggy into the equation to determine time for the buggy, which would be the same for the marble, so they would hit at the same time. That time was 0.73 seconds. We plugged that in to the displacement formula for the marble, and got that the marble had to start at 36.9 cm.

Car Acceleration Lab

Block 6, Rebecca Harvey and Aleksi Arostegui


Setup Photos:

Whiteboard Calculations:

Cart on a Ramp Lab

Block 6 Group 7 Blossom Wong, Rachel Chow, Rebecca Harvey
By: Rebecca Harvey

Summary: In this lab, we set up a cart on a slanted ramp resting on a box. We attached a measure of paper to the cart and strung it through a time ticker machine. We then started the time ticker machine and let the cart go, stopping it at the bottom of the ramp. The machine created dots on the measure of paper at the rate of 60 dots per second.

We then took the paper and determined that six dots would have been created per every tenth of a second. We measured the distances of the intervals of every six dots and created the data table below.


Data Table:


















Graph:

Verbal Model: As the time increases in seconds, the position in centimeters increases increasingly.

Math Model: Position = 39.625(cm/s^2)(time)^2 + 6.759(time) - 0.4664 cm

Explanation of Motion: the cart is moving at a positive consistently increasing rate.

Chart:

Graph:

I knew that the amount of space in the intervals was the displacement, because we had defined the spaces in between the intervals on the tape as such. It wasn't a big leap to determine that if the area under the lines was the displacement, then the graph was a velocity vs. time graph. This graph tells me that the velocity is increasing constantly over a period of time.good

Tables:

Graph:

Verbal model: as the time increases, the instantaneous velocity increases proportionally.

Math model: Instantaneous velocity = 78.786(cm/s/s)(time) + 6.3774 cm/s

Slope: the slope of the graph is the acceleration of the object, showing that the velocity in increasing constantly, because it is a straight increasing line. For every 1 second, the velocity increases by about 79 cm/s.

Y-intercept: our y-intercept should equal 0, but it's close enough to zero to be negligible. The y-intercept is equal to the initial velocity.

An acceleration v. time graph in this case would be a straight, horizontal line in the positive section of the graph. This is to show that the acceleration is positive and constant. The slope of the graph would be zero, because the acceleration does not change, and it would be the slope of the velocity v. time graph (in this case, about 79).good

how about how all slopes/area relate?

The two (and a half) new equations are:

Vfinal = at + Vinitial

Derived from the y = mx + b, used to state the equation of the velocity graph.

(Vf - Vi)/t = a OR (delta V)/t = a

Derived from the first equation, (we solved for a) to find the definition of acceleration.

displacement = 1/2(at)^2 

This is not complete, but was derived from looking at the similarities between the velocity and position graphs, and how their slopes were related.

we did finish these the next day - all three from handwritten sheet

Acceleration -- the rate of change of velocity, how much the velocity changes over time

Average velocity -- how fast the object is travelling over a certain section of timedisplacement/time

Instantaneous velocity -- how fast the object is traveling at an exact point in time

No one should have the exact same results, because the length of the tapes were not exactly the same. Also, the slope of the ramp we let our carts slide down varied from group to group. Our ticker tape machines, while accurate, depended on where we stopped the cart and how long we let it decelerate. Therefore it was very difficult for everyone to get the same exact results. However, a lot of us got similar results, with equations just a couple digits away from being the same. 

This lab was good, in that it was easy to execute, but I feel the way we worked on it was ineffective. Instead of letting us all work on it ourselves and having to explain it a bunch of different times, I think it might have been better to teach us all the basics first and then let us do the lab. I somewhat agree -we should have done the instantaneous velocity part together - that is clear to me in hindsight!  You know what they say...  :)This lab took too long because everyone lagged due to the fact that they didn't really know what was going on. Otherwise, I enjoyed the ticker tapes.

Buggy Challenge

Block 6, Group 1: Rebecca Harvey, Aleksi Arostegui, and Nick Chan
By Rebecca Harvey

Summary: First, we figured out the speed of each buggy in centimeters per second by averaging out our data: the slow buggy was about 15 cm/s and the fast buggy was about 36 cm/s. From there, we constructed a position vs. time graph in which the fast buggy had a negative slope (-36) and the slow buggy had a positive slope (15). The point of intersection on the graph told us that the time would be around 4 seconds, and the position would be around 60 cm. In order to get more specific calculations, we set the equations of both lines equal to each other to find the exact position and time they would meet. Our calculations gave the position of intersection at 58.8 cm.

Picture of Setup and Picture of Whiteboard: