Chapter U3.57, Problem 6E

Interpretation Introduction

Interpretation:

The minimum pressure required in bike tires for a person with mass 150 lb needs to be determined.

Concept introduction:

The pressure is defined as mass per unit area and it is mathematically represented as follows:

$P=\frac{m}{A}$

Here, m is mass and A is area.

Answer to Problem 6E

$66.67\text{ lb/in}{\text{.}}^2$

Explanation of Solution

The given mass is 150 lb and the dimensions of the square where tires touch the ground are 1.5 in. by 1.5 in.

First, calculate the area of the square as follows:

$A=l\times l$

Putting the values,

$A=\left(1.5\times 1.5\right)\text{ in}{\text{.}}^2=2.25\text{ in}{\text{.}}^2$

Now, pressure can be calculated as follows:

$P=\frac{m}{A}$

Putting the values,

$P=\frac{150\text{ lb}}{2.25\text{ in}{\text{.}}^2}=66.67\text{ lb/in}{\text{.}}^2$

Conclusion

Thus, the minimum pressure required in bike tires is $66.67\text{ lb/in}{\text{.}}^2$.