OU PHYS 1205 - The Gravitational Force and the Gravitational Field

Unformatted text preview:

Chapter 6The Gravitational Force and the Gravitational FieldNewton’s Law of Universal GravitationrFˆ2rGMm−=• F is the force of an object with mass M on an object with mass m• r is a unit vector pointing in the direction from the object with mass M to the object with m. • G is Newton’s universal gravitational constant with a value is G = 6.67 × 10-11N⋅m2/kg2Mmr1r2rA spaceship is traveling to the moon. At what point is it beyond the pull of the earth’s gravity? The mass of the moon is 1/80 the mass of the earth, and the surface gravity of the moon is 1/6 that of the earth.A) When it gets out of the atmosphere.B) When it is half-way there.C) When it is 5/6 of the way there.D) When it is 79/80 of the way there.E) It is never beyond the pull of earth’s gravity.Interactive Question1. The force acts over all space. Every object in the universe feels gravity from every other object in the universe. 2. Force is proportional to mass. 3. The force that one object feels from another is equal and opposite to the force the other object feel on the first one. (This is the same as Newton’s third law). The acceleration of the two objects would be different if their mass is different.When the objects are spherical, the distance “between”the objects is measured from their centers. One of the reasons Newton developed calculus to demonstrate that this was true. Observations Regarding Universal GravitationProblem: (a) What is the magnitude of the gravitational force on the moon from the earth? (b) What is the magnitude of the gravitational force on the earth from the moon?Newton’s ReasoningA. ac= v2/r = (2πr/T)2/r = 4π2r/T2• anear Earth/aat Moon= 9.81/0.00272 = 3600• rat Moon/rnear Earth = 3.84 × 108/6.37 × 106= 60• F = ma ⇒ F ∝ 1/r2B. agis independent of mass of objectF = magK(Mm)n/r2= magag= K (Mm)n/mr2= (KMnmn-1)/r2⇒ n = 1The Universal Gravitational force is a vector, as are all forces, and must be added like vectors, by using components. When there are more than two objects involved, we determine each of the forces independently, and then add them together as vectors. This is the principle of superposition.Problem: Find the total gravitational force on the moon from both the earth and sun, assuming that the they are at right angles to each other as shown.Gravity at the surface of the EarthFg= mg = GmmE/rE2g = GmE/rE2= (6.67×10-11N·m2/kg2)(5.97×1024kg) ÷ 6.38×106m2= 9.78 m/s2Problem: How far above the earth must you go for the force you feel to be 1/2 of what it is on the surface of the earth?A pendulum bob is suspended from a long pole in Oklahoma. When the pendulum is at rest, the combined action of gravitation and Earth’s rotation makes the bob:A) deviate toward the east.B) deviate toward the west.C) deviate toward the north.D) deviate toward the south.E) point straight down toward the center of the Earth.EarthNSpolebobNSInteractive QuestionGravitational and Inertial MassLet’s look at Newton’s second law, when there is only the force of gravity acting.∑F = maFg= maGmmE/rE2= maOn the left hand side, m is the mass that interacts by the force of gravity, or the gravitational mass. On the right hand side m is the object’s resistance to acceleration, or the inertial mass. Are these the same? Why should they be?Near the surface of the earth: mg = maSo a = g for all objects only if these are the same.Satellites and “Weightlessness”Examples of objects having only the force of gravity acting on them.When an object is in freefall, we call it “weightless”because a scale would not read any weight. But the object still has weight (the force of gravity acting on it).The Moon does not fall to Earth becauseA) It is in Earth’s gravitational fieldB) The net force on it is zero.C) It is beyond the main pull of Earth’s gravity.D) It is being pulled by the Sun and planets as well as by Earth.E) None of the above.Interactive QuestionAn astronaut is inside a space shuttle in orbit aroundthe earth. She is able to float inside the shuttle becauseA) her weight is zero, and her shuttle’s weight is zero.B) the force of gravity is very small on the astronaut.C) she and her shuttle move with the same constant velocity.D) she and her shuttle move with the same centripetal acceleration.E) The force of the earth on the spaceship and the force of the spaceship on the earth cancel because they are equal in magnitude and opposite in direction.Interactive QuestionThe earth exerts the necessary centripetal force on an orbiting satellite to keep it moving in a circle at constant speed. Which statement best explains why the speed of the satellite does not change even though there is a net force exerted on it?A) The acceleration of the satellite is zero.B) The centripetal force has a magnitude of mv2/r.C) The centripetal force is canceled out by the reaction force.D) The centripetal force is always perpendicular to the velocity.E) The satellite is in equilibrium, which means there is no net force acting on it.Interactive QuestionProblem: What is the speed of a satellite in orbit around the earth at a distance of 12,200 km above the surface of the earth. rE= 6.38× 106md = 1.22 107m• Note that all satellites at the same distance from the earth have the same speed, regardless of their mass. • We often write the speed as a function of the period (T), the time it takes to make one orbit. v = 2πr/TT = 2πr/vProblem: How long does it take the satellite in the previous problem to circle the Earth?Two satellites A and B of the same mass are going around the earth in concentric orbits. The distance of satellite Bfrom center of the earth is twice that of satellite A. What is the ratio of the centripetal force acting on B to that acting on A?A) 1/8B) 1/4C) 1/2D) E) 1 2/1Interactive QuestionTwo satellites A and B of the same mass are going around the earth in concentric orbits. The distance of satellite Bfrom the center of the earth is twice that of satellite A. What is the ratio of the tangential speed of B to that of A?A) 1/2B) C) 1D)E) 22/12Interactive QuestionA satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the surface of Mars, isA) zero.B) the sameC) one-third as much.D) one-ninth as much.E) one-sixteenth as much.Interactive QuestionKepler’s LawsLong before Newton proposed his three laws of motion


View Full Document

OU PHYS 1205 - The Gravitational Force and the Gravitational Field

Download The Gravitational Force and the Gravitational Field
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view The Gravitational Force and the Gravitational Field and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view The Gravitational Force and the Gravitational Field 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?