Preparation problems

1-2. The power output of a typical large power plant is 1,000 megawatts (MW). Express this result in (a) W, (b) kW, (c) GW.

Solution:

Remembering the conversions

1 kW
=
1,000 W
1 MW
=
1,000,000 W
1 GW
=
1,000,000,000 W

We see that 1,000 MW = 1,000 * 1 ×106 W = 1 ×109 W = 1GW.

So the result is

(a) 1 ×109 W,

(b) 1 ×106 kW,

(c) 1 GW.

1-21. An aircraft carrier goes 17 feet on a gallon of fuel. Express this result in (a) miles per gallon (mpg) and (b) kilometers per liter (km/L).

Solution:

(a) We need the conversion for feet to miles. This would convert feet/gallon into miles/gallon. The conversion is:

1  mile = 5160  ft

So

17  ft
1  gallon
 =
17  ft · 1  mile
5160  ft
1  gallon
 = 3.29 ×10-3  mpg .

(b) Now we need the conversion for feet to kilometers and gallons to liters. This would convert feet/gallon into km/L. The conversions are:

1  m
=
0.3048  ft
1  km
=
1000  m
1  gal
=
3.785  L

So

17  ft
1  gallon
 =
17  ft · 0.3048  m
1  ft
 · 1  km
1000  m
1  gallon · 3.785  L
1  gal
= 1.37 ×10-3  km/L.

1-22. A radian is how many degrees?

Solution:

We need the conversion for radians to degrees. The conversion is:

2 p radians = 360  degrees

So

1  radian · 360  degrees
2 p radians
 = 57.296  degrees .

1-32. Add 5.1 × 10-2 and 6.8 × 103 mm, and multiply the result by 1.8 × 104 N. (1 N is the SI unit of force).

Solution:

We should convert all distances into meters, then add them. Since we know

1  cm
=
10-2  m
1  mm
=
10-6  m ,

Then

5.1 ×10-2  cm
=
5.1 ×10-4  m
6.8 ×103  mm
=
+  6.8 ×10-3  m
7.31 ×10-3  m
Now we multiply by the force given, or
( 7.31 ×10-3  m ) ( 1.8 ×104 N ) = 131.58  N ·m

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Solutions translated from TEX by TTH, version 1.57.