Chapter 18, Problem 30A

Consider a model steel bridge that is $1/100$ the exact scale of the real bridge that is to be built.

a. If the model bridge weighs 50 N, what will the real bridge weigh?

b. If the model bridge doesn’t appear to sag under its own weight, is this evidence that the real bridge, built exactly to scale; will not appear to sag either? Explain.

To determine

The real weight of the bridge.

Answer to Problem 30A

The real weight of the bridge is $5000\text{ N}$ .

Explanation of Solution

Given:

The model steel bridge is $\frac{1}{100}$ the exact scale of the real bridge.

The weight of the model bridge is $50\text{ N}$

Formula used:

  $\text{Weight of model bridge}=n\times \text{Weight of real bridge}$

Where,

n is the factor.

Calculation:

The real weight of the bridge using the relation is,

  $\begin{array}{l}\text{Weight of model bridge}=\frac{1}{100}\times \text{Weight of real bridge}\\ \text{50 N}=\frac{1}{100}\times \text{Weight of real bridge}\\ \text{Weight of real bridge}=5,000\text{ N}\end{array}$

Conclusion:

Thus, the real weight of the bridge is $5000\text{ N}$ .

To determine

To identify:Whether it is evident that the real bridge that is built exactly to scale will not appear to sag from the given information.

Answer to Problem 30A

The real bridge will not appear to sag either.

Explanation of Solution

Introduction:

Scaling is the study of how size affects the relation between weight, strength, and surface area.

The proportions of things in nature are in accord with their size.

From part (a), the real weight of the bridge is $5000\text{ N}$ .

The weight of the bridge is increased to $5000\text{ N}$ , then the volume and the cross sectional area also increased.

The model steel bridge is $\frac{1}{100}$ times that of real bridge.When the real bridge is constructed, it should be increased 100 times the model steel bridge.So the real bridge constructed is satisfying the characteristics of the model bridge. If the model bridge doesn’t appeared to sag then the real bridge will also not appear to sag.

Conclusion:

Thus, the real bridge will not appear to sag either.