Chapter 6, Problem 66A

Suppose the masses described in problem 65 are 1 kg and 100 kg, respectively. Compare the accelerations when they are interchanged, that is, for the case where the 1-kg mass dangles over the pulley, and then for the case where the 100-kg mass dangles over the pulley. What does this indicate about the maximum acceleration of such a system of masses?

To determine

To explain: The comparison of acceleration of masses for the given cases. Also, the information about the maximum acceleration of such a system of masses.

Answer to Problem 66A

The acceleration of the $100\text{ kg}$ mass dangles over the pulley is higher compared to the system of masses. The maximum acceleration of such system of masses is g.

Explanation of Solution

Given:

The masses $\left(m\right)$ are $1\text{ kg}$ and $100\text{ kg}$ .

Formula used:

The expression for force is,

  $F=ma$

Here, $m$ is the mass and $a$ is the acceleration.

The expression for weight is,

  $W=F_g=mg$

Here, $F_g$ is the force of gravitation, $m$ is the mass, and $g$ is the acceleration due to gravity.

Calculation:

Consider the acceleration due to gravity as $g=9.8\text{m}/{\text{s}}^{\text{2}}$ and the net force acting on the system will be equal to the weight of the weight that dangles over the pulley.

Consider the case when $1\text{ kg}$ mass is dangled over the pulley while 100 kg mass is lying on the table.

Sketch the pulley diagram as shown in below.

  

The acceleration of the system is,

  $\begin{array}{l}F=ma\\ mg=m_{\text{total}}a\\ \left(1\text{ kg}\right)g=\left(100\text{ kg}+1\text{ kg}\right)a\\ a=\frac{g}{101}\end{array}$

Consider the case when the $100\text{ kg}$ mass dangles over the pulley while 1 kg mass is lying on the table.

Sketch the pulley diagram as shown in Figure below.

  

The acceleration of the system is,

  $\begin{array}{l}F=ma\\ mg=m_{\text{total}}a\\ \left(100\text{ kg}\right)g=\left(100\text{ kg}+1\text{ kg}\right)a\\ a=\frac{100g}{101}\end{array}$

Hence, the acceleration will be more when $100\text{ kg}$ mass is dangled over the pulley is higher compared to the system of masses. Also, the value of maximum acceleration will be g.