91Ó°ÊÓ

The given data can be listed below,

• The mass of the elevator is,$m=600\mathrm{kg}$
• The distance ascended by elevator is, $h=20\mathrm{m}$
• The power of motor is $P=40\mathrm{hp}$
• The average mass of passenger is,$m_p=65\mathrm{kg}$

The rate of doing work with respect to time is called power. Alternatively, we can also describe power as the amount of energy transferred per second.

The total mass$\left(m\right)$ of the elevator can be obtained from the relation-

$$\begin{gathered} P_{av}=\frac{mgh}{t} \\ m=\frac{P_{av}t}{gh} \end{gathered}$$

Here,$P_{av}$ is the power of the motor, g is the acceleration due to gravity, and h is the distance travelled by elevator.

Substitute all the given values in the above equation,

$$\begin{gathered} m=\frac{\left(40\mathrm{hp}\right)\left(746\mathrm{W}/1\mathrm{hp}\right)\left(16\mathrm{s}\right)}{\left(9.80\mathrm{m}/{\mathrm{s}}^2\right)\left(20\mathrm{m}\right)} \\ =2.436×{10}^3\mathrm{kg} \end{gathered}$$

The total mass of passengers is given by,

$$\begin{gathered} m_t=\left(\left(2.436×{10}^3\right)-600\right)\mathrm{kg} \\ =1.836×{10}^3\mathrm{kg} \end{gathered}$$

The number of passengers in the elevator is given by,

$$\begin{gathered} n=\frac{m_t}{m_p} \\ =\frac{1.836×{10}^3\mathrm{kg}}{65\mathrm{kg}} \\ =28 \end{gathered}$$

Thus, the maximum number of passengers that can fit in elevator is 28.