Calculating Kinetic Energy of a Moving Ball

The question asks us to calculate the kinetic energy of a ball given its mass and velocity. Kinetic energy is the energy an object possesses due to its motion. The formula for kinetic energy is well-defined in physics.

Understanding the Kinetic Energy Formula

The kinetic energy ($\text{KE}$) of an object is directly proportional to its mass ($m$) and the square of its velocity ($v$). The standard formula is:

$$ \text{KE} = \frac{1}{2} m v^2 $$

In this formula:

• $\text{KE}$ is the kinetic energy, measured in Joules (J).
• $m$ is the mass of the object, measured in kilograms (kg).
• $v$ is the velocity of the object, measured in meters per second (m/s).

Applying the Values to Calculate Kinetic Energy

We are given the following information:

• Mass of the ball ($m$) = 0.5 kg
• Velocity of the ball ($v$) = 4 m/s

Now, we substitute these values into the kinetic energy formula:

$$ \text{KE} = \frac{1}{2} \times m \times v^2 $$

$$ \text{KE} = \frac{1}{2} \times 0.5 \, \text{kg} \times (4 \, \text{m/s})^2 $$

First, calculate the square of the velocity:

$$ v^2 = (4 \, \text{m/s})^2 = 16 \, \text{m}^2/\text{s}^2 $$

Now, substitute this back into the formula:

$$ \text{KE} = \frac{1}{2} \times 0.5 \, \text{kg} \times 16 \, \text{m}^2/\text{s}^2 $$

Multiply the terms:

$$ \text{KE} = 0.5 \times 0.5 \times 16 \, \text{J} $$

$$ \text{KE} = 0.25 \times 16 \, \text{J} $$

$$ \text{KE} = 4 \, \text{J} $$

So, the kinetic energy of the ball is 4 Joules.

Comparing with Given Options

Let's look at the provided options:

• 12 J
• 8 J
• 4 J
• 16 J

Our calculated value of 4 J matches the third option.

Final Kinetic Energy Result

The kinetic energy of the ball weighing 0.5 kg and moving with a velocity of 4 m/s is 4 J.

Revision Table: Kinetic Energy Calculation

Additional Information: Types of Energy

Energy exists in many forms. Kinetic energy is just one of them. Other common types of energy include:

• Potential Energy: Stored energy due to position or state (e.g., gravitational potential energy, elastic potential energy).
• Thermal Energy: Energy associated with the temperature of an object.
• Chemical Energy: Energy stored in the bonds of chemical compounds.
• Electrical Energy: Energy associated with the flow of electric charge.
• Nuclear Energy: Energy stored in the nucleus of an atom.

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this problem, the ball has kinetic energy because it is in motion.