Question

(a) Calculate the kinetic energy in joules of a \(1200-\mathrm{kg}\) automobile moving at \(18 \mathrm{~m} / \mathrm{s}\). (b) Convert this energy to calories. (c) What happens to this energy when the automobile brakes to a stop?

Short answer

The kinetic energy of the automobile is 194,400 Joules, which is approximately 46,496.38 calories. When the automobile brakes to a stop, the kinetic energy is transformed into other forms of energy, mainly thermal energy due to friction, and it decreases to zero when the automobile comes to a complete stop.

Step-by-step solution

Calculate the kinetic energy

First, we will calculate the kinetic energy of the automobile using the formula \( KE = \dfrac{1}{2}mv^2 \), where m is the mass of the automobile (1200 kg) and v is its velocity (18 m/s). KE = \( \dfrac{1}{2}\times1200\,\mathrm{kg}\times(18\,\mathrm{m/s})^2 \) Now, we will perform the calculation: KE = \( \dfrac{1}{2}\times1200\,\mathrm{kg}\times324\,\mathrm{m^2/s^2} \) KE = \( 600\,\mathrm{kg}\times324\,\mathrm{m^2/s^2} \) KE = \( 194400\,\mathrm{J} \) Therefore, the kinetic energy of the automobile is 194,400 Joules.

Convert the kinetic energy to calories

Now, we will convert the kinetic energy in joules to calories using the conversion factor: \(1\,\text{calorie} = 4.184\,\text{joules}\). To find the energy in calories, we will divide the energy in joules by the conversion factor: Energy in calories = \( \dfrac{194400\,\mathrm{J}}{4.184\,\mathrm{J/cal}} \) Energy in calories = \( 46496.38\,\mathrm{cal} \) Thus, the kinetic energy of the automobile is approximately 46,496.38 calories.

Discuss what happens to the kinetic energy when the automobile stops

When the automobile brakes to a stop, the kinetic energy is transformed into other forms of energy, mainly thermal energy (heat) due to friction between the brakes and the wheels. This thermal energy is dissipated, or spread out, into the surroundings as heat. As a result, the kinetic energy of the automobile decreases to zero when it comes to a complete stop. The process is not perfectly efficient, so some of the energy may also be converted into sound energy or cause wear and tear on the brake system.

Key concepts

Energy Conversion

Energy conversion is a fundamental concept in physics that involves changing energy from one form to another. In the context of a moving automobile, this is illustrated vividly when the vehicle comes to a stop.
As the car moves, it possesses kinetic energy due to its mass and velocity. This energy is initially stored in the car's movement. When the brakes are applied, the kinetic energy does not disappear; instead, it is converted to other forms, primarily thermal energy.

• Braking results in friction between the brake pads and the wheels, generating heat.
• The heat dissipates into the surrounding air, effectively reducing the car’s kinetic energy to zero.
• Some energy might also convert into sound, noticeable when you hear the squeal of brakes.
• Energy can neither be created nor destroyed (conservation of energy principle), only changed in form.

This conversion is crucial in understanding how vehicles can safely stop and the importance of well-functioning brake systems.

Friction

Friction is a resistive force that acts when two surfaces interact with each other, and it plays a significant role in everyday experiences, including the braking of a car.
When a car is moving, friction between the tires and the road helps to maintain control and enable acceleration. However, when stopping, friction takes on a crucial role in dissipating the car's kinetic energy.

• The friction between the brake pads and the wheels generates heat, overpowering the car's kinetic energy.
• This resistance slows down the movement of the wheels, aiding in bringing the car to a complete stop.
• Friction is not entirely efficient. This inefficiency can lead to the production of heat and sometimes sound.

Understanding friction is essential not only for engineers designing braking systems but also for daily drivers to appreciate the mechanisms ensuring safety.

Joule to Calorie Conversion

Understanding the conversion between joules and calories is essential in many scientific and engineering applications, especially in thermodynamics and energy management.
In this exercise, we calculated the kinetic energy of a car in joules and then converted it into calories to understand the energy scale in different units.
The conversion factor between joules and calories is:\(1\;\text{calorie} = 4.184\;\text{joules}\)This conversion allows us to express energy in different units depending on what is more practical for the calculation or the context.

• Starting with energy in joules, you divide by the conversion factor to get calories: \( \dfrac{\text{Energy in Joules}}{4.184\;\text{J/cal}} \)
• In the exercise, we converted 194,400 joules to approximately 46,496.38 calories.
• This can offer a different perspective or insight into the amount of energy involved, especially in fields like nutrition and chemistry.

Knowing how to convert between these units is vital for effective communication and analysis across various scientific disciplines.