Chapter 2 Review of Forces and Moments - Brown University

Selecting a load cell
As an engineer, you may need to purchase a load cell to measure a force. Here are a few considerations
that will guide your purchase.
1. How many force (and maybe moment) components do you need to measure? Instruments that
measure several force components are more expensive…
2. Load capacity – what is the maximum force you need to measure?
3. Load range – what is the minimum force you need to measure?
4. Accuracy
5. Temperature stability – how much will the reading on the cell change if the temperature changes?
6. Creep stability – if a load is applied to the cell for a long time, does the reading drift?
7. Frequency response – how rapidly will the cell respond to time varying loads? What is the
maximum frequency of loading that can be measured?
8. Reliability
9. Cost
2.1.7 Force Laws
In this section, we list equations that can be used to calculate forces associated with
(i) Gravity
(ii) Forces exerted by linear springs
(iii) Electrostatic forces
(iv) Electromagnetic forces
(v) Hydrostatic forces and buoyancy
(vi) Aero- and hydro-dynamic lift and drag forces
Gravitation
Gravity forces acting on masses that are a large distance apart
Consider two masses m
1
and m
2
that are a distance d
e m 2
12
apart. Newton’s law of gravitation states that mass
m1
will experience a force
m
F
1
d
Gm1m
2
F=
e
2 12
d
where e
12
is a unit vector pointing from mass m
1
to mass m
2
, and G is the Gravitation constant. Mass
m
2
will experience a force of equal magnitude, acting in the opposite direction.
In SI units,
G = 6.673×
10 m kg s
−11 3 -1 -2
The law is strictly only valid if the masses are very small (infinitely small, in fact) compared with d – so
the formula works best for calculating the force exerted by one planet or another; or the force exerted by
the earth on a satellite.