Two torsional springs, M = ku, are used to assist in opening and closing the hood of

Chapter 18, Problem C18-2

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QUESTION:

Two torsional springs, \(M = k \theta\), are used to assist in opening and closing the hood of this truck. Assuming the springs are uncoiled (\(\theta = 0^{\circ}\)) when the hood is opened, determine the stiffness \(k (N \cdot m/rad)\) of each spring so that the hood can easily be lifted, i.e., practically no force applied to it, when it is closed in the unlocked position. Use appropriate numerical values to explain your result.

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QUESTION:

Two torsional springs, \(M = k \theta\), are used to assist in opening and closing the hood of this truck. Assuming the springs are uncoiled (\(\theta = 0^{\circ}\)) when the hood is opened, determine the stiffness \(k (N \cdot m/rad)\) of each spring so that the hood can easily be lifted, i.e., practically no force applied to it, when it is closed in the unlocked position. Use appropriate numerical values to explain your result.

ANSWER:

Problem C18-2

Two torsional springs, , are used to assist in opening and closing the hood of this truck. Assuming the springs are uncoiled () when the hood is opened, determine the stiffness k (N  m/rad) of each spring so that the hood can easily be lifted, i.e., practically no force applied to it, when it is closed in the unlocked position. Use appropriate numerical values to explain your result.

                                                           Step by Step Solution

Step 1 of 4

First, it is convenient to draw a representation of the system in its initial and final states. Note that in the initial state the system has just been unlocked and so, the hood still has no angular speed. In the final state (totally uncoiled spring) the hood also has no angular speed because we are looking for the stiffness (k) that allows for this to happen

We have considered for following values in order to do the calculations (see the image):

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