PHL100Y1 Lecture : Descartes.docx

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29 Feb 2012

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Ren descartes (31 march 1596 11 february 1650) First part of his life spent with mathematical and science. Mathematician of the first order and a great physicist. Wrote the meditation and circulated it to friends and a friend of the priest who was the unofficial post draw for all of europe. He spent 18 hours a day writing letters. If you discovered something he would write and sent a letter (12 letters to everyone over. He carefully had left france by then and moved to holland as they were more tolerant. He was then taken to sweden by the queen who killed him by waking him up too early. Frame of the mediations and where he is going. He wants the audience to take in on his work what he calls meditations. Wants you to take it in and turn it in your mind. Read one and don t meditate, read the next until you get into it.

Related Questions

4. 3.5/6.5 points All Submissions Notes Question: SerEssen11.AE.06. .Question part Points Submissions 1 2 3 4 5 6 7 8
.5 .5 .5 1 1 0/1 0/1 0/1
1/15 1/15 1/15 1/15 1/15 5/15 0/15 0/15
Total 3.5/6.5 ... Example 1.6 Cartesian and Polar Coordinates
Goal Understand how to convert from plane rectangular coordinatesto plan polar coordinates and vice versa.

Problem (a) The Cartesian coordinates of a point in the xy-planeare (x, y) = (-3.37, -2.73) m, as shown in Active Figure 1.5 Findthe polar coordinates of this point. (b) Convert (r, ?) = (4.61 m,36.5Â°) to rectangular coordinates.

Strategy Apply the trigonometric functions and their inverses,together with the Pythagorean theorem.
Figure 1.5 Converting from Cartesian coordinates to polarcoordinates.

Solution
(a) Cartesian to Polar
Take the square root of both sides of Equation 1.2 to find theradial coordinate. r =
= 1 m

Use Equation 1.1 for the tangent function to find the angle withthe inverse tangent, adding 180Â° because the angle is actually inthe third quadrant: tan ? = = = 0.810
? = tan-1 (0.810) = 39.0Â° + 180Â°
? = 2Â°

(b) Polar to Cartesian
Use the trigonometric definitions, Equation 1.1. x = r cos? = (4.61m) cos 36.5Â°
x = 3 m

y = r sin? = (4.61 m) sin 36.5Â°
y = 4 m

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Remarks When we take up vectors in two dimensions in Chapter 3, wewill routinely use a similar process to find the direction andmagnitude of a given vector from its components, or, conversely, tofind the components from the vector's magnitude anddirection.

Exercise 1.6 Hints: Getting Started | I'm Stuck

(a) Find the polar coordinates corresponding to (x, y) = (3.11,1.28) m.
r = 5 m
? = 6Â°
Your response differs significantly from the correct answer. Reworkyour solution from the beginning and check each stepcarefully.

(b) Find the Cartesian coordinates corresponding to (r, ?) = (4.07m, 52.5Â°)
x = 7 m
y = 8 m

Anything you could do would help, but please explain slowly. Thanksagain. It is for my technical physics 115 class.

In order to solve the problem you must refer to the first partwhich i already solved and I am 200% sure of the answers, however Iam stuck on the second part and I need help asap. Please do not getscared when you look at this problem and thank you soo much inadvance.

A wheel 75 meters in diameter is mounted vertically on an infinitefrictionless plane at the origin. The infinite frictionless planehas a grid of Cartesian coordinates on it. The moment of inertia ofthe wheel is mr^2. The mass of the wheel is 2000kg. There is anengine connected to the wheel that can produce a torque of 2.34x10^6 Nm. There is a 50 kg object attached to the circumference ofthe wheel that is attached to the wheel with a remote releasemechanism. The wheel is placed on the origin so that the plane ofthe wheel contains the point x=50 meters and y=86.8 m. The wheel ispositioned so that the object is just above the plane at the 6o'clock position. The engine is engaged and begins to apply thetorque to the wheel at 12:00 noon on March 1, 2011. The wheelbegins to rotate in the counterclockwise direction. The torque isapplied for 4 x 10^4 revolutions. At that point the object isreleased from the wheel and a 75 Newton motor accelerates theobject in the direction it is released. The motor is fired for 2.34x 10^4 seconds. (the following questions i have already answered)What is the angular velocity and rotational KE of the object justbefore it is released? (answer for that is 6.39 x 10^2 rad/sec and5.89 x 10^11 J). What angle does the path of the object make withthe x axis? (answer is 60.05 degrees). Where is the object on theinfinite frictionless plane when the motor stops (what are itscoordinates....answer is x=4.85x10^8m y=8.40x10^8m). What is thevelocity and linear KE of the object when the motor stops?(5.91x10^4 m/sec and KE= 8.73 x 10^10J). How much work was done onthe object up until the time the motor stopped? (8.73 x 10^10J).(Hint: the mass of the wheel is 2050 kg while the torque is appliedand the object is attached).

YEA I know what you are thinking at this moment. Difficult right?Please give it a chance and have faith in yourself. Here is thepart I had difficulty with:

After the engine stops firing the object is turned around so thatthe engine can be used to stop the object. The motor is fired atits rated thrust to stop the object. Unfortunately it malfunctionsand shuts down after an hour and the object coasts from then on. Atthe end of an hour of coasting it encounters a ramp that is 2000meters high and slopes up at an angle of 20 degrees. The objectclimbs the ramp and flies off the ramp into the air when it reachesthe end of the ramp. It strikes the plane and digs a crater 5meters deep in the plane and comes to a stop. How far from the endof the ramp does it land? Where does it land on the plane (as incoordinates)? What is the resultant velocity of the object and whatis the acute angle of the resultant velocity with the plane when itstrikes the plane? What is the KE of the object when it hits theplane? What date and time is it when the object lands on the plane?How much work was done on the object to stop it? How long did ittake to stop? What was the deceleration of the object in m/sec^2?What was the force on the object in Newtons to stop it?

If you are from MIT I have faith that you can do this. I am only ajunior in high school taking first year physics that is not evenAP. My teacher is from MIT and said he did this kind of stuff whenhe was there. Please please please help me! I'm desperate.

1. If a car's wheels are replaced with wheels of greater diameter,will the reading of the speedometer change? Explain.

2. Weightlessness in space is known to have harmful effects on thebodies of people in space. To set up inhabitants (people) in space,it has been suggested that rotating cylinders about 10 miles longand 5 miles in diameter be placed in space. The purpose of theirrotation is to simulate gravity for the people so they have weight.Explain how this is possible?
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Please use DragMath to submit the solutions to problems No. 5 and 6of Activity 9A on page 129 of Bendall & Howison.
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1. Why do the string instruments go flat (lower frequencies) andthe wind instruments go sharp (higher frequencies) during aperformance if an orchestra doesn't warm up beforehand?
2. If you were carrying a fish tank filled with water, what willhappen if your walking frequency matches the natural frequency ofthe water in the tank?
Good luck with these questions. I look forward to a heartydiscussion by Friday this week.
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1. Household circuits are always wired so that the electricaldevices are connected in parallel. Why is this so?
2. How are circuit breakers connected in the household circuits(series or parallel)? What is the use of a circuit breaker? Why isit more advantageous to use a circuit breaker compared to using afuse?
Hope to hear your answers soon.
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Mathematical Question:
Try the question on capacitors Activity 14C no. 3. You can useDragmath to submit your solution. If you are scanning your answersand uploading a file, please keep its size small.
Challenge Question:
A fully charged parallel-plate capacitor remains connected to abattery while you slide a dielectric between the plates. Do thefollowing quantities increase, decrease, or stay the same? (a)capacitance, C (b) charge, Q (c) electric field, E between theplates, (d) change in voltage, V (e) energy stored in thecapacitor.
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Twisted wires: In electrical circuits, it is often the case thatinsulated wires carrying currents in opposite directions aretwisted together. What is the advantage in doing this?
Have a go; looking forward to some interesting replies.
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Metal detectors in airports: When you walk through the doorway ofan airport metal detector, you are really walking through a coil ofmany turns, i.e. an inductor connected to a resonant circuit tunedto the resonant frequency when there is no metal in the inductor.So how does this circuit detect any metal that is in your pocketwhen you walk through the metal detector?
Looking forward to your replies.
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PHL100Y1 Lecture : Descartes.docx

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