Ch 01: Units & VectorsWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Solution: Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm

Solution: Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm

Problem

Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm dumped 2.0 in. of rain in 30 min on a town of area 26 km2. What volume of water, in acre-feet, fell on the town?

Solution

Whenever we convert units, the first step is to figure out what our starting and ending units are. We'll place the starting units on the left, an equals sign and ending units on the right, and some conversion factors in between.

Also, remember that if one of the starting units has an exponent (like m3 or s2), the conversion factors for that unit also need to have the same exponent. For example:

starting unitstarting unit2×conversion factor×conversion factor2=ending unitending unit2

The conversion factors must cancel out the starting unit and leave the ending unit. So to cancel out the starting unit in the numerator, the first conversion factor must have that same unit in the denominator.

The exact opposite happens with the starting unit in the denominator. To cancel it, the second conversion factor must have that same unit in the numerator. Other conversion factors may be necessary. Once all the units have canceled and you’re left with the ending units (both numerator and denominator), multiply and divide all the numbers through.

We want to express the volume in acre-feet (acre•ft), but we're given square kilometers and inches. So what we'll do here is convert km2 to acres and inches to, then multiply those results together to get the final answer. (You can also do the whole conversion on one line.)

(You might notice that the problem also gives us a time measurement of 30 minutes, but we don't need that information to answer the question. Real-life data often works that way, and some physics problems try to do the same thing so students get used to the idea.)

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