4/23/2025
*
*
1
2
What is Mass?
What is Mass?
Mass is a fundamental dimension, because it describes the
amount of matter that is contained in an object.
In a frictionless world, an object at rest tends to remain at rest
unless acted on by a force. Likewise, an object moving with a
given velocity tends to stay at that velocity unless acted on by
a force.
Units
kg (SI units)
lbm (US customary units).
Remember F = ma ?
From a physical point of view, the most important characteristic
of mass is that it represents the resistance of an object to a
change in its momentum.
For a given force acting on an object, the bigger the mass, the
smaller the acceleration (change in velocity).
Momentum = mass x velocity.
3
4
What is Density?
Because mass represents resistance to (changing)
motion, engineers often try to minimize the mass of their
designs, especially in the transportation field.
Material Density = mass per unit volume of a material.
We do this by using light materials, that is, materials with
low density.
Units for Density
g/cm 3 (SI units)
lbm/in3 in (US customary).
Density is a constant that depends on the chemical makeup of
the material as well as environmental factors like temperature
and pressure.
(Environmental factors tend to change the volume of an object,
not the mass.)
5
6
1
4/23/2025
The text gives the density of several important engineering materials:
Density vs. Specific Weight?
Material Density = mass per unit volume of a material.
Specific Weight = weight per unit volume of material
Units
N/m3 (SI Units)
lb/ft3 (US Customary Units)
7
8
What is Specific Gravity?
Specific Gravity: Ratio of the Density of a material to the
Density of water
Water Density = 1.000 g/cm3
(used to define a gram!!)
/steel
Therefore Specific Gravity is equal to the Density of the
material when using g/cm3.
9
10
Use of density (?) in calculations:
EXAMPLE:
EXAMPLE:
Water flow through a 10” diameter pipe with a linear speed of 5.0 fps.
What is the MASS FLOW RATE through the pipe in tons/hour?
What is the cost of a 10’ long 1” x ½” steel bar at $1.50 per lb?
What is the specific weight of steel?
Answer: cost = weight x $/lb
weight = density x volume
volume = 120” x 1” x ½” = 60 in3
weight = 60 x .284 lb/in3 = 17.0 lbs
cost = 17.0 lbs x $1.50/lb = $25.5
ANSWER:
Mass flow rate = density x volume flow rate
(mass / time = mass per length3 x length3/time)
volume flow rate = cross-sectional area x speed
area = πD2/4 = (π(10in)2)/4 = 78.54 in2
volume flow rate = 78.54 in2 x 5 fps x 3600 sec/hr x 12in/ft x (gal/231 in3)
= 73440 gph
Mass flow rate = 8.35 lb/gal x 73440 gph x (ton/2000 lb) = (306.6 tph)
= 300 tph
11
12
2