Question

A 13-g goldfinch has a speed of 8.5 m>s. What is its kinetic energy?

Short answer

The kinetic energy of the goldfinch is approximately 0.47 joules.

Step-by-step solution

Identify the Given Quantities

We are given the mass of the goldfinch, which is 13 grams, and its speed, which is 8.5 meters per second. These will be used to calculate kinetic energy.

Convert Mass to Kilograms

Since kinetic energy is usually calculated in the metric system using kilograms for mass, we need to convert the mass from grams to kilograms. \[ 13 \text{ grams} = 0.013 \text{ kilograms} \]

Use the Kinetic Energy Formula

The formula for kinetic energy (KE) is given by \( KE = \frac{1}{2} mv^2 \), where \( m \) is mass in kilograms and \( v \) is velocity in meters per second.

Substitute the Values into the Formula

Substituting the values we have: \[ KE = \frac{1}{2} \times 0.013 \times (8.5)^2 \]

Calculate the Kinetic Energy

First, calculate \( (8.5)^2 = 72.25 \). Then substitute this back into the equation: \[ KE = \frac{1}{2} \times 0.013 \times 72.25 \] \[ KE = 0.0065 \times 72.25 \] \[ KE = 0.469625 \] Therefore, the kinetic energy of the goldfinch is approximately 0.47 joules.

Key concepts

Mass Conversion

In the realm of physics, particularly when dealing with calculations, it's essential to work with consistent units. One common conversion is changing mass from grams to kilograms. This is because the metric system's standard unit for mass in calculations involving kinetic energy and other physical quantities is the kilogram.

To convert grams to kilograms, remember that 1 kilogram is equivalent to 1000 grams. You can find the number of kilograms by dividing the number of grams by 1000. For instance, a mass of 13 grams would be 0.013 kilograms, since \( 13 \div 1000 = 0.013 \).

This conversion ensures that all units are consistent, allowing accurate and meaningful results when applying formulas to calculate energy, force, and other physical phenomena.

Velocity

Velocity is a crucial concept in physics that represents the speed of an object in a specific direction. It's not just about how fast something is moving but also about the direction. This makes it a vector quantity, meaning it has both magnitude and direction.

In our example, the goldfinch's velocity is given as 8.5 meters per second (m/s). The direction is not specified here, so it is likely considered in a straight path. The magnitude, however, which is the numeric value of the speed, is crucial when calculating kinetic energy, since it affects how much energy the object possesses.

The higher the velocity, the more kinetic energy an object has, because kinetic energy depends on the square of velocity. Therefore, slight changes in velocity can significantly impact the energy calculation. This is why accurate measurement and consistent units are important.

Kinetic Energy Formula

Kinetic energy refers to the energy that an object possesses due to its motion. The formula used to calculate kinetic energy is \( KE = \frac{1}{2} mv^2 \). This formula helps determine how much work an object can perform due to its motion.

Here, \( m \) stands for mass in kilograms, and \( v \) is velocity in meters per second. By calculating the kinetic energy, you can understand how energy is transferred when an object is moving.

The term \( \frac{1}{2} mv^2 \) highlights the relationship between mass, velocity, and energy:

• Mass: More massive objects will have more kinetic energy if their velocity is the same as a less massive object.
• Velocity: Since the velocity is squared, it has a greater effect on kinetic energy than mass. This means doubling the velocity will quadruple the kinetic energy.

Understanding this formula allows you to relate the physical movement of objects to the energy exchange in a system.