Learning Goal: To learn how to change units of physical quantities. Quantities w

Question

Learning Goal:

To learn how to change units of physical quantities.

Quantities with physical dimensions like length or time must be measured with respect to a unit, a standard for quantities with this dimension. For example, length can be measured in units of meters or feet, time in seconds or years, and velocity in meters per second.

When solving problems in physics, it is necessary to use a consistent system of units such as the International System (abbreviated SI, for the French Système International) or the more cumbersome English system. In the SI system, which is the preferred system in physics, mass is measured in kilograms, time in seconds, and length in meters. The necessity of using consistent units in a problem often forces you to convert some units from the given system into the system that you want to use for the problem.

The key to unit conversion is to multiply (or divide) by a ratio of different units that equals one. This works because multiplying any quantity by one doesn't change it. To illustrate with length, if you know that 1inch=2.54cm, you can write

1=2.54cm1inch.

To convert inches to centimeters, you can multiply the number of inches times this fraction (since it equals one), cancel the inch unit in the denominator with the inch unit in the given length, and come up with a value for the length in centimeters. To convert centimeters to inches, you can divide by this ratio and cancel the centimeters.

1.

How many centimeters are there in a length 18.2 inches ?

Express your answer in centimeters to three significant figures.

2.

Suppose that a particular artillery piece has a range R = 6310 yards . Find its range in miles. Use the facts that 1mile=5280ft and 3ft=1yard.

3.

What is the speed of a car going v=1.000mph in SI units? Notice that you will need to change from miles to meters and from hours to seconds. You can do each conversion separately. Use the facts that 1mile=1609m and 1hour=3600s.

Express your answer in meters per second to four significant figures.

Express your answer in miles to three significant figures.

Explanation / Answer

1 )

1 inch = 2.54 cm

so 18.2 inches have

18.2 X 2.54 cm = 46.228 cm are there in 18.2 inches.

2 )

R = 6310 yards

1 mile = 5280 ft

and 3 ft = 1 yard

R = 6310 ( 3 ft/ 1 yard ) ( 1 mile / 5280 ft )

R = 6310 X 3 / 5280 mile

R = 3.585 mile

3 )

1 mph = 1 mile / hour

= 1609 m / 3600 sec

1 mile = 0.446944 m/sec

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