/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 151 A solid sphere moves at a termin... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 151

A solid sphere moves at a terminal velocity of \(20 \mathrm{~m} / \mathrm{s}\) in air at a place, where \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\). The sphere is taken in a gravity free hall having air at the same pressure and pushed down at a speed of \(20 \mathrm{~m} / \mathrm{s}\). (A) Its initial acceleration will be \(9.8 \mathrm{~m} / \mathrm{s}^{2}\) downward. (B) Its initial acceleration will be \(9.8 \mathrm{~m} / \mathrm{s}^{2}\) upward. (C) The magnitude of acceleration will decrease as the time passes. (D) It will eventually stop.

Short Answer

Expert verified
The sphere will continue to move with a constant velocity of \(20 \mathrm{~m} / \mathrm{s}\) as there is no gravitational or other forcing frictional force to create an acceleration or deceleration. Therefore, all provided options (A, B, C, D) are incorrect.

Step by step solution

01

Understand Terminal Velocity

Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration. This happens because the upwards force of the air (air resistance or drag) will eventually balance the downward force due to gravity. Therefore, when the sphere moves at terminal velocity of \(20 \mathrm{~m} / \mathrm{s}\), this means the forces acting on it from above and below are balanced.
02

Analyze New Conditions

In a gravity-free hall, the force of gravity does not act on the sphere. However, the description indicates that the solid sphere was pushed down at a speed of \(20 \mathrm{~m} / \mathrm{s}\). Remembering that force is the product of mass and acceleration, and here in absence of gravity, no other force is acting against this motion, so the sphere continues to move with the initial imparted movement.
03

Evaluate Provided Options

(A) and (B) both suggest that there would be an initial acceleration of \(9.8 \mathrm{~m} / \mathrm{s}^{2}\), which is incorrect as there's no force working against the movement of sphere in a gravity-free environment. (C) implies that the acceleration will change over time, however in a gravity-free environment, the body will continue moving at the same speed, meaning the acceleration (rate of change of velocity) will be zero. (D) predicts that the sphere will eventually stop, but without interfering forces, it will continue its motion unchanged.

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