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Chapter 1: Q23DQ (page 228)
The potential energy function for a force is , where is a positive constant. What is the direction of ?
is directed to the negative direction of the x-axis.
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The planet Uranus has a radius of and a surface acceleration due to gravity ofat its poles. Its moon Miranda (discovered by Kuiper in 1948) is in a circular orbit about Uranus at an altitude of above the planet鈥檚 surface. Miranda has a mass ofand a radius of (a) Calculate the mass of Uranus from the given data. (b) Calculate the magnitude of Miranda鈥檚 acceleration due to its orbital motion about Uranus. (c) Calculate the acceleration due to Miranda鈥檚 gravity at the surface of Miranda. (d) Do the answers to parts (b) and (c) mean that an object releasedabove Miranda鈥檚 surface on the side toward Uranus will fall up relative to Miranda? Explain.
In 2005 astronomers announced the discovery of large black hole in the galaxy Markarian 766 having clumps of matter orbiting around once every and moving at . (a) How far these clumps from the center of the black hole? (b) What is the mass of this black hole, assuming circular orbits? Express your answer in kilogram and as a multiple of sun鈥檚 mass. (c) What is the radius of event horizon?
A Tennis Serve. In the fastest measured tennis serve, the ball left the racquet at . A served tennis ball is typically in contact with the racquet forand starts from rest. Assume constant acceleration. (a) What was the ball鈥檚 acceleration during this serve? (b) How far did the ball travel during the serve?
An antelope moving with constant acceleration covers the distance between two points apart in. Its speed as it passes the second point is. What are (a) its speed at the first point and (b) its acceleration?
A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of, and the car has an acceleration of. The car overtakes the truck after the truck has moved. (a) How much time does it take the car to overtake the truck? (b) How far was the car behind the truck initially? (c) What is the speed of each when they are abreast? (d) On a single graph, sketch the position of each vehicle as a function of time. Takeat the initial location of the truck.
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