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Chapter 1: Q37E (page 61)
A juggler throws a bowling pin straight up with an initial
speed of 8.20 m/s. How much time elapses until the bowling pin
returns to the juggler’s hand?
The total time elapsed by the bowling pin is 1.67 s.
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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’s mass. (c) What is the radius of event horizon?
For a spherical planet with mass , volume , and radius ,derive an expression for the acceleration due to gravity at the planet’s surface, , in terms of the average density of the planet, , and the planet’s diameter, . The table gives the values of and for the eight major planets:
(a) Treat the planets as spheres. Your equation for as a function of
and
shows that if the average density of the planets is constant, a graph of
versus
will be well represented by a straight line. Graph
as a function of
for the eight major planets. What does the graph tell you about the variation in average density? (b) Calculate the average density for each major planet. List the planets in order of decreasing density, and give the calculated average density of each. (c) The earth is not a uniform sphere and has greater density near its center. It is reasonable to assume this might be true for the other planets. Discuss the effect this nonuniformity has on your analysis. (d) If Saturn had the same average density as the earth, what would be the value of
at Saturn’s surface?
An point mass and a point mass are held apart. A particle of mass mis released from a point between the two masses from the group along the line connecting the two fixed masses. Find the magnitude and direction of the acceleration of the particle.
How many times does a typical person blink her eyes in a lifetime?
An astronaut has left the International Space Station to test a new space scooter.
Her partner measures the following velocity changes, each taking place in a interval.
What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval?
Assume that the positive direction is to the right.
(a) At the beginning of the interval, the astronaut is moving toward the right along the x-axis at , and at the end of the interval she is moving toward the right at .
(b) At the beginning she is moving toward the left atrole="math" localid="1655276110547" , and at the end she is moving toward the left at .
(c) At the beginning she is moving toward the right at , and at the end she is moving toward the left atrole="math" localid="1655276636193" .
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