As a pendulum moves closer to the equilibrium position, how do the velocity, acceleration, and force change?   a.  the velocity decreases, the acceleration decreases, and the net force decreases. b.  the velocity increases, the acceleration decreases, and the net force decreases. c.  the velocity increases, the acceleration increases, and the net force decreases. d.  the velocity decreases, the acceleration increases, and the net force increases.

B. The velocity increases, the acceleration decreases, and the net force decreases.

Explanation:

- Velocity: as the pendulum moves closer to the equilibrium position, its gravitational potential energy decreases (because the height decreases), and therefore for the law of conservation of energy, the kinetic energy increases. But the kinetic energy is proportional to the square of the velocity:

So, this means that the velocity increases as well.

- Acceleration: the acceleration of the pendulum is equal to the horizontal component of the gravitational acceleration, given by:

where and is the angle the pendulum forms with the vertical. As the pendulum approaches the equilibrium position, becomes smaller, therefore the acceleration decreases.

- Net force: the net force is the force acting on the horizontal direction, i.e. the horizontal component of the weight :

where m is the mass of the pendulum. As the pendulum approaches the equilibrium position, becomes smaller, therefore the net force decreases.

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