Chapter 14.2, Problem 12E

To determine

The amount of energy used, in kilowatt hour, in transporting metric tones of coal.

Explanation of Solution

Given information:

The conveyor belt carries coal up a $22°$ slope through a distance of $5km$ measured along the slope.

Calculations:

Here we draw a schematic diagram of the situation.

  

Here the coal is moving from A to B at a slope of $22°$ .

Therefore gravitational force is acting downward.

Now we draw the force diagram

F shows the force acting on the conveyor belt.

G shows the gravitational pull.

H shows the horizontal force.

Now the gravitational force has magnitude,

  $G=9.8\times 120=1176N$

Therefore,

  $F=1176\times \sin 22°N=440.54N$

Therefore work done in transporting the coal is,

  $\begin{array}{l}F=1176\times \sin 22°N=440.54N\\ W=F\times d=440.54\times 5000=2202686.77Nm\end{array}$

Therefore energy needed in transporting the coal is,

  $\begin{array}{l}W=F\times d=440.54\times 5000=2202686.77Nm\\ \text{Energy needed is }=\frac{2202686.77Nm}{3.6\times {10}^6}=0.612kWh\end{array}$