Chapter 3, Problem 49A

Suppose the string in the figure in Question 48 breaks and the stone slows in its upward motion.

a. Draw a force vector diagram of the stone when it reaches the top of its path.

b. Is the net force on the stone zero at the top?

To determine

To draw: A force vector diagram of the stone when it reaches the top of its path.

Answer to Problem 49A

After reaching the top, no tension force will be applied to it. But, only gravity will act upon it.

The force vector diagram is shown in Figure 1.

Explanation of Solution

Introduction:

For a stable equilibrium, all the forces will balance each other.

As shown in the vector diagram below, both tension and force of gravity are acting upon the stone at starting. As the stone goes up with the external force, the tension in the force decreases, and the force of gravity which is constant supersedes. Once it is reached at the top, tension force disappears but only gravity applies.

  

Figure 1

Conclusion:

Thus, after reaching the top, no tension force will be applied to it. But, only gravity will act upon it. The force diagram is shown in Figure 1.

To determine

To identify: Whether the net force on the stone at the top is zero or not.

Answer to Problem 49A

After reaching the top, only the gravitational force will act upon the stone. Thus, the net force will not be zero.

Explanation of Solution

Introduction:

For a stable equilibrium, all the forces will balance each other.

Gravitational force on any object acts downwards and it is constant with for a mass. Tension in the force is acting upwards or towards the string. When it reaches the top of the string then the tension will not act upon the stone. Thus, only gravitational force will act downwards as shown in Figure 1. The net force is shown after reaching at the top in the third figure. The only force that acts upon the stone is gravitational force downwards. Thus, the net force will not be zero.

Conclusion:

After reaching the top, only gravitational force will act upon the stone. Thus, the net force will not be zero.