Find the ratio of the height h of a cushion on a snooker table to the radius r of a ball as shown in figure 24, such that when the ball hits the cushion with a pure rolling motion it rebounds with a pure rolling motion. (Assume that the force exerted on the ball by the cushion is horizontal during the impact and that the ball hits the cushion normally.) Figure 24
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- Physics An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 43 hours. The mass of the planet is M = 2.7 • 1025 kg. The spaceship enters a circular orbit with an orbital period that is equal to the planet's period for the rotation about its axis, T. Part a) Write an expression for the radius of the spaceship’s orbit R=? Part b) Calculate the orbital radius in metersA coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 5.0 kg object at the origin of the coordinate system, a 10.0 kg object at (0, 2.0), and a 11.0 kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin. magnitude directionYou have a summer internship at NASA and are working on plans for a new space station to be launched into orbit around the Earth. The design of the space station is shown. It is to be constructed in the shape of a hollow ring of mass 51,500 kg. The structures other than the ring shown in the figure have negligible mass compared to the ring. Members of the crew will walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 120 m. The thickness of the ring is very small compared to the radius, so we can model the ring as a hoop. At rest when constructed, the ring is to be set rotating about its axis so that the people standing inside on this deck experience an effective free-fall acceleration equal to g. The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. Your supervisor asks you to determine the following: (a) the time interval during which the rockets must be fired if each…
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