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Chapter 6: Q49P (page 279)
You throw a ball straight up, and it reaches a height of20 mabove your hand before falling back down. What was the speed of the ball just after it left your hand?
The speed of the ball just after it left at the hand was 19.8 m/s .
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In each of the following cases state whether the work done by the specified force is positive, negative or zero. Also state whether the kinetic energy of the object in question increases, decreases or remains the same.
(a) A ball is moving upward, acted on by a downward gravitational force.
(b) A ball is falling downward, acted on by a downward gravitational force.
(c) A car is moving rapidly to the left and Superman exerts a force on it to the right to slow it down, backing up to the left as he pushes to the right.
(d) You throw a ball downward. Consider the force exerted by your hand on the ball while they are in contact.
(e) In a 6 month period the Earth travels halfway around its nearly circular orbit of the Sun. Consider the gravitational force exerted on the Earth by the Sun during this period.
The radius of Mars (from the center to just above the atmosphere) is (3400 km ), and its mass is . An object is launched straight up from just above the atmosphere of Mars. (a) What initial speed is needed so that when the object is far from Mars its final speed is ? (b) What initial speed is needed so that when the object is far from Mars its final speed is ? (This is called the escape speed.)
A runner whose mass is runs in the direction at a speed of . (a) What is the kinetic energy of the runner? (b) Runner turns around and runs in thedirection at the same speed. Now what is the kinetic energy of the runner?
A comet is in elliptical orbit around the Sun. Its closest approach to the Sun is a distance of (inside the orbit of Mercury), at which point its speed is . Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is from the Sun? (This is the approximate distance of Pluto from the Sun.)
You stand on a spherical asteroid of uniform density whose mass is and whose radius is 10Km. These are typical values for small asteroids, although some asteroids have been found to have much lower average density and are thought to be loose agglomerations of shattered rocks.
(a) How fast do you have to throw the rock so that it never comes back to the asteroid and ends up traveling at a speed of 3 m/swhen it is very far away?
(b) Sketch graphs of the kinetic energy of the rock, the gravitational potential energy of the rock plus asteroid, and their sum, as a function of separation (distance from centre of asteroid to rock).
Label the graphs clearly. The asteroid, and their sum, as a function of separation (distance from centre of asteroid to rock).
Label the graphs clearly.
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