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Determine the maximum constant speed at which the 2-Mg car

Engineering Mechanics: Statics & Dynamics | 14th Edition | ISBN: 9780133951929 | Authors: Russell C. Hibbeler ISBN: 9780133951929 123

Solution for problem 13-74 Chapter 13

Engineering Mechanics: Statics & Dynamics | 14th Edition

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Engineering Mechanics: Statics & Dynamics | 14th Edition | ISBN: 9780133951929 | Authors: Russell C. Hibbeler

Engineering Mechanics: Statics & Dynamics | 14th Edition

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Problem 13-74

Determine the maximum constant speed at which the 2-Mg car can travel over the crest of the hill at A without leaving the surface of the road. Neglect the size of the car in the calculation.

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Visual Perception Week 9 Notes 3/10/16 1:25 AM Paper: Terrain influences the accurate judgment of distance by Sinai et al. Introduction Main research question: does the brain select the most resource and time- efficient way to represent the three-dimensional location of objects • More specifically, does the brain use a quasi-two-dimensional coordinate system (X, Y) with respect to the ground surface (s), rather than a three-dimensional coordinate system (x, y, z),in order to simplify and speed up computations Experiment 1 Theory • When the ground surface is disrupted, the visual system can’t establish a reliable reference frame and fails to obtain correct absolute distance • If the texture of the ground surface is changed or there is a gap in the ground surface, the individual won’t be able to determine absolute distance Methods • Manipulation: target on other side of gap in the ground (0.5m d x 1.3m w) from a naïve observer Control • Target 3.66m away over a continuous surface • Experiment: o Blindfolded, turned 90 degrees, asked to walk distance equivalent to remembered absolute distance of the target o Asked to judge the absolute distance of a target, and then to perceptually set the distance of a matching target to be at an equal distance Results • Blindfolded walking manipulation: average distance walked was 4:60 + 0:12m • Blindfolded walking control: average distance walked was 3:69 + 0:12m • Perceptual matching manipulation: average matched distance was 4:24 + 0:6m • Perceptual matching control: average matched distance was 3:54 + 0:07m Experiment 2 Theory • When the ground surface is disrupted, the visual system can’t establish a reliable reference frame and fails to obtain correct absolute distance Methods • Manipulation: target on other side of a larger and deeper gap in the ground (2m d x 4.1m w) from a naïve observer • Control: target 3.66m away over a continuous surface • Experiment: o Blindfolded, turned 90 degrees, asked to walk distance equivalent to remembered absolute distance of the target o Asked to judge the absolute distance of a target, and then to perceptually set the distance of a matching target to be at an equal distance. Experiment 3 Theory • Distance/texture model: Z = (H x G)/3 • Z is perceived absolute distance • H is the observer’s eye height relative to the ground surface • G is the local texture gradient on the ground at the target’s location Methods • Observers stood on an elevated ground surface (2.0 m) and estimated horizontal distance of a target placed on a lower ground surface • 8 participants were tested using the blindfolded test and 5 were tested using the perceptual distance matching test Experiment 3 (part 2) Researchers believed this overestimation may be due to an exaggeration of the observer’s perception of H Methods • 5 observers stand on the higher surface and set the distance of a matching target to equal their perceived eye height above lower ground surface • Then they are asked to set the distance of a matching target to equal their perceived eye height with respect to feet • The participants were finally asked to measure perception of distance between feet and lower ground surface Experiment 4 Theory • Distance/texture model: Z = (H x G)/3 • H is the observer’s eye height relative to the ground surface • G is the local texture gradient on the ground at the target’s location Methods • Two distinct texture regions: grass, concrete. Observer stood on concrete, previewed target on grass, then did the blindfolded walking task. Width of grass field kept constant at 3.05 m while width of concrete was varied from 0.61-4.56 m • in control experiments, people were tested on homogeneous (grass only or concrete only) texture surface; blindfold walk accurate, also consistent with ground theory • The experiment was repeated with people standing on grass and viewing target placed 5.79 m away on concrete Most Important Take-Aways • The internal representation of space, which is based on the common ground surface, is used for both space perception and visually directed performance • Texture gradient of size + eye height influences judgment of absolute distance. Texture gradient on the ground acts as a depth cue for visual system to establish a reference frame. 3/10/16 1:25 AM 3/10/16 1:25 AM

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Chapter 13, Problem 13-74 is Solved
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Textbook: Engineering Mechanics: Statics & Dynamics
Edition: 14
Author: Russell C. Hibbeler
ISBN: 9780133951929

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Determine the maximum constant speed at which the 2-Mg car