Final answer:
To calculate the period of oscillation for the person's leg treated as a physical pendulum, the given formula is used, yielding a period of approximately 1.3 seconds, which corresponds to option E.
Step-by-step explanation:
To determine the period of oscillation for a person's leg treated as a physical pendulum, we can use the formula for the period of a physical pendulum:
T = 2π * √(I / (mgd))
Where:
- T is the period of oscillation,
- I is the moment of inertia,
- m is the mass of the pendulum,
- g is the acceleration due to gravity (approximately 9.8 m/s²), and
- d is the distance from the pivot point to the center of mass.
Given that the person's leg has a mass (m) of 14 kg, a length from the hip to the heel of 1.0 m, and a rotational inertia (I) of 3.1 kg·m², with the center of mass halfway down the leg, we can plug these values into our formula as follows:
T = 2π * √(3.1 kg·m² / (14 kg * 9.8 m/s² * 0.5 m))
Solving for T using a calculator yields:
T ≈ 2π * √(3.1 / 68.6) ≈ 2π * √(0.04518) ≈ 2π * 0.2126 ≈ 1.337 s
Therefore, the period of oscillation is approximately 1.337 seconds, which rounds to 1.3 seconds. This corresponds to option E.