Patterning the World: Connecting Mathematics and Science – Spring 2014
The web-site for an interdisciplinary program that integrates introductory math and physics by finding, generating, and quantifying patterns
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Reading Responses and Reflection 6 – due 6pm Sun May 11
The reading assignment this week is precalculus Ch 8.2, 8.4, and 8.5 and physics Ch 3.2 (review), 3.3, 4.5, and 4.6. Remember to fill in all entries below - what you don't know after reading the texts is just as important to us as what you do.
Lastname, Firstname
*
Precalculus Reading
1. The idea of a trig circle of radius r is used to convert between cartesian coordinates (x,y) and polar coordinates (r, theta). Give exact answers (use a fraction) and use the sqrt() function to type in a square root.
1 a) What are the cartesian coordinates of the point with polar coordinates (1, pi/6)?
1 b) What are the cartesian coordinates of the point with polar coordinates (2, pi/2)?
1 c) What are the polar coordinates of the cartesian coordinates (6,8)? Use degrees for the angle? You can measure it with a protractor if you want.
2. What does the graph of the polar equation r = 3*sin(theta) look like? You may use Desmos if you wish.
3. What is the cartesian form of the equation r = 3*sin(theta)?
4. What is the effect of scaling a vector by -⅓?
5. Suppose due north is the positive y direction and due east is the positive x direction and consider a vector that points due east.
5 a) What is the value of the vector in polar form (r, theta)?
5 b) What is the value of the vector in component form?
Physics Reading
1. The weight of an object on Earth is 1000 N. What is its mass of the object on the Moon?
2 a) A 10 Kg block is at rest on a flat surface. What is the normal force?
2 b) If we have the same 10 Kg block at rest on a 30 degree incline, is the normal force the same as in part a)? (yes, no, don’t know)
3. On a beautiful winter morning, you are with your friend outdoors. You have the option of pushing (downwards) her sledge from behind with an angle of 30 degrees from the horizontal, or pulling (upwards) the sledge from the front with a rope with an angle of 30 degrees. Assume the friction of the sledge is negligible.
3 a) Would you rather push the sledge, pull the sledge, or do you think there’s no difference? (push, pull, no difference, don’t know).
3 b) Explain your answer for part (a)
3 c) Which action has the larger Normal force? (push, pull, same, don’t know)
3 d) Does it make any difference if there is friction between the sledge and the ground? (yes, no, don’t know)
3 e) Explain your answer for part (d).
Reflections
What would you like us to spend class time on from the precalculus readings?
What would you like us to spend class time on from the physics readings?
What material from the past week (or before) are you still having difficulty with? (Please do let us know, but also try to take advantage of all your resources: QuaSR, study groups, appointments with faculty, on-line tutorials & videos, etc.)
Prompt 1: Give specific examples which detail how you have improved your ability to construct viable explanations from evidence and discuss (with an eye to improving) the reasoning of others. If you have not yet made progress towards this goal, please make an appointment to speak with Neal or Krishna. (#9) *