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Universal Gravitation Chapter Review
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Gravity
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Who is Tycho Brahe, and what role did he play in developing Kepler's Laws?
He was an astronomer who devoted 20 years of his life to studying the heavens and mapping the night sky. He recorded the exact positions of the planets and stars. Brahe noticed retrograde motion but thought it was just epicycles
What effect did the church have on science in the 16th and 17th centuries?
The church believed in a geocentric model, where the planets orbited earth in a perfect circle. If anyone contradicted these ideas, then they would be considered heretics and possibly killed.
What are epicycles and how are they used to explain the motion of the solar system?
An epicycle is a smaller circular path followed along a larger circular path. These mini circular orbits helped to support the theory of a perfect circular orbit and explain retrograde motion (apparent motion of a planet in opposite direction).
Explain what Johannes Kepler did to further develop his theories of planetary motion.
He went beyond the views of the church and used geometry and math with a heliocentric system to calculate the motion of the planets. He developed 3 laws that describe the behavior of every planet and satellite.
Define and explain Kepler's Laws of Planetary Motion.
1. The paths of planets are ellipses with the center of the sun at one focus
2. An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals (planet speed varies throughout the orbit, fastest when closest to sun)
3. The ratio of the period squared of 2 planets= ratio of the radii of orbit cubed
What was the difference between Kepler's and Newton's work?
Kepler described the kinematics (how) of planetary motion and Newton tried to explain the dynamics (why)
How did Newton support the Inverse Square Law?
He determined that the force acting on the earth in its orbit varied depending upon where on the ellipse the earth was located. It was revealed that the force acting on the earth and the distance between the earth and the sun were related. This is known as the inverse square law (F is inversely proportional to d squared)
Define and explain the law of Universal Gravitation.
For any pair of objects, each object attracts the other with a force directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between their centers
What did Henry Cavendish accomplish that Newton could not?
Newton knew that there had to be a constant that would allow the units of the equation to yield Newton's and convert the final calculation to a proper magnitude. Unfortunately, he never developed an experiment that measured the value of G. Cavendish was able to many years later.
Explain Cavendish's experiment and its significance.
He attached 2 light masses to a light rod, which was tied to a string. The two light masses were attracted to two large cannonballs, and he calculated G from this. Allowed him to calculate mass of earth.
Explain how Cavendish determined the mass of the earth.
He set the universal gravitation equation equal to mg, where one of the masses is the mass of an object and the other is the mass of the earth. The mass of the object ends up cancelling out, then solve for mass of earth. (d is the radius of the earth)
Is the value of g on the earth a constant? Explain.
The value of g decreases as the distance from the earth's surface increases, but the change in g is negligible on earth's surface. (There are slight variations in g even when you are on the earth's surface because certain areas have increased densities)
Explain how Newton proved the moon falls toward the earth
The moon wants to continue in a straight path, but the force of the earth causes it to fall back to its orbit. This is similar to how a horizontally launched object falls
Is there such a thing as weightlessness? Explain.
No. For the attractive force to be 0, either G or one of the masses must be 0, which is impossible. Since force never equals 0, and F=mg, g can never equal 0.
When does apparent weightlessness occur?
While falling.
Define gravity.
The way in which masses communicate with each other.
What happens to weight when someone is standing on a scale in a stationary elevator?
Weight is normal
What happens to weight when a person is standing on a scale in an elevator that is going up?
The inertia of the person would prefer to remain stationary, so the scale has to push upwards with extra force to make the person accelerate upwards. Therefore, normal force is larger, so the weight reading is higher.
What happens to weight when a person stands on a scale in an elevator that is going down?
The inertia of the person would prefer to stay at rest, so the scale and floor drop out from under the person a little. So the contact force between the person and scale is less, so weight is less.
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