Chapter 10.2, Problem 26PP

a.

To determine

The IMA of the wedge.

Answer to Problem 26PP

  $4$

Explanation of Solution

Given:

The distance upto which the wedge is driver, $d_e=0.20\text{}\text{m}$

The distance by which the log is seperated, $d_r=5.0\text{cm}=0.05\text{m}$

The force needed to split the log, $F_r=1.7\times {10}^4\text{}\text{N}$

The force exerted by the sledgehammer, $F_e=1.1\times {10}^4\text{}\text{N}$

Formula used:

The idea mechanical advantage is the ratio of the distances moved,

  $IMA=\frac{d_e}{d_r}$

Where $d_e$ is the displacement by the effort force, and $d_r$ is the displacement of the load.

Calculation:

Using the given values, IMA of the wedge can be calculated as,

  $\begin{array}{c}IMA=\frac{d_e}{d_r}\\ =\frac{0.20}{0.05}\\ =4\end{array}$

Conclusion:

Thus, IMA of the wedge is $4$ .

b.

To determine

The MA of the wedge.

Answer to Problem 26PP

  $1.54$

Explanation of Solution

Given:

The distance upto which the wedge is driver, $d_e=0.20\text{}\text{m}$

The distance by which the log is seperated, $d_r=5.0\text{cm}=0.05\text{m}$

The force needed to split the log, $F_r=1.7\times {10}^4\text{}\text{N}$

The force exerted by the sledgehammer, $F_e=1.1\times {10}^4\text{}\text{N}$

Formula used:

The mechanical advantage of a system is given by,

  $MA=\frac{F_r}{F_e}$

Where $F_r$ is the resistance force, and $F_e$ is the effort force.

Calculation:

Using the given values, MA of the wedge can be calculated as,

  $\begin{array}{c}MA=\frac{F_r}{F_e}\\ =\frac{1.7\times {10}^4}{1.1\times {10}^4}\\ =1.54\end{array}$

Conclusion:

Thus, MA of the wedge is $1.54$ .

c.

To determine

The efficiency of the wedge as a machine.

Answer to Problem 26PP

  $38.5\%$

Explanation of Solution

Given:

The distance upto which the wedge is driver, $d_e=0.20\text{}\text{m}$

The distance by which the log is seperated, $d_r=5.0\text{cm}=0.05\text{m}$

The force needed to split the log, $F_r=1.7\times {10}^4\text{}\text{N}$

The force exerted by the sledgehammer, $F_e=1.1\times {10}^4\text{}\text{N}$

From part (a), $IMA=4$

From part (b), $MA=1.54$

Formula used:

The efficiency of a machine is the ratio of mechanical advantage and ideal mechanical advantages,

  $e=\frac{MA}{IMA}\times 100$

Calculation:

Using the given values in above, the efficiency of the wedge can be calculated as,

  $\begin{array}{c}e=\frac{MA}{IMA}\times 100\\ =\left(\frac{1.54}{4}\times 100\right)\%\\ =38.5\%\end{array}$

Conclusion:

Thus, the efficiency of the wedge is $38.5\%$ .