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A satellite describes an elliptic orbit about a planet of mass M. The minimum and maximum values of the distance r from the satellite to the center of the planet are, respectively, r1 and r2. Use the principles of conservation of energy and conservation of angular momentum to derive the relation
where h is the angular momentum per unit mass of the satellite and G is the constant of gravitation.
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Vector Mechanics for Engineers: Dynamics
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- 9 Macmillan Learning Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height d. The mass of each object is a multiple of the base mass m: object 1 has mass 4.60m, object 2 has mass 1.71m, and object 3 has mass m. When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. Each answer requires the numerical coefficient to an algebraic expression that uses some combination of the variables m, g, and d, where g is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is 1.23mgd, just enter 1.23) If the objects are positioned on the steps as shown, what is gravitational potential energy Ug,system of the system? If you redefine the reference height such that the total potential energy of the system is zero, how high ho above the bottom of the stairs is the new reference height? Now, find a new…arrow_forwardTwo objects with masses of 2.55 kg and 4.15 kg are connected by a light string that passes over a light frictionless pulley to form an Atwood machine. (a) Determine the tension in the string. (b) Determine the acceleration of each object. (c) Determine the distance each object will move in the first second of motion if they start from rest.arrow_forward113 Blocks on a spring. Two blocks with masses m₁ and m₂ are connected by a spring and are free to slide on a frictionless horizontal surface. The blocks are pulled apart along an x axis and then released from rest. At any later time, (a) what fraction frac₁ of the total kinetic energy of the system will block 1 have and (b) what fraction fracz will block 2 have? (c) If m₁ > m2,which block has more kinetic energy? 中arrow_forward
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