Q58E - University Physics with Modern Physics

Question

An elevator has mass 600 kg, not including passengers. The elevator is designed to ascend, at constant speed, a vertical distance of 20 m (five floors) in 16.0 s, and it is driven by a motor that can provide up to 40 hp to the elevator. What is the maximum number of passengers that can ride in the elevator? Assume that an average passenger has mass 65 kg.

Step-by-Step Solution

Answer

Lift can carry a maximum of 28 passengers.

Step 1: Identification of given data

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, $m_p=65 \mathrm{kg}$

Step 2: Concept/Significance of Average power

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.

Step 3: Determination of the maximum number of passengers that can ride in the elevator

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,

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

The total mass of passengers is given by,

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

The number of passengers in the elevator is given by,

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

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