OPENING QUESTION: <None Today>
LEARNING OBJECTIVES: Getting it done
WORDS O' THE DAY:
- Centripetal ("towards the center")
Centrifugal("away from center")- Gravitational Constant: G = 6.674 × 10-11 Nm2/kg2
- Period ("Time to complete one orbit")
FORMULAE OBJECTUS:
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T2 ∝ A3: The square of the period (in years) of an object orbiting the sun is proportional to the cube of the average distance to the sun (in years). This is kind of archaic in that we rarely see the proportional symbol anymore.
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T2 = a3: The square of the period (in years) of an object orbiting the sun is approximately equal to the cube of the average distance to the sun (in years). We MUST keep in mind this is an observational relationship. Although it gets us close (in most instances) it is not an exact value so the "=" sign isn't really appropriate although it is widely used.
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MsT2 = a3: This version is still approximate but it allows us to substitute in the mass of *other* stars as long as we measure the mass of the other star in terms of the mass of the sun being 1.00
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T2 = (4π2/GM)(a)3 = This version is much more accurate is often referred to as Newton's version of Kepler's Law. Notice ALL values must be in SIU
- v2/r: centripetal acceleration
- mv2/r: centripetal force
- Fg = Gm1m2/r2: This is Newton's famous equation for gravitational attraction. The gravitational force between objects is found by multiplying the mass of each object by the "G" the gravitational constant divided by the square of the distance between those two masses in meters (square). Oddly enough, gravity is a very, very weak force. A simple bit of friction here on Earth causes objects to NOT be drawn together....we'll discuss at length
WORK O' THE DAY:
Work to get the first 3 of these done today! Answers are HERE
1) Let's say that you are orbiting the earth at an altitude of 6.371 x 106 meters above the surface of the earth.
a) Calculate the velocity at which you are orbiting the Earth at that altitude.
b) Why is it that I would orbit the Earth at that exact velocity?
c) Why would a 9,000,000. kg chunk of rock "orbit" at exactly that same velocity?
2) Measure the height of your chair.... *precisely*.
Stand on top of your chair.
Jump off of your chair.
Calculate the force between you and the Earth just the tiniest fraction of a second after you stepped off your chair.
Calculate your acceleration towards the Earth using the force you calculated above and Newton's 2nd Law.
Calculate the acceleration the Earth experienced at that same time.
3) A typical lightweight helicopter blade (mass = 100. kg) rotates at about 450 revolutions per minute. How fast is that in revolutions per second?
a) What is the circumference of the circle swept out by that blade?
b) If the rotor blade is 5.50 meters in diameter, how much force does the blade experience at the outside tip?
4) Fighter pilots typically black out when they experience an acceleration of about 9.0 times the acceleration due to gravity. How fast must the training "centrifuge" (radius 3.15 meters) spin (in meters per second) in order to generate that level of acceleration?
b) How much would your weight change at that time?
c) What would your mass be?
By the by, fight pilots often say (or grunt) the word "HOOK!" during such times... why is that? Try it!
NOTE: Pilots say, yell or grunt the word "HOOK!" when conducting high "g" maneuvers because that's an easy way to forcefully constrict your core muscles which helps drive blood back to their extremities!
6) The planet Mars and the Planet Earth both orbit the Sun. They do not, however, orbit each other.
What is the largest gravitational force experienced between those two planets?
When does that occur?
When is the least gravitational force experienced between those two planets?
Calculate the force between Earth and Mars at that time.