Chapter 10, Problem 71A

a.

To determine

The MA of the given pulley if a force of $1.4\text{N}$ is exerted to lift a $0.50\text{kg}$ mass.

Answer to Problem 71A

  $3.5$

Explanation of Solution

Given:

The mass that is to be lifted, $m_r=0.5\text{kg}$

The distance by which the mass is lifted, $d_r=10.0\text{cm}=0.10\text{m}$

The distance by which the rope is pulled, $d_e=40\text{cm = 0}\text{.4}\text{m}$

The force exerted, $F_e=1.4\text{N}$

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:

The weight of the mass, $F_r=m_{r}g=\left(0.5\right)\left(9.8\right)=4.9\text{N}$

Using the given values, MA of the given pulley system can be calculated as,

  $\begin{array}{c}MA=\frac{F_r}{F_e}\\ =\frac{4.9}{1.4}\\ =3.5\end{array}$

Conclusion:

Thus, MA of the given pulley is $3.5$ .

b.

To determine

The IMA of the given pulley if a force of $1.4\text{N}$ is exerted to lift a $0.50\text{kg}$ mass.

Answer to Problem 71A

  $4$

Explanation of Solution

Given:

The mass that is to be lifted, $m_r=0.5\text{kg}$

The distance by which the mass is lifted, $d_r=10.0\text{cm}=0.10\text{m}$

The distance by which the rope is pulled, $d_e=40\text{cm = 0}\text{.4}\text{m}$

The force exerted, $F_e=1.4\text{N}$

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,

  $\begin{array}{c}IMA=\frac{d_e}{d_r}\\ =\frac{0.4}{0.1}\\ =4\end{array}$

Conclusion:

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

c.

To determine

The efficiency of the given pulley if a force of $1.4\text{N}$ is exerted to lift a $0.50\text{kg}$ mass.

Answer to Problem 71A

  $87.5\%$

Explanation of Solution

Given:

The mass that is to be lifted, $m_r=0.5\text{kg}$

The distance by which the mass is lifted, $d_r=10.0\text{cm}=0.10\text{m}$

The distance by which the rope is pulled, $d_e=40\text{cm = 0}\text{.4}\text{m}$

The force exerted, $F_e=1.4\text{N}$

From part (a), $MA=3.5$

From part (b), $IMA=4$

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 can be calculated as,

  $\begin{array}{c}e=\frac{MA}{IMA}\times 100\\ =\left(\frac{3.5}{4}\times 100\right)\%\\ =87.5\%\end{array}$

Conclusion:

Thus, the efficiency of the given pulley is $87.5\%$ .