Final answer:
When the pendulum's velocity is zero at the peak, the only forces are the weight of the ball and tension in the string, which are equal. If the string's force limit exceeds this tension, it won't snap. The most significant tension occurs at the bottom of the swing, where it must also provide centripetal force.
Step-by-step explanation:
The question is related to the concepts of centripetal force, tension, and static equilibrium in a simple pendulum system. In the scenario provided, a 200 g metal ball is attached to a light string and swings as a pendulum. When a pendulum's velocity is momentarily zero (at the peak of its swing on either side), all of its energy is potential. The forces acting on the ball at that instant are gravitational force, acting downward, and tension in the string, acting upward. Since the pendulum is momentarily at rest and not accelerating, the tension is equal to the weight of the ball, which is the product of its mass and gravitational acceleration. Thus, tension in the string equals mg (mass times gravity).
If the string can withstand a force greater than this tension, then it will not snap. At the bottom of the swing, however, the tension is greatest because it must support both the weight of the pendulum and provide the centripetal force required to keep the ball moving in a circular path. The actual calculation would require additional information about the system's speed at the bottom and the specific strength (N) of the string.
A visual of the forces when the velocity is zero would show an arrow pointing downward representing gravitational force, and an arrow of equal length pointing upward, representing tension. The physical origin of the force stretching the string is the mass's inertia as it moves in a circular path, necessitating a centripetal force to keep it in motion.