. An athlete putts a shot of mass 7 kg a distance of 20 m. Show that the athlete must do to at least 700 J of work to achieve this. [ Ignore the height of the athlete and take g = 10 m s−2.]
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An athlete putts a shot of mass 7 kg a distance of 20 m. Show that the athlete must do to at least 700 J of work to achieve this. [ Ignore the height of the athlete and take g = 10 m s−2.]
Find the work needed to lift a satellite of mass 200 kg to a height of 2000 km above the Earth’s surface. [Take the Earth to be spherically symmetric and of radius 6400 km. Take the surface value of g to be 9.8ms−2.]
Explanation:
STEP--- 1---
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Classical Mechanics (0th) Edition 0521534093 9780521534093
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Classical Mechanics
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CH6
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3P
An athlete putts a shot of mass 7 kg a distance of 20 m. Show that the athlete must do to at least 700 J of work to achieve this. [Ignore the height of the athlete and take g = 10 ms−2.]
Step-by-step solution
Step 1 of 3
Apply law of conservation of energy to find the minimum work done by the athlete in the case of projectile motion.
The expression for a horizontal range in the case of a projected body is given as follows:
Here, is the initial projected speed, is the angle of projection, and is acceleration due to gravity.
Rearrange the equation for.
For least possible kinetic energy or projected speed, the value of should be equal to one that means the projection angle should be.
Substitute for, for andfor in the equation.
Thus, the minimum speed of the shot is.