Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

10.2 Newton’s Laws in Mechanics 261

where

Fattractive force (N)

Guniversal gravitational constant (6.673  10

 11

m

3

/kgs

2

)

m 1 mass of particle 1 (kg, see Figure 10.10)

m 2 mass of particle 2 (kg, see Figure 10.10)

rdistance between the center of each particle ( m)

Using Equation (10.6), we can determine the weight of an object having a massm, on the

earth, by substitutingmfor the mass of particle 1 and substituting for the mass of particle 2 the

mass of Earth (MEarth 5.97  10

24

kg), and using the radius of Earth as the distance between

the center of each particle. Note that the radius of Earth is much larger than the physical dimen-

sion of any object on Earth, and, thus, for an object resting on or near the surface of Earth,r

could be replaced withREarth  6378  10

3

m as a good approximation. Thus, the weight (W)

of an object on the surface of Earth having a massmis given by

And after letting , we can write

(10.7)

Equation (10.7) shows the relationship among the weight

of an object, its mass, and the local acceleration due to gravity.

Make sure you fully understand this simple relationship.

Because the earth is not truly spherical in shape, the value ofg

varies with latitude and longitude. However, for most

engineering applications,g9.8 m/s

2

org32.2 ft /s

2

is

used. Also note that the value ofgdecreases as you get further

away from the surface of Earth. This fact is evident from exam-

ining Equation (10.6) and, the relationship forgleading to

Equation (10.7).

Example 10.3 Determine the weight of an exploration vehicle whose mass is 250 kg on Earth. What is the mass

of the vehicle on the Moon (gMoon1.6 m/s

2

) and the planet Mars (gMars3.7 m/s

2

)? What

is the weight of the vehicle on the Moon and Mars?

The mass of the vehicle is 250 kg on the Moon and on the planet Mars. The weight of the

vehicle is determined fromWmg:

On Mars: W 1 250 kg2a3.7

m

s

2 b925 N

On Moon: W 1 250 kg2a1.6

m

s

2 b400 N

On Earth: W 1 250 kg2a9.8

m

s

2 b2450 N

Wmg

g

GMEarth

R

2

Earth

W

GMEarthm

R

2

Earth

REarth

MEarth

Earth

m

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