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2 86 MECHANICS.
Mass.
The mass of a body is the quantity of matter which it con-
tains. By common consent the unit of mass is, in mechanics,
considered to be that quantity of matter to which one unit of
force can give one unit of accelei’ation in one unit of time;
therefore, when the weight of a body is divided by acceleration
of gravity, the quotient is the mass of the bodv. Thus
:
W
m =
§
W — m X g
w
g = —
111
Momentum.
The product of the mass of a moving body and its velocity
is called its momentum or, also, its quantity of motion. The
unit for momentum is the product when unit of mass is multi-
plied by unit of velocity per second. In mechanical calcula-
tions, using English weights and measures, the unit of mass is
weight divided by 32.2; therefore, unit of momentum will be:
Weight of the moving body in pounds multiplied by velocity in
feet per second and the product divided by 32.2. Thus :
q = m X v m = mass = —: therefore,
cr
£>
w
q = v
g
q = ^- W
g
q = Momentum, or quantity of motion.
W = Weight of moving body in pounds.
v = Velocity of moving body in feet per second.
g= Acceleration of gravity.
g
the formula by which the time in a free fall is
obtained, and, consequently, the momentum of a falling body
can also be expressed by the product of the weight of the body
in pounds and the time in seconds during the fall. This product
is usually called "time effect."
Impulse.
The product of the force and the time in which it is acting
as a blow against a body is called impulse, and it is always
of the same numerical value as the momentum of the moving
body.
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