How do you calculate masses?

Answer 1

"it isn't calculated it is weight in grams or kilograms"

/_\

T

Big Failure to whoever gave this answer. What the answerer was referring to was WEIGHT. NOT MASS.

Mass is the amount of matter inside a body.

Weight is the force that gravitation exerts upon a body, equal to the mass of the body times the local acceleration of gravity: commonly taken, in a region of constant gravitational acceleration, as a measure of mass.

So, let's differentiate mass from weight:

You can take an apple and weigh it. A lot of people should already know is that the mass of this apple CANNOT change without physically changing it (biting a portion of apple, etc.) In other words, (for argument's sake) if you're going to get an apple and bring it to somewhere which is the gravitational pull is in any case different from the Earth like the Moon, in which everyone who went to grade school already know has 1/6 of the gravitational pull compared to Earth's, you will get different WEIGHT but the MASS will not change. It shall remain the same as if you're on Earth.

Computation of Mass:

Relative equation:

Computation of Density: M/V

Computation of Volume: M/D

so,

Computation of Mass: V*D

Although the computation can only be done with the given variables which is related to mass. e.g. Volume, Density, Gravitational force. The formula will change whenever the given variables changes.

Answer 2

The first step in calculating mass properties of an object is to assign the location of the

reference axes. The center of gravity and the product of inertia of an object can have any

numerical value or polarity, depending on the choice of axes that are used as a reference

for the calculation. Stating that a CG coordinate is "0.050 inches" means nothing unless

the position of the reference axis is also precisely defined. Any reference axes may be

chosen. For example, the center of gravity of a cylinder may be 4.050 inches from one

end, 0.050 inches from its midpoint, and 3.950 inches from the other end. Furthermore,

each end of the cylinder may not be perpendicular to the central axis, so that a means of

determining the "end" of the cylinder would have to be further defined.

Three mutually perpendicular reference axes are

required to define the location of the center of

gravity of an object. These axes are usually

selected to coincide with edges of the object,

accurately located details, or the geometric center

of the object.

It is not sufficient to state that an axis is the

centerline of the object. You must also specify

which surfaces on the object define this centerline.

Moment of inertia is a rotational quantity and

requires only one axis for its reference. Although

this can theoretically be any axis in the vicinity of

the object, this axis usually is the geometric center,

the rotational center (if the object revolves on

bearings), or a principal axis (axis passing through

the center of gravity which is chosen so the

products of inertia are zero).

Product of inertia requires three mutually perpendicular

reference axes. One of these axes may be a rotational axis

or a geometric centerline.

For maximum accuracy, it is important to use reference

axes that can be located with a high degree of precision. If

the object is an aerospace item, then we recommend that

this object be designed with two reference datum rings per

section, which can be used to define the reference axes.

These rings can be precision attachment points that are

used to interface the object with another section of a

spacecraft or rocket, or they can be rings that were

provided solely for the purpose of alignment and/or measurement

of mass properties. The accuracy of calculation (and the

subsequent accuracy of measurement of an actual piece of hardwure 2 - Datum Rings

Figure 1 Center of gravity (and

product of inertia) are defined

relative to orthogonal axes

----

the accuracy of the means of locating the reference axes. We

have found that the single largest source of error in mass

properties calculations is the uncertainty of the reference. The

dimensional data provided to the mass properties engineer must

be sufficiently accurate to permit mass properties tolerances to be

met.

For example, if you are asked to make precise calculations of

mass properties of a projectile, you should establish the error due

to reference misalignment as the first step in your calculations. If

you are required to calculate CG within an accuracy of 0.001

inch and the reference datum is not round within 0.003 inch, then you

cannot accomplish your task. There is no sense in making a detailed

analysis of the components of an object when the reference error prevents

accurate calculations. Furthermore, it will be impossible to accurately measure such a

part after it is fabricated and verify the accuracy of your calculations. The location and

accuracy of the reference axes must be of the highest precision.

If your task is to calculate the mass properties of a vehicle that is assembled in sections,

then serious thought should be given to the accuracy of alignment of the sections when

they are assembled. Often this can be the biggest single factor in limiting the degree of

balance (if the vehicle was balanced in sections because the total vehicle is too big for the

balancing machine). Alignment error is amplified for long rockets . . . a 0.001 inch lean

introduced by alignment error on a 12 inch diameter can result in a 0.007 inch CG error

on a 15 foot long rocket section. This is discussed in detail in the sections of this paper

that present the math for combining the mass properties of subassemblies.

The accuracy required for various types of calculations is summarized in later sections of

this paper.

Choosing the Location of the Axes

The axes in Figure 3 do not make a good reference because a small error in squareness

of the bottom of the cylinder causes the object to lean away from the vertical axis. The

axes below (Figure 4) make a better choice.

Figure 3

The first step in calculating mass properties is to establish the location of the X,

Y, and Z axes. The accuracy of the calculations (and later on the accuracy of

the measurements to verify the calculations) will depend entirely on the

wisdom used in choosing the axes. Theoretically, these axes can be at any

location relative to the object being considered, provided the axes are mutually

perpendicular. However, in real life, unless the axes are chosen to be at a

location that can be accurately measured and identified, the calculations are

meaningless.

Figure 4

----

Reference axes must be located at physical points on

the object that can be accurately measured. Although

the center line of a ring may exist in midair, it can be

accurately measured and is therefore a good reference

location as can the center of a close tolerance hole

which could be identified as the zero degree reference

to identify the X axis (Fig. 4).

An axis should always pass through a surface that is

rigidly associated with the bulk of the object. In Figure

5 it would be better to locate the origin at the end of the

object rather than the fitting that is loosely dimensioned

relative to the end.

Answer 3

mass = (density)(volume).