Final answer:
The potential energy of the pendulum at its highest point is calculated using the conservation of mechanical energy. Since the total mechanical energy is 70 J and the kinetic energy at the lowest point is 60 J, the potential energy at the highest point is 10 J.
Step-by-step explanation:
The problem you've given is a classic example of the conservation of mechanical energy principle in physics, specifically within the context of pendulum motion. To find the potential energy at the highest point of a pendulum, we can use the principle that the total mechanical energy in a closed system remains constant if we ignore air resistance and friction. This total mechanical energy is the sum of kinetic and potential energy. At the highest point of its swing, the pendulum's kinetic energy is 0, and all the mechanical energy is potential energy.
Given that the maximum kinetic energy at the lowest point is 60 J and the total mechanical energy is 70 J, we can infer that the potential energy at the highest point must be:
Potential Energy (at the highest point) = Total Mechanical Energy – Kinetic Energy (at the lowest point)
Potential Energy (at the highest point) = 70 J – 60 J
Potential Energy (at the highest point) = 10 J
Therefore, the potential energy of the pendulum at its highest point is 10 joules.