At theta = -theta_max, which statement is true?

At theta = -theta_max, which statement is true?

• A. F_restoring = 0; a_t = 0; U = 0; KE = max; v = max
• B. F_restoring = max; a_t = max; U = mgh = max; KE = 0; v = 0
• C. F_restoring = 0; a_t = max; U = max; KE = max; v = 0
• D. F_restoring = max; a_t = 0; U = max; KE = 0; v = 0

Answer: (B)

At the farthest point from the bottom (the extreme angle), the pendulum is momentarily at rest, so velocity and kinetic energy are zero. The weight provides the restoring force along the arc, and its tangential component is largest in magnitude at this point, since it scales with sin(theta). That means the tangential (restoring) acceleration is also as large as possible toward the equilibrium position. The height is greatest at this extreme, so the gravitational potential energy mgh is maximum. Since the energy is all potential at this turning point, the kinetic energy is zero. Putting it together: restoring force magnitude is maximal, tangential acceleration is maximal, potential energy is maximal, while kinetic energy and velocity are zero. This aligns with the described option.

At the farthest point from the bottom (the extreme angle), the pendulum is momentarily at rest, so velocity and kinetic energy are zero. The weight provides the restoring force along the arc, and its tangential component is largest in magnitude at this point, since it scales with sin(theta). That means the tangential (restoring) acceleration is also as large as possible toward the equilibrium position.

The height is greatest at this extreme, so the gravitational potential energy mgh is maximum. Since the energy is all potential at this turning point, the kinetic energy is zero.

Putting it together: restoring force magnitude is maximal, tangential acceleration is maximal, potential energy is maximal, while kinetic energy and velocity are zero. This aligns with the described option.