Archimedes Challenge

Archimedes screw

  • design and building process/ construction of invention 

day one:

1.design drawing


2. made holes on 3 bottles

day two: cut off bottom of two bottles

day three:connect 3 bottles together, and twine the tube around the bottle.(same like drawing design)  

day four: mix water and ink. put the water into the bottle.

 

  • History

On a Sunday, Archimedes and his classmates went on a wooden boat, driving slowly on the Nile, and his eyes were dazzled by the charming scenery. Suddenly he saw a group of people carrying water in a bucket. “why do they carry water?” he asked.
“The river bed is low and the farmland is high, so the farmer has to carry the water.” A local student told him. “So the efficiency of carrying water is too low, and it is not sure how many barrels are to be carried by the water.” Archimedes had a sympathy for the peasants. The student said disapprovingly, “people do this. Do you have any good ideas?”
When Archimedes came back, he always had a picture of the farmer struggling with water. “Can you let the water run high?” Archimedes began to think about this problem. Gradually, in Archimedes’ mind, there was a vision: “make a big spiral and put it in a cylinder. In this way, when the spiral is turned, the water can be carried aloft along the spiral groove.
Archimedes immediately drew a sketch of the idea. He took this sketch to find the carpenter and asked the master to help him with a tool for pumping water. By Archimedes’s advice, the carpenter made a strange thing. Archimedes moved this thing to the river and put one end of it into the water, then gently shook the handle. The water was shaking the handle and coming out from the top of the thing. The water was flowing high.
The farmer, who came to see, was fascinated by this amazing thing. They praised Archimedes for doing a great deed for the peasants. Soon, the spiraling pumps were spreading in the Nile valley, even wider. This pump is called the archimedean screw pump. Until now, some modern factories still use this archimedean screw pump to move fluid and powder.

  • Explanation of physics involved  

Produced by using mechanical rotating centrifugal force, make the water produces the speed, following the upward spiral pipe wall, in the water rushed to the pipe wall, the pipe wall will continue to generate thrust, making the water flow from the bottom to the top.

To move stationary water from one place to another, force has to be applied. The forces involved are gravitational and normal forces. When the screw turns a half rotation, it scoops up water and holds it in a fixed position. Because the angle of the screw (Archimedes’ screw cannot be vertical), gravity and the normal forces in the screw thread and wall cause the water to be in a stable equilibrium position (a state in which opposing forces are balanced).

 

  • Reference

https://zhidao.baidu.com/question/1693911927468659268.html

https://wenku.baidu.com/view/ae995061ddccda38376bafb9.html

https://zhidao.baidu.com/question/1385953321594911500.html

https://en.wikipedia.org/wiki/Archimedes%27_screw

http://www.softschools.com/inventions/history/archimedes_screw_history/14/

https://en.wikipedia.org/wiki/Archimedes%27_screw

 

 

week 12 in pc

This week in Pre-Calc we learned about Solving Quadratic Inequalities in One Variable, Graphing Linear Inequalities in Two Variables, and Solving Quadratic Systems of Equations.

When solving Quadratic Systems of Equations you would solve algebraically, either with substitution, or elimination. You could also graph, but if your point of intersection is not on a prefect point, you will not be able to be completely accurate. To solve get everything equal to zero.

Example:

  • y = x2 – 5x + 7
  • y = 2x + 1

 

Make both equations into “y=” format:

They are both in “y=” format, so Set them equal to each other

x2 – 5x + 7 = 2x + 1

 

Simplify into “= 0” format (like a standard Quadratic Equation)

Subtract 2x from both sides: x2 – 7x + 7 = 1
Subtract 1 from both sides: x2 – 7x + 6 = 0

 

Start with: x2 – 7x + 6 = 0
Rewrite -7x as -x-6x: x2 – x – 6x + 6 = 0
Then: x(x-1) – 6(x-1) = 0
Then: (x-1)(x-6) = 0

Which gives us the solutions x=1 and x=6

Use the linear equation to calculate matching “y” values, so we get (x,y) points as answers

The matching y values are:

  • for x=1: y = 2x+1 = 3
  • for x=6: y = 2x+1 = 13

 

Our solution: the two points are (1,3) and (6,13)

mandala project

  1. Yes i was able to be an active listener and support & encourage others. At first my partner have no idea with what kind of mandalas does she want to do, so I share my ideas whit her. We did third one together, we mix our ideas.
  2. I hear different points of view from others but I am not disagree. I am ok with use others opinions.
  3. I share my ideas with my group, and did 2.5 mandalas(third one is I with another group member did)
  4. All our mandalas are connected. And our opinion is same.
  5. I took on a thinker role in my group, consider what kind of color or type.

 

week 11 in pc

This week in Pre Calculus 11 we learned about Graphing Linear Inequalities in two variables. The solutions to these inequalities are represented by a boundary line and shading one side of the line.

Ex:

key notes

 

choosing any coordinate (the easy one  is 0,0) and seeing if the statement is true or false.

 

Newton’s Three Laws

In Newton’s first law of motion states that an object will not change its speed of direction unless an unbalanced force affects it. In this video, we give the pen an apply force to make it move and accelerate. When there is no more force acts on the pen that was still moving at the same direction. One potential situation where the law may not apply is if the angle of the dask was altered, influencing the velocity of the pen.

 

In Newton’s second law of motion, more commonly known as F=ma where F refers to the total force, m is the mass of the object, and a is the acceleration of the object. It can be seen that if all existing forces are unbalanced, the resulting net force will cause acceleration of a mass. The acceleration of an object depends on the net force that acting on an object and mass of the object. As the acting force increased, the acceleration that is acting on an object is decreased. The Fnet (net force) equals mass times acceleration, an acceleration is produced by the Fnet. In the second video, there are two backpacks which means mass is increased. I used same amount of force to push the cart, and in the second video, the cart did not travel the same distance as the cart in the first video. The two videos show that given the same force is applied, when the mass is different, the acceleration also changes. These videos followed the rule of Newton’s second law of motion.

Errors: The ground was not flat, so it might cause an error. Forces that I put might not exactly the same, so it might cause an error. The videos that I used were not filmed well and was not long enough to see the results, so these might cause an error as well.

 

In Newton’s third law of motion, according to the formula F1=-F2 we could know that every action there is always opposed an equal reaction: or the mutual actions of two objects upon each other are always equal, and directed to contrary parts(that is why F2 is negative) .

In the video Justina pushed the wall, she gives a force to a wall, and a wall gives a force of equal size and opposite direction, and the counterforce makes Justina backward.

Newton’s third law applies only to practical forces, The imaginary force (such as inertial force and centrifugal force) is not applicable to Newton’s third law, and the imaginary force has no force of force and therefore has no reaction force.

 

 

week 8 in pc

This week in pc we analyzed the quadratic function. In the equation each variable represents something that can change the graph.

positive sign, the graph moves up, negative sign, the graph moves down.

positive sign, the graph moves right, negative sign, the graph moves left.

positive sign, the graph opens up, negative sign, the graph opens down.

greater than 1, the graph is stretched vertically, between 0 and1,

the graph is compressed vertically.