Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

What minimum coefficient of friction is needed between the legs and the ground to keep the sign in Figure 9.35 in the position shown if the chain breaks? (b) What force is exerted by each side on the hinge?

The coefficient of friction is \(0.551\).
The force exerted by each side on the hinge is \({\rm{21}}{\rm{.6}}\;{\rm{N}}\)

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Data

Given:

The sign’s mass is \(m = 8\;{\rm{kg}}\).

The diagram is shown below:

Step 2: Calculation of the force

The net force is zero in equilibrium. So,

\({N_L} + {N_r} - {w_s} = 0\)

Normal forces should be equal by symmetry. So,

\({N_L} = {N_r} = N\)

We write,

\(\begin{align}2N - {w_s} &= 0\\N = \frac{{{w_s}}}{2}\\N &= \frac{{8 \times 9.8}}{2}\\N &= 39.2\;{\rm{N}}\end{align}\)

The total tension on each leg is\(39.2\;{\rm{N}}\).

So, this tension is equal to the weight of the sign board.

\(39.2 \times 2 = 78.4\;{\rm{N}}\)

The net force,

\({F_t}\sin \varphi - N - w = 0\)

And

\({F_t}\cos \varphi = T\)

So,

\(\begin{align}\sin \varphi &= 0\\\varphi &= 0^\circ \end{align}\)

\(\) \({F_t}\cos \varphi = T = 21.6\;{\rm{N}}\)

If the chain breaks, the tension will be zero and the force on the hinge will be balanced by the friction.

\(\begin{align}\mu N &= {F_t}\cos \varphi \\\mu &= \frac{{{F_t}\cos \varphi }}{N}\\\mu &= \frac{{21.6 \times 1}}{{39.2}}\\\mu &= 0.551\end{align}\)

Step 3: Calculation of the force exerted by each hinge

The force calculated in the part (a) is,

\({F_t}\cos \varphi = T = 21.6\;{\rm{N}}\)

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College Physics (Urone)

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Short Answer

What minimum coefficient of friction is needed between the legs and the ground to keep the sign in Figure 9.35 in the position shown if the chain breaks? (b) What force is exerted by each side on the hinge?

Step by Step Solution

Step 1: Given Data

Step 2: Calculation of the force

Step 3: Calculation of the force exerted by each hinge

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College Physics (Urone)

Answers without the blur.

Short Answer

What minimum coefficient of friction is needed between the legs and the ground to keep the sign in Figure 9.35 in the position shown if the chain breaks? (b) What force is exerted by each side on the hinge?

Step by Step Solution

Step 1: Given Data

Step 2: Calculation of the force

Step 3: Calculation of the force exerted by each hinge

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