Question:
The pendulum is suspended by a string a length 250 cm. The bob has a mass of 200 g and is displaced sideways such that the string makes an angle of 60° with the vertical, as illustrated. Upon releasing the bob from this position, determine the maximum speed (in m/s) it achieves during its motion.
Non-conservative forces such as friction and air drag are not mentioned in the problem. It is assumed that non-conservative forces are absent in the given problem. Hence, conservation of mechanical energy can be applied. That is, the total initial energy will be equal to the total final energy of the system.
The amount of work done in raising a bob to a height ‘h’ from the lowest point is stored as potential energy in the bob. “If you do work against forces like gravity or a spring’s pull, that energy doesn’t disappear—it gets stored as potential energy.” Therefore, at a height ‘h,’ the bob has purely potential energy.
As the bob is released from a height ‘h,’ the pendulum swings, and as it moves down, the potential energy decreases, and the stored potential energy gets converted into kinetic energy. Therefore, at the lowest point, the potential energy becomes zero; thus, the bob has purely kinetic energy at the lowest point.
The total initial energy of the bob, such as potential energy, must be equal to the total final energy of the bob, such as kinetic energy, at the bottom. Since, at the lowest point, the kinetic energy is the maximum, the speed of the bob at the lowest point will be the maximum. Solving the conservation equation gives the value of maximum speed.
