Simple machine project

TOILET PAPER


There are two practical usage of this object.
One is to turn it.
The other is to tear a part of it.
Therefore, there are two possible mechanical advantage of each movement.
Assumption : People pull off paper perpendicularly to the roll.

1. TURN (wheel)
     Force is applied, and it is increased by the distance (11.43 cm).
     Torque force is F*.11
     Actual applied force is acted 2.5 cm away from center.
     Therefore, .11/.025 = 4.4 is MA
2. TEAR (lever)
     F*x = force of tearing
     The force of resistance is acted at the center of mass, which is x/2
     Therefore, MA is 2

TREBUCHET PRoject

Youshin Kim, Daniel Jung, Rin Enatsu, Peter Han
Physics, Block 2
Mr. Elwer

Trebuchet Project

I. Introduction
    1. Background Info
        - Trebuchet uses potential energy of counterobject to throw an object.
        - The potential energy of counterobject will become the kinetic energy of a throwing object.
        - The team who will earn the highest efficiency will win provided that other elements like weight of counter object is same.
    2. Purpose
        - Students were to throw an egg using a trebucheet of their own.
        - The egg was to hit the point that was 25m away from the trebuchet. (Accuracy)
        - Students could feel the real world physics with real world experiment.
    3. Hypothesis
        - As the size of the trebuchet is limited, the one who can pull the most amount of potential
          energy, torc power, and least amount of energy loss will win.

II. Materials
     - Enough wood board
     - Two wood stick (throwing arm)
     - Basic design (We used FAT(Flying Arm Trebuchet), but changed into the classic one)
     - Cutting & assembling devices ( Zigsaw, saw, screws, a drill, etc )
     - a strong string (sling)
     - a bag to put an egg in.
     - screwable metal thing that is curved to form a hole
     - long metal stick
III. Experiment Design
     1. Prepare the place to work on. Buy all needed supplies, or collect left-overs that can be used as
          materials.
     2.  Sketch the design on the wood board.
     3. Cut the wood
     4. Assemble the wood using screws. (Pre-screwing is essential)
     5. After the assembly of body, prepare to make the slinger with the bag and string.
     6. Make two holes in the opposite site of the bag.
     7. Tie a string firmly on the holes.
     8. Make a trigger by putting two metal things on the board and putting a metal stick through them.
     9. Make throwing arm by connecting two long wood sticks.
    10. Put a nail with about 45 degrees at the end of the throwing arm. It is to put the slinger and let it
          go smoothly in the right direction.
     11. Test, and fix accordingly.

IV. Variables
     1. When competitng with other teams, the place and time should be same as different wind and
         geographicl features results in a totally different data. (Control)
     2. The counterweight should be less than 50 pounds. (Independent Variable)
     3. The size of a trebuchet has to be less than 1m^3 (Control)

V. Design
     1. Our trebuchet had 1m x 1m x 1m size.
     2. Its design was classic (thus, no reference page was needed in this project).
         The only difference was that its sling wasnt connected to the throwing arm.
     3. The slinger was made up of a string and a plastic bag.
     4. Other design is described at III.

VI. Data Table

Launch 1	Launch 2	Launch 3
∆x=16. 2 m	∆x= 11.4 m	∆x=13.6 m
Height of Angle = 42 degrees	Height of Angle= 38	Height of Angle= 43
Mass of an Egg = 60g	Mass of Counter Weight = 13.6 kg	Launch time = 2.6 s

 VII. Calculations.

	Launch 1	Launch 2	Launch 3
Max Height	3.6m	6.4 m	3.7 m
Launch Vy	9.1 m/s	11 m/s	9.2 m/s
Launch Vx	6.2 m/s	4.4 m/s	5.2 m/s
Launch angle & Velocity	55 degrees 11 m/s	68 degrees 12 m/s	61 degrees 11 m/s
Average Acceleration of Trebuchet	12 m/s2	13 m/s2	12 m/s2
Force and Impulse of Trebuchet	.74 N .63 Ns	.80 N .66 Ns	.70 N .72 Ns
Mechanical Advantage and Efficency	1 (due to inaccurate numbers and less sig. fig.)	1.16 (simply wrong. Due to inaccurate measurement- probably at the launch time)	.84 (acceptable(?))

VIII. Conclusion

   The launch angle was significant element that could be overlooked. Inaccurate models had capricious angle values; thus, the distance was varying as well. In other words, besides the body, the slinger was important factor in the efficiency of a trebuchet.

Mouse Trap Car Project

I. Intro
  By using a mousetrap as a single power generator, students had to build a car that can go at least five meters.
II. Hypothesis
  As the force is proportional to the mass and acceleration, the heavier a car is, the slower and lesser the car will go.
III. Project
  Daniel and Armoni met few times at evenings in each other's houses for average two hours. At sunday, we built the basic design. At monday, we checked that we had some technical difficulties to carry out the design. Thus, we decided to use last year's leftovers instead. It turned out that the last year's one was too heavy. The body's conjuncture point with the wheels also had so much friction as well. At last day, we finally figured out how to use the last year's one.
IV. Success and Failures
   The car was relatively light, so it went all it could go in a few quick seconds. The technique we used to move the car caused so much friction in the axis of the wheel that we assume we lost much power. After tying the string in the axis, we put it in the base of a car that has a hole for the string to come out. When we actually used it, the string had to have the force enough to turn the axis as well as to move the axis enough for the string to be in line with the hole.
V. Discoveries
   .We found out that the wheels had to have certain amount of friction to flowly go on a surface. We discovered that the stick that we used is better off when it's long because of basic principles of torc power. However, the length had to be enough for the stick not to break off. The wheel, in the same way as the stick, is better off when it is large. However, it can't be too heavy.
VI. Laws
    F=ma
    Torque=Fr
    Friction= coefficent of friction * Normal force
VII. Conclusion
    The lighter, the faster. However, it doesn't always mean the longer because the car has cerain efficiency in using power.

Experiment : Trajectory LAB

Daniel Jung
Eddie Park, Peter Han
Physics/ 2
Mr. Elwer
Procedure
    1. Prepare materials : balls , cones for measurement, a tape measure, angle measurers.
    2. Go to an even field.
    3. Stand in an appropriate place to throw and set an approximate point for the ball to fall.
    4. Find the midpoint between the throwing point and falling point.
    5. Another person have to stand on the midpoint. Step back perpendicularly so that the person can measure the angle of the ball in the air.
    6. Throw the ball.
    7. The second person will measure the angle of the ball at the highest point by using the angle measurer.
    8. The other person will set the cone at the point at which the ball's dropped at.
   
    9.  Measure the distance between the starting point and the dropped point.
   10. Calculate the initial velocity of the ball.



















< The ball's thrown by x degree from the horizontal line>

Data&Analysis

Trials	1st	2nd
Distance	15.9m	15.0m
	15.45m
Angle	52⁰	60⁰
Average Height	12m

    1. The highest height can be measured by trigonometric method. We can get the averaged length by calculating (2.0+7.0tan52+2.0+7.0tan60)/2 = 12.
    2. Using the background knowledge that the ball's vertical velocity is zero at its highest point, we can come up with this equation. -12 indicates the height.

h = h_i + v_it + at²/2= (-12) = 2+ 0 + (-9.81)t²/2

t= 1.689 = 1.7s (the time for the ball to reach its highest point)

Then, we can figure out the initial, vertical velocity (v_y).

0 = v_y + at = v_y + (-9.81)(1.689)
Thus,
v_y = 16.5735 = 17 m/s

As the horizontal velocity is constant,

v_x = 15.45/1.689 = 9.14742 = 9.1 m/s

Using pitagorian theorem,

vi = (9.1² + 17² )^1/2= 19 m/s

Degree x= arctan((12-2)/7.725) = 54 degrees

Experiment: Acceleration on an Inclined Track

Daniel Jung
Tyler Moore, Dil Querido
Physics/ 2
Mr. Elwer

Introduction
   1. Background info
      Acceleration is equal to the rate of a change of velocity. Thus, in the velocity versus time graph, the slope is acceleration (m/s^2). The coefficient of the acceleration is reveals the direction related to the sensor.
      If a cart moves on a tilted plane with the angle of θ, the force to move it along the surface is equal to mgsinθ. g is the acceleration constant of gravity on Earth. gsinθ is the actual acceleration on the tilted plane.
   2. What concept is being explored/ investigated
      The relationships between acceleration, velocity, and position. The meaning of the plus and minus signs of them. The motion of an object on a tilted plane where there is no other major forces except gravity.
   3. Purpose of the experiment
      Students will get accustommed to Xplorer GLX. Students will know the relationships between position, velocity, and acceleration by graphs measured by GLX.
   4. Hypothesis
      As the force is constant by mgsinθ, acceleration will be constant by sin θ. As the cart starts away from the sensor, comes, stops, and goes away, the velocity will start from negative value to positive value. The slope of the velocity graph will be constant. The position-time graph will be from positive(as the position is the distance from the sensor) ,and it will decrease and increase, showing u shaped graph.

Materials
   1. a mini-car
   2. a PASCO track for the car to move on
   3. a xplorer GLX
   4. a GLX motion sensor
   5. couple of books to make an inclined track
   6. a computer to save graphs from GLX

Experimental Design
   1. The experiment will measure the position of a mini-car according to time. The position should be varied only by gravity. Thus, the track should be plain and has as little, or regular friction as possible. The car will move along the track linearly, and the motion sensor that's attached to the track will measure the exact distance between itself and the car. The car will be pushed by hand softly.
   2. Controlled Variables :
     a. The angle of the inclined track, or gravitational acceleration (g sinθ).
     b. The friction of the track. The track should be dry, clean and even.
     c. The shape and mass of the mini-car
     d. The force toward the car will exist only at the first time where a hand pushes the car. Thus, the experiment will be done in an isolated room without any fan or airconditioner.
     * As this experiment is to see the relationship with position, velocity, and acceleration, there will be no independent (or manipulated ) variable.
   3. Dependent Variables :
     a. both average and instantaneous position, velocity, and acceleration.

Procedures
   1. Attach the motion sensor to GLX.
   2. Turn the GLX on.
   3. Make an inclined track using books. Beware to make the track as even as possible, so avoid using uneven books.
   4. Attach the motion sensor at the end of a track where books are located.
   5. Put the mini-car at the bottom of the track.
   6. Activate the sensor through your GLX.
   7. Push the car softly but firmly toward the sensor. Control the strength so that the car can stop no closer than 15cm to the sensor. Otherwise, the measurement will become inaccurate.
   8. Finish the measurement through your GLX when the car returns to the initial position.
   9. Repeat the measurement until the graph seems natural and without radical change.
   10. Record the position-time graph.
   11. Change the y-axis to velocity (m/s) on GLX. (check-check-menu-more-velocity)
   12. Use the arrow keys to put the cursor to the point on the graph where the linear movement started.
   13. Press F3 to open the 'Tools' menu.
   14. Select 'Linear Fit' and press the check button.
   15. Record the data and graph.
   16. Again, press F3 to open the tools menu. Deselect 'Linear Fit'.
   17. Change the y-axis to acceleration as it's done in 11.
   18. Move the cursor to the initial point of the movement.
   19. Press the check button to open the tools menu. Activate the 'Statistics'.
   20. Record the data and graph.

Data Table (Data is included in the graphs) (SI units (m, s) are used)
   1. Velocity-Time graph

2. Acceleration-Time graph



   3. Relationships
     The slope of velocity-time graph is same as the average acceleration. Both are some 1.0 .
     Also, the slope of the position-time graph is same as the velocity. The sign of the velocity shows the direction of the car.

Conclusion
   1. The slope of position-time graph was same as the velocity. The slope of the velocity-time graph was same as the acceleration.
   2. The sign of the values represented direction of the car 
   3. Visible Errors : The graph, especially acceleration-time graph, is not completely even. The error can be derived from uneven friction of the track, uneven, or rusted wheel of the mini-car, or inaccuracy of the sensor.
   4. Recommended Improvement : The most accurate, if possible, way to measure this relationship will not include a wheel. Also, it may be done on a evenly-cut ice to reduce the friction.
   5. Questions from the worksheet
       1. The sensor can calculate the distance between itself and a moving object. Thus, if the object comes toward a sensor, it means the total distance becomes shorter. That' why the distance value in the graph decreases as the object, a cart, moves up the inclined plane.
       2. The velocity was increasing. The slope of the velocity was constant.
       3. Accelaration value didn't show major change. The slight curves inside the straight line may suggest the unevenness of the surface, or inaccuracy of the sensor.
       4. The correlation between the slope of velocity and the average acceleration is very strong. They are almost same.

Experiment: Physics and Measurement

Data

Block #	K	G	F	P	10	M
Trial #	1	2	3	4	5	6
Length (cm)	7.55	3.60	3.55	7.50	7.75	7.30
Width (cm)	7.35	3.60	3.70	7.35	10.15	7.50
Thickness (cm)	4.30	5.90	5.50	3.65	3.85	4.25
Mass (kg)	.0824	.03872	.03890	.16108	.17726	.09665

Analysis

1.

Trial	1	2	3	4	5	6
Volume (cm3)	238.	76.5	72.2	201.	303.	233.

2. The textbook's experiment was different from what we did. We didn't measure one wooden block over and over. Instead, we used many different ones. As a result, number 2 can't be answered. However, it's obvious that multiplying inaccurate numbers can result in a huge discrepency between the real, and calculated value.

3. The initial height that the blocks fell was not long. It was as tall as three forths of a experimenter, and it made the blocks fall quickly. Then, the short amount of time brings a trouble. It's because experimenters could make mistakes using stop watch. The mistake could change the whole result by significant amount. In short, the values aren't 100% reliable.

    However, the result does show that the blocks are falling in similar amount of time. Most of them are surprisingly falling at the same time. The others are falling at the similar time, but the values are slightly different in our data.

    This slight differences can also mean that heavier blocks cost more time to fall than lighter blocks. Validity of the values aren't high, so it's hard to conclude.

4.

    x - axis : distance
    y -axis : time
    < Detail >

Trial #	Distance (m)	Time (s)
1	1	.41
2	1	.41
3	1	.41
4	1	.56
5	1	.50
6	1	.56

Conclusions

5.

Trial	1	2	3	4	5	6
Ratio (kg/cm3)	0.000346	0.000506	0.000539	0.000801	0.000585	0.000415

The ratio is density. Although all wooden blocks were made from same material, their density varies in our data.

6. An experimenter dropped the wooden block according to the rhyme from the one who held the stop watch. 

"one, two, three, four!"

The two experimenters could be bad at rhymes, so this might cause an error.

Meanwhile, the one who held stop watch could click it later or sooner than reality.

This might be another reason.

Also, while measuring the blocks, experimenters confidently recorded estimated values, as well. In this process, subjectivity might come in, and it could lead to an error.

7. The suggested exercise may reduce personal errors. It may be more accurate than experiments with a single measurer. However, this doesn't solve all problems. The problem occurs because it's human that measures the time. However fast the reaction time is, there is still a reaction time. In short, an average value doesn't mean an accurate value.