Kinetic Energy Calculation for a Cricket Ball

Understanding the energy an object possesses due to its motion is fundamental in physics. This energy is known as kinetic energy. For a moving object like a cricket ball, its kinetic energy depends on its mass and its speed. Let's calculate the kinetic energy of the 160 g cricket ball when it is thrown at a speed of 22 m/s.

Understanding Kinetic Energy

Kinetic energy is the energy an object has because of its motion. The faster an object moves and the more massive it is, the more kinetic energy it possesses. The standard unit for kinetic energy is the Joule (J).

The formula used to calculate kinetic energy (KE) is:

$$\text{KE} = \frac{1}{2}mv^2$$

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

Given Data for the Cricket Ball

From the question, we are provided with the following information about the cricket ball:

Mass Conversion

Before we can use the kinetic energy formula, we need to ensure all units are consistent with the standard SI units. The mass is given in grams (g), but for kinetic energy calculations in Joules, mass must be in kilograms (kg).

To convert grams to kilograms, we divide by 1000:

$$m = 160 \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}}$$

$$m = 0.160 \text{ kg}$$

Applying the Kinetic Energy Formula

Now that we have the mass in kilograms and the speed in meters per second, we can substitute these values into the kinetic energy formula:

$$\text{KE} = \frac{1}{2}mv^2$$

Substituting the values:

$$\text{KE} = \frac{1}{2} \times (0.160 \text{ kg}) \times (22 \text{ m/s})^2$$

First, calculate the square of the speed:

$$(22)^2 = 22 \times 22 = 484 \text{ m}^2/\text{s}^2$$

Now, substitute this back into the formula:

$$\text{KE} = \frac{1}{2} \times 0.160 \times 484$$

Perform the multiplication:

$$\text{KE} = 0.080 \times 484$$

$$\text{KE} = 38.72 \text{ J}$$

Final Kinetic Energy Result

The kinetic energy of the 160 g cricket ball when it is thrown at a speed of 22 m/s is 38.72 Joules.

Comparing this result with the given options:

• 176 J
• 1.76 J
• 3872 J
• 38.72 J

The calculated kinetic energy matches the option 38.72 J.