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Chapter 1: Problem 25

(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

Expert verified
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

01

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.
02

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.
03

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.

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Most popular questions from this chapter

Two positively charged particles are first brought close together and then released. Once released, the repulsion between particles causes them to move away from each other. (a) This is an example of potential energy being converted into what form of energy? (b) Does the potential energy of the two particles prior to release increase or decrease as the distance between them is increased.

Classify each of the following as a pure substance or a mixture. If a mixture, indicate whether it is homogeneous or heterogeneous: (a) rice pudding, (b) seawater, (c) magnesium, (d) crushed ice.

(a) How many liters of wine can be held in a wine barrel whose capacity is 31 gal? (b) The recommended adult dose of Elixophyllin', a drug used to treat asthma, is 6 \(\mathrm{mg} / \mathrm{kg}\) of body mass. Calculate the dose in milligrams for a 185 -lb person. (c) If an automobile is able to travel 400 \(\mathrm{km}\) on 47.3 \(\mathrm{L}\) of gasoline, what is the gas mileage in miles per gallon?(d) When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee \((4\) cups \(=1\) qt). How many kg of coffee are required to produce 200 cups of coffee?

Indicate the number of significant figures in each of the following measured quantities: (a) \(3.774 \mathrm{km},\) (b) 205 \(\mathrm{m}^{2}\) , (c) \(1.700 \mathrm{cm},(\mathbf{d}) 350.00 \mathrm{K},(\mathbf{e}) 307.080 \mathrm{g},(\mathbf{f}) 1.3 \times 10^{3} \mathrm{m} / \mathrm{s}\) .

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