Engineers are developing an experimental railway cart system for use in a new theme park. A small motor drives the main cart via a gear train and the secondary cart is connected to the main cart's driveshaft via a universal joint $($Figure $3).$ The motor specs are as follows: $7\mathrm{.}2kW,1200rpm,60Hz,3-$phase. The gear train is comprised of three gears with the following diameters: $8cm,6\mathrm{.}4cm$ and $5\mathrm{.}48$ cm $,$ with each gear having a pitch of $10($in cm $)$ and an efficiency of $96\%.$ If the pinion's shaft is directly coupled to the main cart's driveshaft, determine:

The speed of the main cart's driveshaft.

$[3]$

The power transferred to the main driveshaft.

$[2]$

Figure $3$: Schematic of driveshaft and universal joint

Two masses $($A and B$)$ are attached to the shafts. The masses are $1\mathrm{.}8$ kg and $2\mathrm{.}7$ kg respectively, attached at radial distances of $400$ mm and $620$ mm $,$ and at the angular positions of $45$ and $150$ respectively. The angular positions are measured counter$-$clockwise from the reference line along the x $-$axis. Determine the amount of the counter$-$mass at a radial distance of $250$ mm required for the static balance.

$12$

rigure $4$: wriveshatt during misalignment