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MSTC Physics C

MSTC Physics C. Study Guide Chapter 11 Sections 1 & 4. Newton’s Law of Universal Gravitation.

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MSTC Physics C

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  1. MSTC Physics C Study Guide Chapter 11 Sections 1 & 4

  2. Newton’s Law of Universal Gravitation • Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers F = G m1 m2 / d2 G = 6.67 x 10-11 Nm2/kg2

  3. Sample Problem • Three 0.3 kg billiard balls are placed on a table at the corners of a right triangle. Find the net gravitational force on the cue ball (designated as m1) resulting from the forces exerted by the other two balls. .5 m .4 m m1 .3 m

  4. Acceleration due to Gravity • Since F = ma and F = G m1 m2 / d2 ma = G m1 m2 / d2 • if we are talking about an object a distance d from the center of the earth mg = G m M / d2 • So g = G M / d2 where g is the acceleration due to gravity for an object at some distance from a massive object

  5. Sample Problem • An astronaut standing on the surface of Ceres, the largest asteroid, drops a rock from a height of 10 m. It takes 8.06 s to hit the ground. (a) Calculate the acceleration of gravity of Ceres. (b) Find the mass of Ceres, given that the radius of Ceres is 510 km. (c) Calculate the gravitational acceleration 50 km from the surface of Ceres.

  6. Gravitational Potential Energy • Recall W = F dr and W = ∆U • This means F dr = Uf – Ui ( GmM/r2 )dr = Uf – Ui GmM (-1/r) ] = Uf – Ui -GmM ( 1/rf – 1/ri ) = Uf – Ui • Let Ui = 0 when ri = infinity • This means - GmM/r = U gravitational PE

  7. Sample Problem • An asteroid with a mass of 1 x 109 kg comes from deep space, effectively from infinity, and falls toward Earth. (a) Find the change in potential energy when it reaches a point 4 x 108 m from Earth, assuming if falls from rest at infinity. In addition, find the work done by the force of gravity. (b) Calculate the speed of the asteroid at that point.

  8. Orbital Speed • An object orbiting experiences a centripetal acceleration due to the force of gravity F = mv2 / r GmM / d2 = mv2 / r GM / d = v2 v = √ (GM / d) orbital speed of an object * note independent of mass of object

  9. Sample Problem • A satellite moves in a circular orbit around Earth at a speed of 5000 m/s. Determine (a) the satellite’s altitude above the surface of the Earth, and (b) the period of the satellite’s orbit.

  10. Escape Velocity • Consider an object launched straight up with initial speed vi • Since energy is conserved KE + Ugi = Ugf at maximum height ½ mvi2 – GmM/ri = -GmM/rf ½ vi2 – GM/ri = - GM/rf vi2 = 2GM (1/ri – 1/rf ) • Let rf = infinity then vi = escape velocity vesc2 = 2GM/r vesc = √ 2GM/r escape velocity

  11. Sample Problem • In Jules Verne’s classic novel, From the Earth to the Moon, a giant cannon dug into the Earth in Florida fired a spacecraft all the way to the Moon. If the spacecraft leaves the cannon at escape speed, at what speed is it moving when 1.5 x 105 km from the center of the Earth?

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