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Chapter 2: Q19CQ (page 79)
What is the last thing you should do when solving a problem? Explain.
After solving the problem, the last thing to do is to check that the answer matches the real-life situation.
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The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit\({\bf{1}}{\bf{.06 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\;{\bf{m}}\)in diameter. (a) If the average speed of the electron in this orbit is known to be\({\bf{2}}{\bf{.20 \times 1}}{{\bf{0}}^{\bf{6}}}{\bf{ m/s}}\), calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron’s average velocity?
A soft tennis ball is dropped onto a hard floor from a height of \[{\bf{1}}.{\bf{50}}{\rm{ }}{\bf{m}}\]and rebounds to a height of\[{\bf{1}}.{\bf{10}}{\rm{ }}{\bf{m}}\]. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts\[{\bf{3}}.{\bf{50}}{\rm{ }}{\bf{ms}}{\rm{ }}\left( {{\bf{3}}.{\bf{50}} \times {\bf{1}}{{\bf{0}}^{ - {\bf{3}}}}{\bf{s}}} \right)\]. (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?
In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, with a maximum speed of\({\bf{183}}.{\bf{58}}{\rm{ }}{\bf{mi}}/{\bf{h}}\). The one-way course was\({\bf{5}}.{\bf{00}}{\rm{ }}{\bf{mi}}\)long. Acceleration rates are often described by the time it takes to reach\({\bf{60}}.{\bf{0}}{\rm{ }}{\bf{mi}}/{\bf{h}}\)from rest. If this time was\({\bf{4}}.{\bf{00}}{\rm{ }}{\bf{s}}\), and Burt accelerated at this rate until he reached his maximum speed, how long did it take Burt to complete the course?
(b) Now calculate the distance taking into account the time for sound to travel up the well. The speed of sound is 332.00 m/s in this well.
A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 11.5 m/sand accelerates at the rate of 0.500for 7.00 s.
(a) What is his final velocity?
(b) The racer continues at this velocity to the finish line. If he was 300 mfrom the finish line when he started to accelerate, how much time did he save?
(c) One other racer was 5.00 mahead when the winner started to accelerate, but he was unable to accelerate, and travelled at 11.8 m/suntil the finish line. How far ahead of him (in meters and in seconds) did the winner finish?
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