A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light, thin cords 1.50 m long. If a minor earthquake occurs, how many swings per second will these fixtures make?

Verified step by step guidance

1. Identify the type of motion: The bulbs swinging due to the earthquake can be modeled as simple pendulums.
2. Write down the formula for the period (T) of a simple pendulum: T = 2\pi \sqrt{\frac{L}{g}}, where L is the length of the pendulum and g is the acceleration due to gravity (approximately 9.81 m/s^2).
3. Substitute the given values into the formula to find the period T. Use L = 1.50 m and g = 9.81 m/s^2.
4. Calculate the frequency (f) of the pendulum's swings, since frequency is the reciprocal of the period: f = \frac{1}{T}.
5. The result from the previous step gives you the number of swings per second the light fixtures will make during the earthquake.

Key Concepts

Simple Harmonic Motion

Simple Harmonic Motion (SHM) describes the oscillatory motion of an object around an equilibrium position, where the restoring force is directly proportional to the displacement. In this context, the light fixtures can be modeled as pendulums that swing back and forth when disturbed, such as during an earthquake. The frequency of these swings is determined by the mass of the bulbs and the length of the cords.

Pendulum Frequency

The frequency of a simple pendulum is the number of complete swings it makes per second. It is influenced by the length of the pendulum and the acceleration due to gravity. The formula for the frequency (f) of a simple pendulum is f = 1/(2π) * √(g/L), where g is the acceleration due to gravity and L is the length of the pendulum. This relationship is crucial for calculating how many swings the light fixtures will make.

Effect of Gravity

Gravity is the force that pulls objects toward the Earth, and it plays a significant role in the motion of pendulums. The acceleration due to gravity (approximately 9.81 m/s² on Earth) affects the speed and frequency of the swings. In the case of the light fixtures, understanding how gravity interacts with the mass of the bulbs and the length of the cords is essential for determining the oscillation frequency during the earthquake.