PASCO ME-9426A AMUSEMENT PARK PHYSICS - Manual (Page 8)

Amusement Park Physics 012-03776E
4
All the spring is doing is supporting the weight of the
cylinder. This is also true if the device is moving up or
down with constant velocity.
If the weight is accelerating upward, the spring must exert
not only the weight but enough additional upward force
to provide the acceleration (1b). With F
s
greater than mg,
the net acceleration is greater than zero and upward. In
this case, the spring will have stretched more than when
at rest and the weight will be below the "1g" position.
If the weight is accelerating downward (1c), the spring
must be applying less force than the weight It will have
stretched less than when at rest and the cylinder will be
above the "1g" position. In this case, the weight helps to
accelerate the mass downward.
The device registers the acceleration as seen in the frame
of reference of the rider. Consider the weight of the
accelerometer to be a "plumb bob". Its direction response
is the same as that of a plumb bob. In this case, the amount
of stretch of the spring gives the weight of the cylinder
in the combined gravitational and acceleration fields of
the ride.
You cannot tell the gravitational field in one direction
from an acceleration in the opposite direction. You cannot
feel the difference between a force due to gravity and a
force due to the ride pushing on you. The scale readings
give what you feel is the local gravitational field. Since
it registers the acceleration in the reference frame of the
rider, the accelerometer readings agree with what the rider
"feels."
A negative or downward acceleration occurs after the tops
of roller coaster hills, when an elevator begins its down-
ward trip, or when one begins to slide downhill. Riders
have a sinking feeling because less force is being applied
upward than they are accustomed to. On some rides the
downward force is partly a push from the safety bar. This
downward push feels as if the rider has suddenly become
lighter and is rising out of the seat. Sure enough, the
accelerometer reads less than one "g."
Upward or positive accelerations are felt in elevators as
they begin to rise, and at the bottom of vertical loops on
roller coasters and swings. As the elevator begins to rise,
the floor must push up with a force greater than the rider's
weight. The rider interprets this as an increase in down-
ward force and feels heavier. The accelerometer spring,
stretching to provide the additional force for the weight,
registers more than one "g". Both the direction and mag-
nitude of the readings agree with the rider’s feeling of an
altered gravitational field.
Upside down, at the top of a vertical circle such as a roller
coaster loop or rotating ride, the rider may feel little if
any force from the seat. The rider feels almost "weight-
less". At the same point the accelerometer shows little if
any pull being applied by the spring. They are in agree-
ment. At the bottom of the same loop the strong upward
push from the seat feels like a force pushing the rider
down into the ground. This upward force is applied to the
cylinder by the spring which stretches strongly giving a
large reading. In both cases, the rider sees the spring being
pulled "down" toward the rider's seat, which conforms
with what the rider feels.
The Horizontal Accelerometer
With horizontal accelerometers, as opposed to vertical
accelerometers, there is not the same confusion between
the subjective experience and the accelerometer reading.
At rest, the BB's in the horizontal accelerometer settle to
the bottom of the curved plastic tube. There is no hori-
zontal force applied and no horizontal acceleration.
When the BB's are above the bottom, as in Figure 2, the
inside of the curved plastic tube applies a force to them.
The applied force has a vertical component equal to the
weight of the BB's and a horizontal component equal to
the mass of the BB's times their horizontal acceleration.
The applied force acts along the line making the angle q
with the vertical, center line of the accelerometer.
Since the components are perpendicular to one another
and the horizontal force, ma, is opposite the angle
θ:
and
ma = mg tan θ.
We can divide both sides by the mass of the BB's to obtain:
a = g tan θ;
where a, the horizontal acceleration, is always directed
forward toward the front of the device.
To measure the horizontal acceleration in the direction
you are moving, just hold the accelerometer level with
the straw pointed in the direction you are moving.
θ tan
ma
mg
------- =