Chapter 5, Problem 71GP

To determine

The acceleration of the elevator and the direction of the acceleration.

Answer to Problem 71GP

The acceleration of the elevator is $2.56\text{m}/{\text{s}}^2$ and the direction of the elevator is in upward direction.

Explanation of Solution

Given:

The mass outside elevator is, $m_0=65\text{kg}$ .

The mass inside elevator is, $m_i=82\text{kg}$ .

Formula Used:

The expression to calculate the acceleration of the elevator is,

  $\begin{array}{c}{m}_{o}a=m_{i}g-m_{o}g\\ a=\left(\frac{m_i-m_o}{m_o}\right)g\end{array}$

Where,

  $a$ is the acceleration of the elevator.

  $g$ is the acceleration due to gravity.

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}a=\left(\frac{82\text{kg}-65\text{kg}}{65\text{kg}}\right)\left(9.8\text{m}/{\text{s}}^2\right)\\ =2.56\text{m}/{\text{s}}^2\end{array}$

The acceleration of the elevator is positive, so the elevator is moving in upward direction.

Conclusion:

Thus, the acceleration of the elevator is $2.56\text{m}/{\text{s}}^2$ and the direction of the elevator is in upward direction.