511-problem solving strategy

 

Nilgün ÖZTÜRK /PHED / Assignment – 1

PART 1

‘Just before finals you decide to visit an amusement park set up in the Metrodome. Since it is a weekend, you invite your favorite niece along. She loves to ride on a Ferris wheel, and there is one at the amusement park. The Ferris wheel has seats on the rim of a circle with a radius of 25 m. The Ferris wheel rotates at a constant speed and makes one complete revolution every 20 seconds. While you wait, your niece who has a mass of 42 kg, rides the Ferris wheel. To kill time you decide to calculate the total force (both magnitude and direction) on her when she is one quarter revolution past the highest point. Because the Ferris wheel can be run at different speeds, you also decide to make a graph which gives the magnitude of the force on her at that point as a function of the period of the Ferris wheel.’

FOCUS ON THE PROBLEM Construct a mental image Described objects – Ferris wheel Initial situation – It is not important for this problem. Final situation – Quarter revolution past the highest point. How do the objects move or change? – Ferris wheel rotates at a constant speed. Interactions between the objects? – Forces between niece and the seat of the ferris wheel. Sketch a picture Are all the important objects, times, motions and interactions shown in the sketch? – Yes. Determine the question A) What is the total force in both magnitude and direction on niece when she is one quarter revolution past the highest point? B) Make a force versus period graph for the Ferris wheel.
	Summarize useful given information What information do we really need? – We need m of niece, r of Ferris wheel, period, acceleration due to gravity. What information don’t we need? – We need all information given in the problem to solve it. Is there any information we can reasonably infer? – No Select a qualitative approach for describing the motion and interactions of objects Which physics principles could be used in solving this problem? – Vertical Circular Motion ; Weight and Normal Force, No Radial Force Components. Are there any special conditions required in order to use these principles? – No Is all the necessary information given to use this approach? – Yes. Would it be useful to break the problem into two or more simpler sub-problems? – Net force is one part and the sketching a graph is another.

DESCRIBE THE PHYSICS Construct motion diagrams to show important space and time relationships of each object. What coordinate axes are useful? – X horizontal Are other diagrams necessary? – Yes for more detailed vector components of F.                            Assign specific symbols to the variables in diagrams and defined the variables, specifying knowns and unknowns .                  Declare target variable Which of the unknowns must be determined to answer the question? – Q must be determined and the speed of the niece must be determined. State general quantitative principles and relations What general relationships hold between the variables described in the diagrams? –       Fcos(Q) = m v2/r and Fsin(Q) = mg During what time intervals do these relationships hold? –       When she is one quarter revolution past the highest point.

  

PLAN THE SOLUTION Construct specific equations: v = 2πr / T find v. Fcos(Q) = m v2/r Fsin(Q) = mg By using these equations find Q. F = √[(mg)² +(mv² / r)²] find F. Checked for sufficiency.  It’s o.k.

SOLUTION The niece’s velocity is; v = 2 π r / T                                           = 2 π 25m / 20s                                           = (3,14) × (2,5) m/s =  7,85 m/s = v = × (25 m) / (7,85m/s)² 88,2 º The direction of force is 88.2 º above the horizontal. Squaring and adding  Fcos(Q) = m v2/r  and  Fsin(Q) = mg ; Therefore F= 424,42 Newton Therefore the magnitude of the force is 424,42 Newton and 88,2 º above the horizontal. If T increases, v will decrease so F will also decrease.

EVALUATION Is the answer properly stated? – Yes, units are convenient because we found force’s unit as Newton and tetha’s unit as ‘degree’as we guessed. Is the answer reasonable? – Yes all values are logical because for a 42 kg object and 25 m radius of ferris wheel the magnitude of the force as 424.42 newton is reasonable. Tetha is also in the sama vein. Is the answer complete? – Yes.

REFERENCES:

–        For the format of problem solving strategy the worksheet given and the online document below is used.

[Online Document] http://serc.carleton.edu/sp/library/context_rich/problem_solving.html

–        For the physical solution of the problem Young & Freedman (12th edition) is used as a guide.

PART 2

Problem: After a tiring week, you want to do entertaining activities in weekend then call your boyfriend. He suggest to play with his remote-control car with mass 1.60kg which you gived to him as a birthday gift last weekend. Then you accept the proposal.  When you play with the car you realized that it moves at a constant speed of 12.0 m/s. Then you decide to make a metal cylinder that has a radius of 5.00m from your boyfriend’s small fry to make the play more entertaining.  After that you put the car in this vertical circle inside a hollow metal cylinder. Car turns in the cylinder a lot of times then your boyfriend wonder how the car do not drop from the top point. At that time, you decide to explain him firstly the magnitude of the normal force exerted on the car by the walls of the cylinder at the bottom of the vertical circle. After that you want to answer his question by finding the magnitude of the normal force again but this time at the top of the vertical circle. Do it! :)

FOCUS ON THE PROBLEM Construct a mental image: Described objects – Car and a hollow metal cylinder Initial situation – Car is at the bottom Final situation – Car is at the top How do the objects move or change? – Car moves at a constant speed in circle. Are there interactions between the objects? – Forces between the hollow metal cylinder and the car. Sketch a picture : Are all the important objects, times, motions and interactions shown in the sketch? – Yes.

Determine the question: A) What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point B(bottom)? B) What is the magnitude of the normal force exerted on the car by the walls of the cylinder at point T(top)? Summarize useful given information: What information do we really need? – We need m of car, r of path, speed of car and acceleration due to gravity. What information don’t we need? – We need all information given in the problem to solve it. Is there any information we can reasonably infer? – No Select a qualitative approach for describing the motion and interactions of objects: Which physics principles could be used in solving this problem? –        Vertical Circular Motion ; Weight and Normal Force, No Radial Force Components. Are there any special conditions required in order to use these principles? –        No Is all the necessary information given to use this approach? –        Yes. Would it be useful to break the problem into two or more simpler sub-problems? –        Yes, because it has two sub-parts principally.

DESCRIBE THE PHYSICS Construct motion diagrams to show important space and time relationships of each object. What coordinate axes are useful? – Y vertical Are other diagrams necessary? – No. Assign specific symbols to the variables in diagrams and defined the variables, specifying knowns and unknowns. Declare target variable. Which of the unknowns must be determined to answer the question? – centripetal acceleration must be determined. State general quantitative principles and relations. What general relationships hold between the variables described in the diagrams? and

PLAN THE SOLUTION Construct specific equations:   Check for sufficiency: Three unknowns and three equations. Outline the math solution: Solve third equation then by using it solve first and second equations.

SOLUTION:

EVALUATION Is the answer properly stated? – Yes, units are convenient because we found forces’ unit as Newton as we guessed. Is the answer reasonable? – Yes all values are logical because for a 1.60 kg object and 5.0 m radius of cylinder the magnitude of the force as 61.8 and 30.4 newton is reasonable. Is the answer complete? – Yes.

REFERENCES:

–        For the format of problem solving strategy the worksheet given and the online document below is used.

[Online Document] http://serc.carleton.edu/sp/library/context_rich/problem_solving.html

–        For the writing a context rich problem the websites below are used as a guide.

[Online Document] http://groups.physics.umn.edu/physed/Research/CRP/crcreate.html

[Online Document] http://groups.physics.umn.edu/physed/Research/CRP/crintro.html    

–        For the skeleton of the problem Young & Freedman (12th edition) is used as a guide.

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