Chapter 2, Problem 60E

A 60-kg person stands on a scale in an elevator. How many newtons does the scale read (a) when the elevator is ascending with an acceleration of 1 m/s²; (b) when it is descending with an acceleration of 1 m/s²; (c) when it is ascending at a constant speed of 3 m/s; (d) when it is descending at a constant speed of 3 m/s; (e) when the cable has broken and the elevator is descending in free fall?

To determine

The reading on the scale when the elevator is ascending with an acceleration of $1{\text{m/s}}^2$.

Answer to Problem 60E

The reading on the scale when the elevator is ascending with an acceleration of $1{\text{m/s}}^2$ is $648\text{N}$.

Explanation of Solution

Given Info: The mass of the person is $60\text{kg}$.

Write the expression for the force.

$F=mg+ma$

Here,

$F$ is the force.

$m$ is the mass.

$a$ is the acceleration.

$g$ is the acceleration due to gravity.

Substitute $60\text{kg}$ for $m$, $1{\text{m/s}}^2$ for $a$ and $9.8{\text{m/s}}^2$ for $g$ to find $F$.

$\begin{array}{c}F=\left(60\text{kg}\right)\left(9.8{\text{m/s}}^2\right)+\left(600\text{kg}\right)\left(1{\text{m/s}}^2\right)\\ =648\text{N}\end{array}$

Conclusion:

Therefore, the reading on the scale when the elevator is ascending with an acceleration of $1{\text{m/s}}^2$ is $648\text{N}$.

To determine

The reading on the scale when the elevator is descending with an acceleration of $1{\text{m/s}}^2$.

Answer to Problem 60E

The reading on the scale when the elevator is descending with an acceleration of $1{\text{m/s}}^2$ is $528\text{N}$.

Explanation of Solution

Given Info: The mass of the person is $60\text{kg}$.

Write the expression for the force.

$F=mg-ma$

Substitute $60\text{kg}$ for $m$, $1{\text{m/s}}^2$ for $a$ and $9.8{\text{m/s}}^2$ for $g$ to find $F$.

$\begin{array}{c}F=\left(60\text{kg}\right)\left(9.8{\text{m/s}}^2\right)-\left(600\text{kg}\right)\left(1{\text{m/s}}^2\right)\\ =528\text{N}\end{array}$

Conclusion:

Therefore, the reading on the scale when the elevator is descending with an acceleration of $1{\text{m/s}}^2$ is $528\text{N}$.

To determine

The reading on the scale when the elevator is ascending at a constant speed of $3{\text{m/s}}^2$.

Answer to Problem 60E

The reading on the scale when the elevator is ascending at a constant speed of $3{\text{m/s}}^2$ is $588\text{N}$.

Explanation of Solution

Given Info: The mass of the person is $60\text{kg}$.

Write the expression for the force.

$F=mg$

Substitute $60\text{kg}$ for $m$ and $9.8{\text{m/s}}^2$ for $g$ to find $F$.

$\begin{array}{c}F=\left(60\text{kg}\right)\left(9.8{\text{m/s}}^2\right)\\ =588\text{N}\end{array}$

Conclusion:

Therefore, the reading on the scale when the elevator is ascending at a constant speed of $3{\text{m/s}}^2$ is $588\text{N}$.

To determine

The reading on the scale when the elevator is descending at a constant speed of $3{\text{m/s}}^2$.

Answer to Problem 60E

The reading on the scale when the elevator is descending at a constant speed of $3{\text{m/s}}^2$ is $588\text{N}$.

Explanation of Solution

Given Info: The mass of the person is $60\text{kg}$.

Write the expression for the force.

$F=mg$

Substitute $60\text{kg}$ for $m$ and $9.8{\text{m/s}}^2$ for $g$ to find $F$.

$\begin{array}{c}F=\left(60\text{kg}\right)\left(9.8{\text{m/s}}^2\right)\\ =588\text{N}\end{array}$

Conclusion:

Therefore, the reading on the scale when the elevator is descending at a constant speed of $3{\text{m/s}}^2$ is $588\text{N}$.

To determine

The reading on the scale when the cable has broken, and the elevator is descending in freefall.

Answer to Problem 60E

The reading on the scale when the cable has broken, and the elevator is descending in freefall is zero.

Explanation of Solution

Given Info: The mass of the person is $60\text{kg}$.

When the object is in freefall, the object feels weightless. This is because the acceleration of the object is same as the acceleration due to gravity. And thus, the object is weightless.

For the person in the lift, the reading on the scale depends on the acceleration of the lift. In freefall, the person feels no weight. And the reading on the scale is zero.

Conclusion:

Therefore, the reading on the scale when the cable has broken, and the elevator is descending in freefall is zero.