Chapter 10, Problem 70A

a.

To determine

The IMA of the given pulley system if a force of $375\text{N}$ is exerted to lift a $1345\text{N}$ weight.

Answer to Problem 70A

  $4$

Explanation of Solution

Given:

The weight that is to be lifted, $F_r=1345\text{N}$

The distance by which the weight is lifted, $d_r=0.975\text{m}$

The distance by which the rope is pulled by Paul, $d_e=3.90\text{m}$

The force exerted by the Paul, $F_e=375\text{N}$

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 given pulley system can be calculated as,

  $\begin{array}{c}IMA=\frac{d_e}{d_r}\\ =\frac{3.90}{0.975}\\ =4\end{array}$

Conclusion:

Thus, IMA of the given pulley system is $4$ .

b.

To determine

The mechanical advantage of the given pulley system if a force of $375\text{N}$ is exerted to lift a $1345\text{N}$ weight.

Answer to Problem 70A

  $3.59$

Explanation of Solution

Given:

The weight that is to be lifted, $F_r=1345\text{N}$

The distance by which the weight is lifted, $d_r=0.975\text{m}$

The distance by which the rope is pulled by Paul, $d_e=3.90\text{m}$

The force exerted by the Paul, $F_e=375\text{N}$

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 given pulley system can be calculated as,

  $\begin{array}{c}MA=\frac{F_r}{F_e}\\ =\frac{1345}{375}\\ =3.59\end{array}$

Conclusion:

Thus, mechanical advantage of the given pulley system is $3.59$ .

c.

To determine

The efficiency of the given pulley system if a force of $375\text{N}$ is exerted to lift a $1345\text{N}$ weight.

Answer to Problem 70A

  $89.75\%$

Explanation of Solution

Given:

The weight that is to be lifted, $F_r=1345\text{N}$

The distance by which the weight is lifted, $d_r=0.975\text{m}$

The distance by which the rope is pulled by Paul, $d_e=3.90\text{m}$

The force exerted by the Paul, $F_e=375\text{N}$

From part (a), $IMA=4$

From part (b), $MA=3.59$

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 given pulley system can be calculated as,

  $\begin{array}{c}e=\frac{MA}{IMA}\times 100\\ =\left(\frac{3.59}{4}\times 100\right)\%\\ =89.75\%\end{array}$

Conclusion:

Thus, the efficiency of the given pulley system is $89.75\%$ .