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 5 – due 6pm Sun. May 4
The reading assignment this week is precalculus Ch 5.2, 5.3, 5.5, and Ch 5.4 pp333-335. Physics reading is Ch 6.1 and Ch 4.1 to 4.4. 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. In the following questions, use the letters pi to stand for the number π in your answers.
1(a) Convert pi/3 radians to degrees.
1(b) Convert 45 degrees to radians.
1(c) How many radians are in a full circle of radius 1?
1(d) What is the arc length along a circle of radius 4 that subtends (draws out) an angle of 270 degrees?
2. Consider an angle theta associated with a point (x,y) on a circle of radius r (see first figure in Section 5.3).
2(a) Which of the following ratios is sin(θ)?
x/r
y/r
x/y
r/y
y/x
r/x
2(b) Which of the following ratios is cos(θ)?
x/r
y/r
x/y
r/y
y/x
r/x
3. What are the (x,y) coordinates of a point on a unit circle at an angle 60 degrees? Use sqrt() to express a square root, e.g., sqrt(2) is the square root of 2.
4. A right triangle has a hypotenuse of length 10 and a leg of length 6. What is the length of the other side?
5. Consider the relationship v = ω r
5(a) What physical quantity is represented by v?
5(b) What physical quantity is represented by ω ?
5(c) What physical quantity is represented by r?
6. Review Example 6.1 in Physics Ch. 6, and Example 12 in Pre-calculus Section 5.2. Describe specific details of questions you have from these related examples.
Physics Reading
1. Review the discussions of Newton’s Laws of Motion.
1(a) In words that make sense to you, what is Newton’s First Law of Motion? Give an illuminating example.
1(b) In words that make sense to you, what is Newton’s Third Law of Motion? Give an illuminating example.
2. What are the similarities and differences between mass, inertia, and weight?
3. The standard unit for force is a Newton (N). Which of the following is equivalent to a N?
kg
m/s^2
kg m/s^2
kg/(m/s^2) = kg s^2/m
Don't know how to tell
4. An object near the surface of the earth has mass 19.6 kg. What is the object’s weight?
2 N
9.8 N
19.8 N
192.08 N
Don't know how to tell
5. A net force of 10 N is applied to an object, resulting in an acceleration of 2 m/s^2. What is the object’s mass?
0.2 kg
2 kg
5 kg
10 kg
20 kg
Don't know how to tell
6. Review Example 4.2 in Physics Ch. 4.3.
6(a) Why are the forces N and w shown on the free-body force diagram not used for the calculations in this example?
6(b) In line (4.12), why is there a negative sign in front of f?
6(c) Describe specific details of questions you have from this example.
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 reason analytically and quantitatively. If you have not yet made progress towards this goal, please make an appointment to speak with Neal or Krishna. (#2)
Prompt 2: Give specific examples which detail how you have improved your ability to make sense of problems and persevere in solving them. If you have not yet made progress towards this goal, please make an appointment to speak with Neal or Krishna. (#1)
Retrospective
We are in week 5, the middle of the quarter. This seems a good time to consider your progress in the program so far. Tell some specific stories about high points of your learning over the past 5 weeks. Details are more compelling to your reader than generalities (as this sentence exemplifies).
Prospective
We are still in week 5, the middle of the quarter. This seems a good time to consider what you would like to accomplish in the next 5 weeks. Describe some specific successes you would like to have in the second half of the quarter.