Chapter 5, Problem 46P

To determine

The acceleration of the elevator and its direction.

Answer to Problem 46P

Solution:

  $a=2.37{\text{m/s}}^{\text{2}}$ in the upward direction.

Explanation of Solution

Given:

The actual mass of the person, $m=62\text{kg}$

Mass of the person in the elevator, $m_n=77\text{kg}$

Formula Used:

  $F_{net}=F_n-F_g$

Where $F_n$ is the normal force

  $F_g$ is the actual force

Calculation:

The net force is

  $F_{net}=F_n-F_g$

  $ma=m_{n}g-mg$

Substituting all the values:

  $62\times a=77\times 9.81-62\times 9.81$

  $\begin{array}{l}a=\frac{\left(77\times 9.81-62\times 9.81\right)}{62}\\ a=2.37{\text{m/s}}^{\text{2}}\end{array}$ .

Since the value of acceleration is positive, the elevator is moving in the upward direction.

Conclusion:

Therefore, the acceleration of the elevator is $a=2.37{\text{m/s}}^{\text{2}}$ and is in the upward direction.