Problem 2: We discussed gravitational acceleration near the ground to be a constant g, which gives the position of an object in free fall as quadratic in time. Let's say that, in the remote future, a cataclysmic event has destabilised the Earth's interior, and the planet is disintegrating. The gravity near the surface of the collapsing Earth is then found as: Iomt (t) = ge¬at² where t > 0 is time, a 2 0 is some constant, and g is the original surface gravitational acceleration. During the cataclysm, a small rock was ejected straight off the surface at some speed vo at time t = 0. The near-surface gravity, however, was still strong enough that it started pulling the rock back. Unlike the constant surface gravity case, however, notice lim-∞ Gomt (t) = 0, implying that this rock will have a terminal velocity it will settle into. What is the rock's terminal speed v»? When calculating væ, you may run into a definite integral that is not easily solvable. Fortunately, this is a well-known and important result in STEM. You may search up this integral, and write a brief paraphrase of how your source solves the integral. BTW, the indefinite counterpart of the integral is not known as a closed form, so make sure you have a definite integral set up.
Problem 2: We discussed gravitational acceleration near the ground to be a constant g, which gives the position of an object in free fall as quadratic in time. Let's say that, in the remote future, a cataclysmic event has destabilised the Earth's interior, and the planet is disintegrating. The gravity near the surface of the collapsing Earth is then found as: Iomt (t) = ge¬at² where t > 0 is time, a 2 0 is some constant, and g is the original surface gravitational acceleration. During the cataclysm, a small rock was ejected straight off the surface at some speed vo at time t = 0. The near-surface gravity, however, was still strong enough that it started pulling the rock back. Unlike the constant surface gravity case, however, notice lim-∞ Gomt (t) = 0, implying that this rock will have a terminal velocity it will settle into. What is the rock's terminal speed v»? When calculating væ, you may run into a definite integral that is not easily solvable. Fortunately, this is a well-known and important result in STEM. You may search up this integral, and write a brief paraphrase of how your source solves the integral. BTW, the indefinite counterpart of the integral is not known as a closed form, so make sure you have a definite integral set up.
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter10: Motion In A Noninertial Reference Frame
Section: Chapter Questions
Problem 10.12P
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