Chapter 4, Problem 10STP

To determine

To Draw: The free body diagram.

To Find: The effect on the apparent weight of the dog under given circumstances.

Answer to Problem 10STP

Free body diagram

  

Explanation of Solution

Given:

Let, the mass of the dog $=m$

Acceleration of the elevator $=a$

Gravitational acceleration $=g$

Normal force on the dog $=N$

Formula used:

Newton’s law of motion:

  $F=ma$

Where,

  $a$ is the acceleration.

  $m$ is the mass

Calculation:

Free body diagram of the dog sitting on the scale

  

When elevator is in rest

Acceleration is zero.

In this case apparent weight of the dog is the actual weight of the dog.

  $\begin{array}{l}F=N-mg\\ ma=N-mg\\ 0=N-mg\\ N=mg\end{array}$

Case 1: when elevator accelerates upward

The net force on the dog is acting upward

  $\begin{array}{l}F=N-mg\\ ma=N-mg\\ N=ma+mg\\ N=m\left(a+g\right)\end{array}$

In this case apparent weight is more than actual weight.

Case 2: When the elevator travels at a constant speed downward.

In this case acceleration is zero.

Therefore, net force on the dog is also zero.

  $\begin{array}{l}F=mg-N\\ ma=mg-N\\ 0=mg-N\\ mg=N\end{array}$

In this case apparent weight of the dog is the actual weight of the dog.

Case 3: when the elevator falls freely downward

In this case acceleration, $a=g$

  $\begin{array}{l}F=mg-N\\ mg=mg-N\\ 0=N\end{array}$

In this case the weight of the body is zero.

Conclusion:

Apparent weight is more than the actual weight when the elevator accelerates in upward direction.

Apparent weight is equal to actual weight when the elevator goes down with constant velocity.

Apparent weight is equal to zero during the free fall.