Question

A student makes a simple pendulum by attaching a mass to the free end of a 1.50-meter length of string suspended from the ceiling of her physics classroom. She pulls the mass up to her chin and releases it from rest, allowing the pendulum to swing in its curved path. Her classmates are surprised that the mass doesn't reach her chin on the return swing, even though she does not move. Explain why the mass does not have enough energy to return to its starting position and hit the girl on the chin.

Answer 1

The mass has likely lost some of its mechanical energy to resistance on its path.

Step-by-step explanation:

The mechanical energy of an object is the sum of its kinetic and potential energies (KE and PE.) Ideally, the mechanical energy of a simply pendulum should be "conserved." In other words, the sum of the kinetic and potential energy of the simply pendulum should stays the same as it travels along its path.

Indeed, as the pendulum travels, some of its PE will convert to KE and back. However, the sum of these two energies is supposed to stay the same.

• When the pendulum moves from the highest point to the bottom of the path, some of its PE converts to KE. (The pendulum speeds up in this process.)
• When the pendulum moves from the bottom of its path to the opposite side, its KE is converted back to PE. (The pendulum slows down as it moves towards the other side of the path.)

However, in practice, the mechanical energy of pendulums isn't always conserved. For example, various kinds of resistances (such as air resistance) act on the pendulum as it moves. That would slow down the pendulum. Some of the pendulum's energies would be converted to heat and is lost to the surroundings.

In effect, the mechanical energy of the pendulum would become smaller and smaller over time. When the pendulum travels back towards the girl, its potential energy would be smaller than the initial value when at the girl's chin.