Question

The acceleration due to gravity is approximately \(9.81 \mathrm{~m} / \mathrm{s}^{2}\) (depending on your location). What is the acceleration due to gravity in centimeters per second squared?

Short answer

The acceleration due to gravity is \(981 \text{ cm/s}^2\).

Step-by-step solution

Understand the Conversion Factor

To convert from meters to centimeters, remember that 1 meter is equivalent to 100 centimeters.

Apply the Conversion

Since the original acceleration due to gravity is given as \(9.81 \text{ m/s}^2\), and we need to convert meters into centimeters, we multiply \(9.81\) by the conversion factor, which is 100.

Calculate the Result

Multiply the value of gravity in meters per second squared by 100: \(9.81 \times 100 = 981\).

Write the Final Answer in the Required Units

Therefore, the acceleration due to gravity is \(981 \text{ cm/s}^2\).

Key concepts

Acceleration Due to Gravity

The acceleration due to gravity, often represented by the symbol \( g \), is a measure of the force with which gravity pulls on objects towards the Earth's surface. It is considered to be approximately \( 9.81 \text{ m/s}^2 \) at sea level. This value can vary slightly depending on where you are on Earth due to factors like altitude and latitude.Gravity causes objects to accelerate downwards, and this constant acceleration means that for every second an object falls, its velocity increases by \( 9.81 \text{ m/s} \).
Understanding the acceleration due to gravity is crucial in fields like physics and engineering, as it influences the motion of objects and can impact everything from the calculations in mechanical systems to understanding projectile motion.

Metric System

The metric system is a universal measurement system used globally, characterized by its simplicity and ease of conversion. It is based on the meter as the basic unit of length and includes additional units such as the gram for weight and the liter for volume. All conversions in the metric system revolve around powers of 10, making it very logical.For instance:

• 1 meter = 100 centimeters
• 1 kilogram = 1000 grams
• 1 liter = 1000 milliliters

Because of its consistency and decimal-based structure, scientists and educators often prefer the metric system for scientific calculations and teaching.In our exercise, converting \(9.81 \text{ m/s}^2\) to centimeters per second squared was simple because it only involved multiplying by 100, reflecting the rule that 1 meter equals 100 centimeters.

Measurement Units

Measurement units are the standards we use to quantify and understand the world around us. They allow us to measure physical quantities like length, mass, and time in a fashion that is consistent and comparable.It's important to know that these units can differ across systems, but conversion factors help bridge this gap.
In physics, for example, acceleration units might be meters per second squared \((\text{m/s}^2)\), but sometimes conversions to other units such as centimeters per second squared \((\text{cm/s}^2)\) can be useful for practical applications or consistency with other measurements.Using the right units for a problem is crucial for accurate communication and computation. With our exercise, understanding how to correctly switch from meters to centimeters was key to finding the acceleration due to gravity in the desired units.