62. What is gravitation?

The attraction that every particle of matter in the universe has for every other particle.

63. When the moon comes' between the sun and the earthy how does that affect the attraction between the sun and the earth ?

Such interposition of matter has no effect on the attract-

ive force originally existing.

64. What is the first law of gravitation?

The attractive force (gravitation) between two bodies varies as the product of the masses of the two bodies.

65. Illustrate this law.

If two bodies contain 5 and 10 pounds of matter respectively, the product may be represented by 5a \\ two

other bodies contain 4 and 25 pounds of matter respectively, the product may be similarly represented by

100. Acting at like distances, the attraction between the second two will be twice (=Vrf') as great as the at-

traction between the first two.

66. How would doubling the matter in one of the bodies affect their gravitation?

It would double one of the factors, and thus the product, and thus the gravitation.

67. How would doubling the weight of both of the bodies affect their gravitation ?

It would double each of the two factors, and thus increase product and gravitation fourfold.

68. What is the second law of gravitation ?

Gravitation varies inversely as the square of the distances between the centers of mass of the two bodies.

69. What is the center of mass of a body ?

The point about which all the matter of a body may be balanced.

7) Illustrate the second law of gravitation-.

Two bodies a foot apart (between centers) attract each other four times as much as do the same bodies when placed two feet apart.

71. How would doubling the product of the masses and doubling the distance affect gravitation ?

It would divide the attraction by two.

72. How would trebling the quantity of matter in each of the two bodies and doubling the distance between them affect the gravitation?

It would |3X3__^ \ increase it two and a quarter times.

73. How does gravitation pull?

It is generally conceived of as Kpull^ but it is more likely to be a push. At the present time, the mechanical

nature of the action is unknown.

74. What is gravity?

The attraction between the earth and a body on or near its surface.

75. How is gravity measured?

By the weight that it gives to a body.

76. In what direction does it act?

Vertically downward ; i, e. toward the center of the earth.

77. How is this direction easily illustrated?

By a plumb line.

78. Where does a body have the greatest weight ?

At the surface of the earth.

79. How does carrying a body below the surface of the earth affect its weight f

It decreases it as the distance from the center of the earth is decreased.

80. Why is this?

In descending, the matter left behind or above attracts it upward and neutralizes part of the attraction of the

matter still below it

81. How does carrying a body above the surface of the earth affect its weight?

It decreases it as the square of the distance from the center of the earth increases.

82. How much will a pound of iron weigh 4000 miles above the earth's surface?

The distance from the center of the earth has been multiplied by two, therefore its weight will be divided by

the square of two which is four. It will weigh a quarter of a pound.

83. Considering the earth as a hollow sphere.what would a body in its interior weigh ?

It has been mathematically demonstrated that a particle of matter within a spherical shell is equally attracted

in all directions by the matter of the shell. Hence, a body would have no weight anywhere within the shell

of such an earth.

84 Illustrate a method of finding the center of mass of a body.

Drive a tack in a slate frame. Tie the middle of a string around the tack and a weight (plumb-bob) to one end of the string. Suspend the slate by the free part of the string and mark the direction of the plumb-line across

the slate. Change the position of the tack and repeat the process. The intersection of the two lines thus

marked on the slate "will approximately indicate its center of mass.

85. How may this be proved?

Place the point thus found upon the finger-tip ; the slate will balance.

86. When is a body in stable equilibrium ?

When it is so supported that when it is slightly displaced it seeks to return to its original position.

87. Illustrate.

A stick supported from its upper end; a pendulum; a hemispherical oil-can.

88. When is a body in unstable equilibrium ?

When it is so supported that when it is slightly displaced it seeks to fall further from its original position.

89. Illustrate.

A stick balanced on its lower end ; an ^^'g standing on its end.

90. When ts a body in neutral equilibrium?

When it is so supported that when slightly displaced, it seeks to move neither toward nor from its original

position.

91. Illustrate.

A ball resting on a table.

92. What is the line of direction f

The path of the center of mass of a body when the body falls.

93. Give another definition.

A line drawn vertically downward from the center of mass.

94. What is the base of a body ?

The side on which it rests, or the surface bounded by lines joining its points of support.

95. When will a body stand?

When its line of direction falls within its base.

96. When will a body fall?

When its line of direction falls without its base.

97. How may the stability of a body be increased?

By increasing its base or lowering its center of mass.

98. How do we determine the height that a body is raised?

By the distance its center of mass is raised.

99. Why is it easier to lift one end of a plank a yard than it is to lift the middle of the plank that distance f

• In the first case, the center of mass is lifted only half as high as in the second case.

100. What is the base of a sphere supported on a horizontal plane ?

A point.

loi. What is the base of a cylinder supported on a horizontal

plane?

A line.

102. Why is a sphere easily rolled on a horizontal plane ?

Because such motion does not raise the center of mass.

103. Why is a cylinder easily rolled on a horizontal plane?

For the same reason.

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