Chapter 1, Problem 31P

To determine

The mass of rubber put into atmosphere per year .

Answer to Problem 31P

The mass of rubber put into atmosphere per year is $4.52\times {10}^8\text{kg/year}$

Explanation of Solution

Given:

The density of rubber $\rho =1200{\text{kg/m}}^{\text{3}}$

Average life of a tire $=3\text{year}$

Formula used:

Suppose there are 100 million vehicles each having 4 tires.

The mass of rubber put into atmosphere per year

  $\begin{array}{c}m=\frac{\text{no of vehicle(}n\text{)}\times \rho \times volume(v)}{3\text{year}}\\ =\frac{\text{no of vehicle(}n\text{)}\times \rho \times (W\times d\times 2\pi r)}{3year}\end{array}$.......... (1)

Here is $\rho$ density of rubber is width and d is depth and r is radius

Calculation:

Substitute $\text{(100}\times {\text{10}}^6\text{vehicles)(4tire/vehicle)}$ for n , $1200{\text{kg/m}}^{\text{3}}$ for $\rho$ , $\text{15}\times {\text{10}}^{-2}\text{m}$ for W ,

  ${10}^{-2}m$ ford , $30\times {10}^{-2}\text{m}$ for r in equation (1), to find the mass of rubber put into atmosphere per year

  $\begin{array}{c}m=\frac{(100\times {10}^6)\times (4)\times (1200{\text{kg/m}}^{\text{3}})(15\times {10}^{-2}\text{m})({10}^{-2}\text{m})2\pi (30\times {10}^{-2}\text{m})}{3\text{year}}\\ =4.52\times {10}^8\text{kg/year}\end{array}$

Conclusion:

Thus, The mass of rubber put into atmosphere per year is $4.52\times {10}^8\text{kg/year}$ .