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:

Buggy Lab

Block 6 Group 1, Rebecca Harvey, Nick Chan, Aleksi Arostegui

Pre-Lab Notes:
-swerves left
-moves forward (position)
-lights up (flashes per sec)
-time

Focus on time and position -- IV/DV
Constant velocity (linear) equation: Xf =VT + Xo

Purpose: The purpose of this lab is to test the relationship between the time in second that the buggy is moving and its position as measured in meters.ok

Prediction: As the amount of time increases, the position of the buggy will increase proportionally.ok

Apparatus:

• Buggy
• Tape
• Meter stick
• Stopwatch/timer

Procedure:
1. Mark a flat area with tape to serve as the starting line. Make sure there is plenty of space in front of this line. This starting line is 0 meters.
2. Set the buggy directly behind the starting line, so that the front wheels are barely touching the edge of the tape.This buggy is facing a positive direction.good!
3. Ready the stopwatch.
4. Carefully, without moving the buggy, flip the start switch and start the stopwatch at the same time.
5. At five seconds, stop the buggy and use the meter stick to record its position.
6. Repeat steps 2-5, adding five seconds to the time each trial (10 seconds, 15 seconds, 20 seconds, etc.). Make 25 seconds your final time recorded, for a total of 5 trials.
7. Repeat all five trials, except start the buggy at -5 meters instead of 0 meters, still facing in a positive direction.good

Data Collection:
             Test 1                                                                    Test 2

Data Analysis: Test 1

Verbal Model: As the time in seconds increases, the position in meters increases proportionally.

Math model: position = 0.4748(meters/second)(time) - 0.28 meters

Slope: For every 1 second of time that passes, the position of the buggy moves by 0.4748 meters.

Y-intercept: When no time has passed, the position of the buggy is at -0.28 meters. This is close enough to 0 to be negligible.

Test 2

Verbal Model: As the time in seconds increases, the position in meters increases proportionally.
Math model: position = 0.4748(meters/second)(time) - 5.28 meters
Slope: For every 1 second of time that passes, the position of the buggy moves by 0.4748 meters.
Y-intercept: When no time has passed, the buggy's position is at -5.28 meters. This is close enough to -5 (the starting point) to be negligible.

Conclusion:
        The purpose of this lab was to test the relationship between the time in second that the buggy is moving and its position as measured in meters. In order to do this, we set up a starting point at 0 meters. We placed the buggy at this starting point and let it run for five second intervals. We recorded its position at each 5 second interval. We then created a starting point at -5 meters. We repeated the same tests, and recorded the data at 5 second intervals.
       We found that in both of the trials that as the time in seconds increased, the position in meters increased proportionally. We figured out a math model for the line of best fit for the first trail: position = 0.4748(meters/second)(time) - 0.28 meters. The second trial's equation was very similar: position = 0.4748(meters/second)(time) - 5.28 meters. Our slope for both trials was the same, at 0.4748 meters per second. This meant that in both trials, for every 1 second of time that passed, the position of the buggy moved by 0.4748 meters. This slope is the velocity of the buggy in both trials. The y-intercept represents the starting point of the buggy, or the initial position. Our y-intercepts were off by about 0.28 meters. This is about 2.5% error, and so within the general realm of error.good
       Our results supported our prediction, in that as the amount of time increased, the position of the buggy increased proportionally. This was true for both trials.
       The general physics equation derived form the x vs. t graph is Xfinal = velocity(time) + Xinitial. We got this from combining our regular y = mx + b equation with our math models to show velocity. The slope, again, represents the velocity, while the y-intercept represents the initial position.good
       In comparison with other groups, our results were very different at first glance, but when examined, we find that they weren't so different. Among groups, the average velocity recorded was about 45 cm per second. Ours was 0.47 meters per second. When you convert from meters to centimeters, you find that our results were similar. should we all have had same slopes?  why or why not?  However, with the second trial, there were several discrepancies. This is because groups were not performing the same experiment. Some groups started at different initial positions than we did, thereby affecting the final positions. Some groups moved in different directions, like we moved in a positive direction the entire time while some moved in negative directions. This leads us to conclude that with such different variables, the groups should not have gathered similar results in the second trial.
       Some sources of error include the fact that the buggy veered slightly to the left, meaning that it usually traveled a greater distance than we were able to measure accurately.excellent!   We could have changed our procedure to measure in a shorter amount of seconds, because the longer the buggy moved, the more off-course it veered, thus leading to more inaccuracy.perfect! Also, the reaction time from stopping the stopwatch and the buggy at the same time likely had a small effect, as it was unlikely that we stopped at exactly the right time. This is difficult to fix without some form of robotic help.ooh - coming soon!  just wait! There were probably discrepancies in measuring, because we had to stack meter sticks on top of each other. A tape measure would likely improve this aspect.
Distance -- how far something has traveled (path length)
Displacement -- change in position: Xfinal - Xinitial
Position -- location of something in relation to the origin (0)
Speed -- the measurement of how fast
Velocity -- speed and direction
        I enjoyed this lab because it was fun working with the buggies, and designing our lab's second trial was stimulating. In order to improve this lab I would suggest a shorter conclusion, because I feel like we covered all the necessary information in class or in our data analysis. yes  I know!  everyone hates the conclusion!  :)  great job!

Graphing Project

Block 6, Group 6, Rebecca Harvey, Aleksi Arostegui, and Blossom Wong

By Rebecca Harvey

Purpose: The purpose of the lab is to test how the height that a ball was dropped from would affect the bounce of that ball.

Independent Variable: The independent variable is the initial height (in ft) that the ball was dropped from. We chose this because it was easy to control and regulate.

Dependent Variable: The dependent variable is the highest point (in inches) that the ball bounced to. We chose this because it was easy to observe in its variations and use in calculations.

Controlled Variables: The dependent variables include the constant mass of the ball, constant conditions (no wind, even floor)

Summary: In this experiment, we set up a meter stick against a wall, so that the measurements would be accurate. We marked the heights that we were dropping the ball from (1 ft, 2 ft, 3 ft, 4 ft and 5 ft). We then held the ball at those marked heights and dropped it, without throwing it or using any sort of force. We carefully observed how high the ball bounced at each height and recorded it.

Photos:

Graph:

Analysis:

     Verbal Model: As the height in feet increases, the bounce in inches increases proportionally.

     Math Model: Bounce = 6.6 inches/feet (height) + 0.9 inches

     Slope: For every 1 foot in height, the bounce increases by about 6.6 inches.

     Y-intercept: When the ball is dropped from 0 ft above the ground (a.k.a. the ball is not dropped at all) it bounces about 0.9 inches. This data is significant enough to be problematic, meaning that our data is probably off. excellent work!