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Question
steering and suspension - final exam
this exam consists of 25 questions. answer each question.
6
two technicians are discussing coil springs with equal wire diameter and material.
technician a says that the coil spring with coils that are closer together has a higher (stiffer) spring rate.
technician b says that the coil spring with coils that are further apart has a higher (stiffer) spring rate.
who is correct?
neither technician a or b.
technician a only.
both technicians a and b.
technician b only.
To determine the correct technician, we analyze the spring rate formula for coil springs. The spring rate \( k \) of a coil spring is given by \( k=\frac{Gd^{4}}{8D^{3}n} \), where \( G \) is the shear modulus (material - related), \( d \) is the wire diameter, \( D \) is the mean coil diameter, and \( n \) is the number of active coils. For springs with equal wire diameter (\( d \)) and material (\( G \)), if the coils are closer together, the number of active coils (\( n \)) is larger. Since \( k \) is inversely proportional to \( n \) (from \( k=\frac{Gd^{4}}{8D^{3}n} \)), a larger \( n \) (closer coils) leads to a smaller \( k \) (softer spring), and a smaller \( n \) (farther - apart coils) leads to a larger \( k \) (stiffer spring). Wait, no, let's re - examine. Wait, actually, when coils are closer together, the number of active coils is more. The formula for spring rate of a coil spring is \( k=\frac{Gd^{4}}{8N_{a}D^{3}} \), where \( N_{a} \) is the number of active coils. So, if \( N_{a} \) increases (coils closer together), \( k \) decreases (spring is softer). If \( N_{a} \) decreases (coils farther apart), \( k \) increases (spring is stiffer). Wait, but the question says "coils that are closer together" - if coils are closer, the number of coils in a given length is more, so \( N_{a} \) (active coils) is higher. So from the formula, higher \( N_{a} \) means lower \( k \), so a spring with closer coils is softer, not stiffer. A spring with farther - apart coils has fewer active coils, so higher \( k \) (stiffer). Wait, but the options: Technician A says closer coils have higher spring rate (stiffer) - that's wrong. Technician B says farther - apart coils have higher spring rate (stiffer) - that's correct? Wait, no, maybe I messed up the formula. Wait, the correct formula for the spring rate of a helical spring is \( k=\frac{Gd^{4}}{8D^{3}n} \), where \( n \) is the number of active coils. So, if the coils are closer together, \( n \) (number of active coils) is larger. So as \( n \) increases, \( k \) decreases. So a spring with closer coils is softer (lower spring rate), and a spring with farther - apart coils has fewer \( n \), so higher \( k \) (stiffer). So Technician B is correct? Wait, but the original selected option was "Neither", but that might be a mistake. Wait, let's check again. Wait, maybe the question is about the "pitch" of the coils. The spring rate is also related to the pitch. A spring with a smaller pitch (coils closer together) has a higher spring rate? No, no, the formula shows the opposite. Wait, perhaps I got the formula wrong. Let's recall: The spring rate \( k \) is the force required to compress the spring by a unit distance. For a helical spring, the formula is \( k=\frac{Gd^{4}}{8D^{3}N} \), where \( G \) = shear modulus, \( d \) = wire diameter, \( D \) = mean coil diameter, \( N \) = number of active coils. So, if \( N \) (number of active coils) increases, \( k \) decreases. So, if coils are closer together, \( N \) is larger (more coils in the same length), so \( k \) is smaller (softer spring). If coils are farther apart, \( N \) is smaller, so \( k \) is larger (stiffer spring). So Technician B is correct? But the original selection was "Neither". Wait, maybe there's a misunderstanding. Wait, maybe the question is about the "solid height" or something else. Wait, no, the key is the formula. So Technician B says that the coil spring with coils further apart has a higher spring rate - that is correct. Wait, but let's check the options again. The options are: Neither Technician A or B; Tech…
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Technician B only.