Question

(a) Calculate the kinetic energy, in joules of a 1200 -kg automobile moving at 18 \(\mathrm{m} / \mathrm{s}\) . ( b ) Convert this energy to calories.(c) When the automobile brakes to a stop is the "lost" kinetic energy converted mostly to heat or to some form of potential energy?

Short answer

The kinetic energy of the 1200 kg automobile moving at 18 m/s is 194,400 Joules. This energy is equivalent to approximately 46,488.29 calories. When the automobile brakes to a stop, the "lost" kinetic energy is mainly converted into heat due to friction between the brake pads and the brake rotors, rather than potential energy.

Step-by-step solution

Calculate the kinetic energy in Joules

To find the kinetic energy (KE) of the automobile, we will use the following formula: \[ KE = \frac{1}{2}mv^2 \] where m is the mass of the automobile (1200 kg) and v is its speed (18 m/s). Plugging in the known values: \(KE = \frac{1}{2}(1200\,\text{kg})(18\,\text{m/s})^2\) Now, we calculate the kinetic energy: \(KE = \frac{1}{2}(1200\,\text{kg})(324\,\text{m}^2/\text{s}^2)\) \(KE = (600\,\text{kg})(324\,\text{m}^2/\text{s}^2)\) \(KE = 194400\, \text{J}\) So, the kinetic energy of the automobile is 194,400 Joules.

Convert the calculated kinetic energy to calories

To convert the kinetic energy from Joules to calories, we will use the following conversion factor: 1 calorie = 4.184 Joules So, we can convert as follows: \(194400\, \text{J} \times \frac{1\,\text{cal}}{4.184\,\text{J}}\) Now, we perform the calculation: \(\frac{194400\,\text{cal}}{4.184}\) \(46488.29\,\text{cal}\) So, the kinetic energy of the automobile is approximately 46,488.29 calories.

Determine whether the "lost" kinetic energy is converted mostly to heat or potential energy

When a moving automobile comes to a stop, the kinetic energy is mostly transformed into heat due to friction between the brake pads and the brake rotors. This heat is then dissipated into the surroundings. So, when the automobile comes to a complete stop, the "lost" kinetic energy is mainly converted into heat rather than potential energy.

Key concepts

Energy Conversion

Energy conversion is the process where energy changes from one form to another. In automobiles, kinetic energy—the energy of motion—plays a central role.
When a car is moving, it possesses kinetic energy due to its mass and velocity. You can calculate it using the formula: \[ KE = \frac{1}{2}mv^2 \] where \( m \) is the mass and \( v \) is the velocity.
When the vehicle brakes and stops, this kinetic energy doesn't just vanish; it converts predominantly into different forms, mainly heat. This happens due to the friction between the brake components.
Here's what happens during energy conversion when a car brakes:

• The brake pads create friction against the brake disc or drum.
• This friction converts kinetic energy into thermal energy, effectively producing heat.
• The heat then dissipates into the air, ensuring the vehicle slows down and eventually stops.

This type of energy conversion is a common occurrence in everyday mechanical systems.

Mechanical Energy

Mechanical energy is a form of energy associated with the motion and position of an object. It is the sum of kinetic and potential energy. During the motion of an automobile, these two main types of mechanical energy come into play:
1. **Kinetic Energy:** As shown earlier, it's the energy a vehicle has due to movement, calculated using the mass and velocity.
2. **Potential Energy:** Typically, it refers to the energy stored in an object due to its position or arrangement. However, in the context of braking, very little potential energy is involved.
In everyday use, mechanical energy is efficiently transformed from potential energy in the form of fuel into kinetic energy as the car moves. As you can see, most of the mechanical energy associated with a stopping vehicle converts into heat during braking, rather than being stored as potential energy.

• This process demonstrates mechanical energy's dynamic transition involving kinetic energy loss playing a large role in stopping vehicles through brakes.
• Understanding it helps in comprehending broader implications of energy conservation and efficiency.

Calorimetry

Calorimetry is a technique to measure the amount of heat exchanged in chemical reactions or physical changes, and it can be applied to understand energy transformations in mechanical systems too.
While the word might seem complex, the concept is simple enough. By converting kinetic energy into calories, we use principles akin to calorimetry to measure energy changes. In the problem solved earlier:

• The kinetic energy of 194,400 Joules, when a vehicle moves, was converted to calories using a conversion factor.
• Knowing that 1 calorie is equivalent to 4.184 Joules allows us to convert Joules into a more tangible form like calories for easier understanding.

This transformation helps simplify the visualization of energy amounts and better appreciate how much energy is involved, similar to how we understand food energy. Calorimetry also underscores the efficiency of energy usage and conversion within mechanical systems, reminding us of the significant thermal aspect involved in every energy interaction.