AP Physics – Gravitation Notes

Gravitation
Definition:
Newton’s Universal Law of Gravitation:
What is true about gravitational forces between two bodies?
What is true about the gravitational force on an object outside a uniform sphere or spherical shell?
What is true about the gravitational force inside a uniform shell?
Principle of Superposition
Define:
How is gravitational force determined for an extended body? / Practice Problem: Find the attractive force between two 1 kg masses separated by 1m.
Practice Problem: Three particles arranged such that particle 1, mass 6.0 kg, has a particle 2, mass 4.0 kg, a distance of 2.0 cm above it and particle 3, mass 4.0 kg, a distance 4.0 cm to the left, forming a right angle.
Draw a force diagram.
Determine the gravitational force that acts on particle 1 due to the other particles.
Practice Problem: A particle of mass equal to 0.67 kg is a distance, d, of 23 cm from one end of a uniform rod with a length (L) of 3.0 m and mass (M) of 5.0 kg. What is the magnitude of the gravitational force (F) on the particle due to the rod?

Practice Problem: A solid sphere of uniform density has a mass (m) of 1 x 104 kg and a radius (R) of 1.0 m. What is the gravitational force due to the sphere on a particle of mass, mp, located at a distance of
a)  …1.5 m
b)  …0.5 m
…from the center of the sphere? / c)  Write a general expression for the gravitational force on the mass, mp, at a distance, r less than or equal to 1.0 m (R) from the center of the sphere.
Practice Problem: A spaceship is on a straight line path between Earth and its moon. At what distance from Earth is the net gravitational force on the spaceship equal to zero? / Gravitational Acceleration
Equation:
Why is gravitational acceleration not equal to free fall acceleration?
Orbital velocity
Definition:
Equation:
Orbital Period
Definition:
Equation
Practice Problem: If you weigh 800 N on Earth, what will you weigh on a planet with half the mass of Earth and a radius that is twice the radius of Earth?
Practice Problem: You weigh 530 N at sidewalk level outside a very tall building in New York City. You then ride to the top of this building a distance of 410 m. Ignoring Earth’s rotation, how much less would you weigh at the top? / Practice Problem: An astronaut is 1.70 m in height and floats feet down in an orbiting space shuttle 6.77 x106 m from the center of the earth.
a)  What is the difference between the gravitational acceleration at the astronaut’s feet and at her head?
b)  If the astronaut is in orbit about a black hole of mass 1.99 x 1031 kg where the orbital radius is still 6.77 x 106 m, what is the difference in the gravitational acceleration?
c)  What happens if the astronaut gets closer?
Practice Problem: A satellite is orbiting a planet a radial distance, r, from center at velocity, v. What will the radial distance of this satellite be if its velocity should be half its speed at r?
Gravitational Potential Energy
What is the new reference point where potential energy is zero?
Equation:
What happens to gravitational potential energy as masses come closer together?
What happens to gravitational potential energy as displacement approaches infinity? / Practice Problem: Derive the equation for gravitational potential energy, U, of a mass, m, as it is moved from a distance, r, to infinity away from a mass, M.
Conservation of Energy and Energy of orbit
Equation for Energy of orbit:
How can Energy of orbit be described in terms of kinetic energy?
How can Energy of orbit be described in terms of potential energy?
Escape Velocity
Definition:
What is escape velocity not equal to?
Equation:
Practice Problem: What minimum initial speed must be given to a mass, m, at the surface of the earth so it can completely escape the gravitational pull of earth? / Practice Problem: An asteroid headed directly toward earth has a speed of 12 km/s relative to the planet when it is a distance of 10 earth radii from earth’s center. Determine the asteroids velocity when it reaches earth’s surface neglecting affects of earth’s atmosphere.
Practice Problem: A satellite inn an elliptical orbit has a speed of 9.00 km/s when it is at its closest approach to the earth (perigee). The satellite is 7.00 x 106 m from the center of the earth at this time. When the satellite is at its greatest distance from the center of the earth (apogee), its speed is 3.66 km/s. How far is the satellite from the center of the earth at apogee?
Radius of earth = 6.37 x 106 m; mass of earth = 5.97 x 1024 kg

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