Final answer:
To calculate the total energy of a pendulum, we use conservation of energy, equating gravitational potential energy at the highest point to the maximal kinetic energy at the lowest point of the swing. The total energy remains constant throughout the pendulum's motion in the absence of external forces.
Step-by-step explanation:
To calculate the total energy of a pendulum, we use the principle of conservation of energy. The total mechanical energy in a pendulum system is conserved if we ignore air resistance and friction. At the lowest point of its swing, the pendulum has its maximum kinetic energy and zero potential energy as potential energy is defined to be zero at this point. When the pendulum reaches its highest point, all of its energy is stored as gravitational potential energy.
The gravitational potential energy (U) at a height is given by U = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above the lowest point. At the top of the swing, this is equal to the total mechanical energy. The kinetic energy (K) at the lowest point can be calculated using K = ½mv², where v is the velocity. Since the system's total energy is conserved, the energy calculated at the highest point is equal to the energy at the lowest point, where the potential energy is zero and kinetic energy is at its maximum.
To find the total energy, we must know the mass of the pendulum, the height at the top of the swing, and the velocity at the bottom. Without these values, we cannot provide a numerical answer. However, the student is advised that the total energy will be the sum of potential and kinetic energies at any point in the pendulum's swing and is constant throughout the motion if there is no external work done on the system.