Astronomy quiz question: in the moon's umbra

Astronomy 210 Quiz 3, fall semester 2011
Cuesta College, San Luis Obispo, CA

What type of eclipse is seen by an observer on the side of Earth facing the sun, located in the umbra of the moon?
(A) An annular solar eclipse.
(B) A partial solar eclipse.
(C) A total solar eclipse.
(D) A total lunar eclipse.
(E) A partial lunar eclipse.

Correct answer: (C).

Section 70158
Exam code: quiz03sO1L
(A) : 2 students
(B) : 6 students
(C) : 17 students
(D) : 11 students
(E) : 0 students

Success level: 52% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.52

Section 70160
Exam code: quiz03N1rE
(A) : 4 students
(B) : 5 students
(C) : 14 students
(D) : 1 students
(E) : 3 students

Success level: 54% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.86

Whiteboards: concept mapping, single-error problem solving

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http://www.flickr.com/photos/waiferx/6196377403/
Originally uploaded by Waifer X

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http://www.flickr.com/photos/waiferx/6196377471/
Originally uploaded by Waifer X

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http://www.flickr.com/photos/waiferx/6196889284/
Originally uploaded by Waifer X

Student whiteboard concept maps for "commuting to Cuesta," Physics 205A, Cuesta College, San Luis Obispo, CA. Photo taken by Cuesta College Physical Sciences Instructor Dr. Patrick M. Len.

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http://www.flickr.com/photos/waiferx/6196889524/
Originally uploaded by Waifer X

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http://www.flickr.com/photos/waiferx/6196378079/
Originally uploaded by Waifer X

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http://www.flickr.com/photos/waiferx/6196378265/
Originally uploaded by Waifer X

Student whiteboard concept maps for "Newton's laws," Physics 205A, Cuesta College, San Luis Obispo, CA. Photo taken by Cuesta College Physical Sciences Instructor Dr. Patrick M. Len.

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http://www.flickr.com/photos/waiferx/6196889686/
Originally uploaded by Waifer X

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http://www.flickr.com/photos/waiferx/6196378133/
Originally uploaded by Waifer X

Student whiteboard concept maps for "friction," Physics 205A, Cuesta College, San Luis Obispo, CA. Photo taken by Cuesta College Physical Sciences Instructor Dr. Patrick M. Len.

110929-1270028
http://www.flickr.com/photos/waiferx/6196378315/
Originally uploaded by Waifer X

Student whiteboard solution with a deliberately inserted (and subsequently highlighted) error for Giambattista/Richardson/Richardson, Physics, 2/e, Problem 3.55(b)-(c), Physics 205A, Cuesta College, San Luis Obispo, CA. Photo taken by Cuesta College Physical Sciences Instructor Dr. Patrick M. Len.

110929-1270029
http://www.flickr.com/photos/waiferx/6196890124/
Originally uploaded by Waifer X

Student whiteboard solution with a deliberately inserted (and subsequently highlighted) error for Giambattista/Richardson/Richardson, Physics, 2/e, Practice problem 4.13(b), Physics 205A, Cuesta College, San Luis Obispo, CA. Photo taken by Cuesta College Physical Sciences Instructor Dr. Patrick M. Len.

Astronomy quiz archive: telescopes

Astronomy 210 Quiz 3, fall semester 2011
Cuesta College, San Luis Obispo, CA

Section 70158, version 1
Exam code: quiz03sO1L

Section 70158

Quiz 3 results (max score = 40):
   0- 8.0 : **  [low = 6.0]
 8.5-16.0 : **********
16.5-24.0 : ************  [mean = 20.5 +/- 8.3]
24.5-32.0 : ********
32.5-40.0 : ****  [high = 40.0]

Section 70160, version 1
Exam code: quiz03N1rE

Section 70160

Quiz 3 results (max score = 40):
   0- 8.0 : *  [low = 7.0]
 8.5-16.0 : **
16.5-24.0 : **********
24.5-32.0 : *******  [mean = 24.9 +/- 8.3]
32.5-40.0 : ******  [high = 40.0]

Physics presentation: energy

Isn't there a better way to get up a steep hill with a bicycle? Well, other than walking your bike up the hill...

Oh wait, I guess there is. And only just a few kröner? This ride would be a bargain at any price. (Video link: "Bicycle Lift ‘Steep is nothing’ -Panasonic ecoideasnet.")

We'll introduce different forms of energy and one particular form of energy transfer, and apply the principle of conservation of energy to situations like this.

Starting off with three forms of mechanical energy--translational kinetic energy, gravitational potential energy, and elastic potential energy (with a few more to follow later on in this course.) And a form of adding or subtracting mechanical energy: work.

Translational kinetic energy is the energy of motion. (We'll deal with rotational motion later on.)

Translational kinetic energy depends quadratically on speed, and the resulting units of kg·m^2/s^2 are also expressed as joules. A stationary object has no translational kinetic energy, and the faster the object moves, the more translational kinetic energy it has.

Gravitational potential energy, as all potential energy forms, is a stored form of energy. Here an object that is at the top of its trajectory has a maximum amount of gravitational potential energy, which here will soon be converted to translational kinetic energy.

Gravitational potential energy (for objects near the surface of Earth) depends linearly on height, and the units are again, also expressed as joules. An object at ground level has no gravitational potential energy, and the higher an elevated object is, the more gravitational potential energy it has.

Elastic potential energy is another form of potential, or stored energy. An object that exerted on by a restoring force has elastic potential energy, which here will soon be converted to translational kinetic energy.

Elastic potential energy depends on the strength of the elastic material (e.g., the "strength" of the spring, or bungee cord), and quadratically on the displacement of the elastic material from its equilibrium (whether by compressing or stretching). The units of elastic potential energy are given in N·m, or yet again, joules.

To start off, or to end all these transfers between these three (so far) mechanical energy forms, "non-conservative" work needs to be done, which occurs when we add energy in, or remove energy from mechanical energy forms. In general, work is not a form of energy, but transfer to or from energy forms.

Work is accomplished by exerted a force on an object, but in such a way that the object moves through a displacement ∆r, and the angle between the tail-to-tail force and displacement vectors is anything besides 90°. The units of work are given in N·m, or yet again, joules, so keep in mind that work can be transferred into or out of any mechanical energy form or forms.

Let's put all these concepts together by applying the principle of energy conservation.


Limiting the scope of our discussion to mechanical energy forms, they can either change by increasing or decreasing (resulting mathematically in positive or negative delta signs), but all changes on the right-hand side of this equation, overall, must be balanced by a corresponding amount of non-conservative work on the left-hand side.

Consider this catapulted squirrel. Assuming that the trajectory of the squirrel is approximately horizontal (such that there is no change in gravitational potential energy), and neglecting friction and drag (so no non-conservative work done), how do the remaining terms in the energy conservation equation increase or decrease? (Video link: "squirrelcatapult.gif.")

A kid sliding down an (ideally frictionless) slide. With no springs or bungee cords involved, and neglecting friction and drag (so no non-conservative work done), how do the remaining terms in the energy conservation equation increase or decrease? (Video link: "Whoosh!")

Don't blink, or you'll miss Mrs. P-dog in action! Note that she starts from rest below the screen, and then reaches the highest point in her trajectory, momentarily stationary, such that there is no initial-to-final change in kinetic energy. Neglecting friction and drag (so no non-conservative work done), how do the remaining terms in the energy conservation equation increase or decrease? (Video link: "110530-1230869-excerpt.")

Note as this car stops, the brakes glow from the heat generated! Since this is a horizontal track, and no springs or bungee cords are involved, then both gravitational potential energy and elastic potential energy forms do not change. So how does the remaining translational kinetic energy term in the energy conservation equation increase or decrease, along with the amount of non-conservative work done? (Video link: "McLaren SLR review - Top Gear - BBC.")

As a closing example, let's just watch and appreciate the perfect storm of energy conservation with an all-terrain vehicle performing non-conservative work on stretching a bungee cord (with elastic potential energy) attached to a raft and rider at the top of a ramp (with gravitational potential energy), all of which transfer to...translational kinetic energy. Whee! (Video link: "Human Slingshot Slip and Slide - Vooray.")

Physics presentation: uniform circular motion

Playground roundabout--check. Rear wheel of a motor scooter--check. Video camera--check. Willing participants--check. What could possibly go wrong? (Video link: "Roundabout, Crawley, West Sussex, UK" (video no longer available). Related link: "'Lethal' Playground Stunt Blasted.")

Why did the riders on the roundabout get flung off? What would have been needed for them to stay on the roundabout? Well, why is...those things? Because...physics.

First we'll look at the requirements for circular motion, and then we'll apply those concepts to several real-world examples of circular motion.

Recall that circular motion is covered by Newton's second law. Even restricted to uniform circular motion (constant speed along circle), Newton's second law still applies, as the direction is continuously changing, and the acceleration a = v²/ralways points in towards the center.

In fact, this is the requirement for uniform circular motion--in order to maintain constant speed along a circular trajectory, with acceleration directed in towards the center, the net force (the addition of all forces acting on the object) must be exactly equal to mv²/r, and be directed in towards the center.

Most simply we can satisfy this net force requirement with just one force. Here a mallet continuously taps inwards on a bowling ball, and as a result the bowling ball undergoes uniform circular motion. The net force (supplied by tapping) points inwards, which is along the centripetal ("center-seeking") direction.

No tapping, no inwards net force, and no uniform circular motion--the bowling ball then rolls at constant speed in a straight line, subject to Newton's first law. (Video link: "David and Alan hit a ball so that it travels in a circle.")

Similarly, pulling on a string can satisfy this net force requirement by pulling inwards on a donut, and as a result the donut undergoes uniform circular motion. The net force (supplied by the string) points inwards, which is along the centripetal ("center-seeking") direction.

(If the string breaks, then there would be no inwards net force, and no uniform circular motion, such that the donut undergoes free fall--subject to Newton's second law vertically, but Newton's first law horizontally, and thus would be seen moving in a straight line seen from above). (Video link: "Filippenko and the moon’s orbit demonstration.")

What about centrifugal ("center-fleeing") forces? For the purposes of this course (limited to Newtonian physics in inertial reference frames), we'll consider centrifugal forces as being "fictitious forces," as someone undergoing uniform circular motion (such as this stuntman) would describe themselves as being flung outwards. However, analysis of the actual forces acting on that person undergoing uniform circular motion would in fact be inwards (here, supplied by the stuntwoman on the stuntman). It's perfectly natural to think about "feeling" centrifugal forces when personally experiencing uniform circular motion, but in applying Newton's laws, concentrate on the actual forces that act on you when undergoing uniform circular motion.

Let's apply this centripetal requirement for net force to various examples of objects experiencing uniform circular motion.

As the car and motorcycle both undergo uniform circular motion, what direction is the net force on them? Which force(s) contribute to the net force? (Video link: "Motorcycle vs. Car Drift Battle.")

As the woman (momentarily) undergoes uniform circular motion at the bottom of her swing, what direction is the net force on her? Which force(s) contribute to the net force? (Video link: "hanging rock rope swing bella.")

As the motor scooter undergoes uniform circular motion, what direction is the net force on it? Which force(s) contribute to the net force? (Video link: "WALL OF DEATH (homemade) the SCOOTER did it amazing.")

As the car (momentarily) undergoes uniform circular motion at the top of the loop-the-loop, what direction is the net force on it? Which force(s) contribute to the net force? (Video link: "Fifth Gear Loop the Loop.")

As a person undergoes uniform circular motion in this carnival ride, what direction is the net force (as seen from the side)? Which force(s) contribute to the net force? (Video link: "Blake and Chris being kicked off the Rotor at Luna Park.... lol.")

As the car (momentarily) undergoes (an approximation of) uniform circular motion careening over the top of this hill, what direction is the net force on it? Which force(s) contribute to the net force? (Video link: "DC Shoes: Ken Block’s Gymkhana Five: Ultimate Urban Playground; San Francisco.")

As the skateboarder (momentarily) undergoes uniform circular motion at the top of the loop-the-loop, what direction is the net force on him? Which force(s) contribute to the net force? (Video link: "Bob Burnquist Loop of Death.")