Chapter 11.6, Problem 10P

(a)

To determine

To Calculate: That how far the column has driven inside the earth on the 60^th drive.

Answer to Problem 10P

The pile moves 0.011 m on the 60^th drive.

Explanation of Solution

Given Information:

Piledriver pounds a steel column inside the earth.

The first penetration depth is 1.5m

Every succeeding drive moves the pile 92% of the previous depth penetrated into the earth.

Calculation:

With every drive keeps moving the pile moves 92% of the previous drive of the pile.

Considering the previous drive to be $x$ depth.

Therefore,

  $1.5{(0.92)}^{n-1}=1.5{(0.92)}^{60-1}$

Which is approximately 0.011 m

Hence, on the 60^th drive the pile moves 0.011 m.

(b)

To determine

To Calculate: That what will be the total distance that the column moves after the 60^th drive.

Answer to Problem 10P

The column moved 18.62 m after the 60^th drive.

Explanation of Solution

Given Information:

Piledriver pounds a steel column inside the earth.

The first penetration depth is 1.5m

Every succeeding drive moves the pile 92% of the previous depth penetrated into the earth.

Calculation:

The series that will be formulated will be a geometric series with $a=1.5$ and $r=0.92$ .

Therefore,

  $\begin{array}{c}{\displaystyle {\sum }_{n=1}^{60}1.5{(0.92)}^{n-1}}=1.5{\displaystyle {\sum }_{n=1}^{60}{(0.92)}^{n-1}}\\ =a\frac{1-r^n}{1-r}\\ =(1.5)\frac{1-{0.92}^{60}}{1-0.92}\end{array}$

Which gives and approximate distance of 18.62 m

Hence, the column moved 18.62 m after the 60^th drive.