10) Derive the differential equation governing the motion of a body that issubject to both the force of gravity and by a force that is proportional tothe square of the velocity of the body.11) A 10 – kg mass is attached to a spring, stretching it 0.7 m from its naturalposition. The mass is started in motion from the equilibrium position with aninitial velocity of 1 in the upward direction. In addition, an external force5 sin t(in newtons) is applied to the system. Derive a differential equationgoverning the subsequent motion of the spring if the force due to airresistance is 90*N.12) Supposed a student carrying a COVID-19 virus returns to an isolatedcollege campus of 1000 students. Determine a differential equation forthe number of people x(t) who have contracted the virus if the rate atwhich the disease spreads is proportional to the number of interactionsbetween the number of students who have the virus and the number ofstudents who have not yet been exposed to it.

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Answered: 10) Derive the differential equation…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 26P

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Scurrilous con artists have been known to represent gold-plated tungsten ingots as pure gold and sell them to the greedy at prices much below gold value but deservedly far above the cost of tungsten. With what accuracy must you be able to measure the mass of such an ingot in and out of water to tell that it is almost pure tungsten rather than pure gold?
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10) Derive the differential equation governing the motion of a body that is subject to both the force of gravity and by a force that is proportional to the square of the velocity of the body.