Force is defined as mass times acceleration. Starting with SI base units, derive a unit for force. Using SI prefixes, suggest a convenient unit for the force resulting from a collision with a 10-ton trailer truck moving at 55 mi per hour and for the force resulting from the collision of a molecule of mass around 10 - 20 kg moving almost at the speed of light (3×108 m/s) with the wall of its container. (Assume a 1-second deceleration time for both collisions.)
Ch.1 - Matter, Measurement & Problem Solving
Chapter 1, Problem 114
The value of the euro was recently $1.15 U.S., and the price of 1 liter of gasoline in France is 1.42 euro. What is the price of 1 gallon of gasoline in U.S. dollars in France?
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Convert the price of 1 liter of gasoline from euros to U.S. dollars using the given exchange rate: $1.15 \text{ U.S. dollars} = 1 \text{ euro}$. Therefore, the price in U.S. dollars is $1.42 \text{ euro} \times 1.15 \text{ U.S. dollars/euro}$.
Calculate the price of 1 liter of gasoline in U.S. dollars using the conversion from the previous step.
Convert the price from per liter to per gallon. Note that 1 gallon is approximately 3.78541 liters.
Multiply the price per liter in U.S. dollars by the number of liters in a gallon to find the price per gallon.
The result from the previous step gives the price of 1 gallon of gasoline in U.S. dollars in France.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Currency Conversion
Currency conversion is the process of exchanging one currency for another, based on the current exchange rate. In this case, to find the price of gasoline in U.S. dollars, we need to convert euros to dollars using the given exchange rate of $1.15 per euro.
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Conversion Factors
Volume Conversion
Volume conversion involves changing measurements from one unit to another, such as liters to gallons. Since the price of gasoline is given in euros per liter, we must convert liters to gallons to find the equivalent price in U.S. dollars, knowing that 1 gallon is approximately 3.785 liters.
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Common Conversion Factors
Unit Price Calculation
Unit price calculation determines the cost per unit of a product, which in this case is gasoline. After converting the price from euros to dollars and the volume from liters to gallons, we can calculate the price per gallon in U.S. dollars, providing a clear understanding of the cost of gasoline in France.
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SI Units
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