Final answer:
The tension in the pendulum cable is greatest at the bottom of the arc, where it must support the weight of the bob and provide centripetal force. It can be calculated using the mass, gravitational acceleration, and velocity of the bob at that point.
Step-by-step explanation:
During the motion of a pendulum, tension in the cable changes throughout its arc. At the bottom of the arc, the tension is at its maximum. This is because the tension at this point has to support the entire weight of the pendulum bob and provide the centripetal force required for its circular motion. The tension T in the cable can be expressed as T = mg + (mv²/r), where m is the mass of the bob, g is the acceleration due to gravity, v is the velocity of the bob at the bottom of the arc, and r is the radius of the pendulum's arc.
For example, if we take a 2 kg metal ball suspended from a rope as a pendulum, the velocity of the ball at point B (the bottom of the arc) can be found using energy conservation principles. The potential energy at the release point is converted to kinetic energy at the bottom of the arc. Using the formula (1/2)mv² = mgh, where h is the vertical height from which the ball was released, we can find that the velocity v is independent of the mass.