PASCO ME-9426A AMUSEMENT PARK PHYSICS - Manual (Page 7)

012-03776E Amusement Park Physics
3
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Accelerometers measure accelerations by measuring
forces. The vertical accelerometer in this kit consists of
a cylindrical weight hung from a spring. Its operation can
be understood in terms of Hooke's law:
where F
s
is the force applied by the spring to the weight,
x is the extension of the spring, and k is a constant that
depends on the spring. The negative sign indicates that
the force is in the direction opposite to the extension. As
the force applied by the spring to the weight increases,
the stretch increases in direct proportion. Thus the posi-
tion of the end of the spring indicates the amount of force
being applied to the weight by the spring.
Calibration of the device can be in newtons for the spring
force, or, in the ratio
where a is an acceleration, since the mass of the cylinder
remains constant for all uses. With the unstretched spring
position taken as the zero point, the weight of a single
cylinder defines the position corresponding to a restoring
force which has magnitude equal to the weight of the
cylinder, or .
Note that if the device is calibrated in units of "g" instead
of m/sec
2 , it should be pointed out that the unit "g" used
here is related to the local acceleration due to gravity only
in that it has the same magnitude. Since the symbol "g"
means local gravitational field strength, a reading of 2.0
g on an accelerometer does not mean that the gravitational
field has increased. It means that the rider feels a force
which is twice the magnitude of the rider's weight.
When the device is held vertically, the net force on the
F
s
kx – =
F
s
m
----- a =
F
s
m
----- 9.8
m
s
2
---- =
cylinder is given by:
where mg is the weight of the cylinder.
A diagram of the spring and weight is shown in Figure
1. When the accelerometer is held at rest (1a), the spring
force is equal to the weight but in the opposite direction,
so the net acceleration is zero.
and the scale reads "1g".
F
net
F
s
mg – =
F
net
0 F
s
mg = = =
F
s
mg =
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Accelerometers: Theory and Operation
(a) (b) (c)
F
s
F
s
F
s
mg
mg
mg
a
a
No
Acceleration
Upward
Acceleration
Downward
Acceleration
F
s
= -mg
a = 0
F
s
> -mg
a > 0
F
s
< -mg
a < 0
Figure 1: Diagram of the Vertical Accelerometer