How does the law of conservation of energy apply in a swinging pendulum?

• A. Energy is created and destroyed as the pendulum moves, violating the conservation principle.
• B. The pendulum's energy is always entirely kinetic.
• C. Energy continually transforms between potential energy and kinetic energy; total mechanical energy remains constant in an ideal pendulum with no friction.
• D. The sum of kinetic energy and potential energy increases over time due to gravity.

Answer: (C)

The idea being tested is that mechanical energy is conserved in an ideal pendulum. As the bob swings, gravitational potential energy and kinetic energy continually transform into each other, but their total stays the same when there are no losses. At the highest point, the speed is zero, so all energy is gravitational potential energy. As it swings down, height decreases and kinetic energy increases, reaching a maximum kinetic energy at the bottom where potential energy is minimal. The sum of kinetic plus potential energy remains constant in this ideal case.

In the real world, tiny amounts of energy are lost to friction and air resistance, so the total mechanical energy gradually decreases over time, and the pendulum’s swings become smaller.

Why the other statements don’t fit: energy isn’t created or destroyed as the pendulum moves, which would violate conservation. The energy is not always entirely kinetic—the bob has potential energy at the top of the swing. Gravity doesn’t make the total energy increase over time; it only converts energy from potential to kinetic and back, leaving the total unchanged in an ideal setting.