A three wheeled OTV has been designed such that the forces from the wheels and motors are uniform, hence the reaction forces at the point of contact with the upper surface can be modeled as a single vertical reaction support. The platform is a square with side length
200 mm
and has a thickness of
20 mm
. Plywood has a density of
0.33 g/cm ∧
3
. For the purposes of finding the platform weight,
W
, ignore any holes in the plywood for motor mounts. Due to a misscommunication in the team, the motor mounts
M1,M2
, and
M3
were not attached symmetrically! The potential consequences of this are a difference in reaction forces at the platform to keep it balanced. This difference in reaction forces will result a different normal force at each wheel, and hence the potential for different traction forces, leading to an inability to drive the OTV straight. A coordinate system has been defined, such that middle of the board is 0,0 . In this system the location of the vertical support forces (in
mm
) are: -
F 1
​
:(−75,−75)
-
F 2
​
:(85,−75)
-
F 3
​
:(15,85)
The propulsion team has asked the structures team to locate the battery, with mass
520 g
at
y=−10 mm
, and to compute an X location for the battery, such that the reaction forces, F1 and F2 are equal. Given these constraints, find: Subsequently to this construction, the motor M3 has failed, the team wants to move the battery to reduce the friction at the front wheel. What location
Y
in
mm
should the battery be placed to make
F 3
​
/W total ​
=0.25
? \begin{tabular}{l|l|l|} \hline
y=
& number
(
rtol
=0.01
, atol
=1e−05)
&
mm
\end{tabular}