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Chapter 5: Problem 15

(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

Expert verified
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

01

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.
02

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.
03

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.

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