Problem 25 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Calculate the kinetic energy, in joules, of a 15-g bullet moving at \(120 \mathrm{~m} / \mathrm{s}\). (b) Convert this energy to calories. (c) When the bullet is stopped by a bulletproof vest, which form of energy does the kinetic energy of the bullet convert to?

Step-by-Step Solution

Answer

The bullet has a kinetic energy of 108 Joules or approximately 25.8 calories. When it is stopped by a bulletproof vest, the kinetic energy mainly converts to heat energy.

Step 1: Calculate the Kinetic Energy

First, we need to find the kinetic energy (KE) of the bullet. We have the mass in grams (15g), but we need it to be in kilograms for the calculation. To convert mass m from grams to kilograms, divide by 1000: m = 15g / 1000 = 0.015 kg Now we can calculate the kinetic energy using the formula: KE = (1/2)mv^2 Plug in values for mass (m) and velocity (v): KE = (1/2)(0.015 kg)(120 m/s)^2

Step 2: Convert Joules to Calories

Now, we can find the value of the kinetic energy (KE) in Joules: KE = 108 Joules To convert this to calories, we can use the following formula: Calories = Joules / 4.184 Calories = 108 J / 4.184

Step 3: Energy Conversion When Bullet is Stopped by a Bulletproof Vest

When the bullet is stopped by a bulletproof vest, its kinetic energy is converted to another form of energy, mainly heat energy due to the friction between the bullet and the vest's material. Some deformation of the bullet and vest material can also lead to a small amount of other internal energy being generated.

Step 4: Summary

The kinetic energy of the bullet is 108 Joules or approximately 25.8 calories. When the bullet is stopped by a bulletproof vest, the main form of energy it is converted to is heat energy.

Key Concepts

Energy Conversion

Energy conversion is the process of changing one form of energy into another. It's a fundamental concept in physics and is evident in many everyday phenomena. For instance, consider a bullet slowing down when it hits a bulletproof vest.
The kinetic energy it carries is transformed, primarily into heat energy, as it comes to a halt.
This transformation occurs due to the interactions and friction between the bullet and the vest's material, converting its kinetic motion into thermal energy. When objects in motion are stopped, like our bullet example, their energy must go somewhere. It often changes forms, such as:

• Heat Energy: Generated by the friction and deformation of materials.
• Sound Energy: Occasionally, the conversion process can produce sound, although minimal in this case.
• Deformation Energy: Seen when the bullet or vest is physically altered during the impact.

Understanding energy conversion helps in analyzing how systems manage and dissipate energy, ensuring safer and more efficient designs.

Joules to Calories Conversion

Joules and calories are both units of energy, and understanding their conversion is essential for various scientific calculations. A Joule is the standard unit in the International System of Units (SI), while a calorie is often used in chemistry and nutrition.
To convert energy from Joules to calories, the key conversion factor is that 1 calorie is equal to 4.184 Joules. The steps for conversion typically involve:

• Calculating the total energy in Joules. In this example, the bullet's kinetic energy is 108 Joules.
• Using the conversion formula: Calories = Joules / 4.184.
• Substituting the values: Calories = 108 J / 4.184 = approximately 25.8 calories.

Thus, when discussing energy transformations, it often becomes necessary to move between these units, especially in fields where both metrics are used. This simple conversion allows scientists and engineers to communicate more effectively.

Heat Energy Transformation

Heat energy transformation is a crucial aspect of energy conversion, especially when dealing with kinetic energy that dissipates into heat. In our bullet scenario, when the bullet is stopped by a bulletproof vest, significant heat is generated.
This heat results from the friction between the vest material and the bullet's surface, illustrating a common type of energy transformation. The implications of heat energy transformation are:

• Safety: Understanding how kinetic energy converts to heat can help improve safety measures. Bulletproof vests must manage the heat generated to prevent burns or material degradation.
• Material Science: Engineers must select materials that dissipate heat efficiently to ensure longevity and effectiveness.
• Energy Efficiency: By minimizing unwanted heat loss, systems maintain higher energy efficiency.

This explains why many industrial and engineering applications focus on managing heat energy transformation to optimize system performance and safety.