A haulage gear is driven by a motor which develops $15$ kW at the full speed of $750re\frac{v}{m}in.$ The haulage drum is $1\mathrm{.}5$ m diameter and the total reduction ratio of the gearing between motor and drum is $18\mathrm{.}5.$ The efficiency of the gear is $75$ per cent, the gradient is I in $25$ and the rail friction is $135$ N per tonne of load. The masses of the gear are equivalent to a total mass of $2\mathrm{.}3$ Mg $,$ radius of gyration of $0\mathrm{.}5$ m $,$ at the drum shaft. Calculate the total load that can be hauled at the full speed.

If the motor can give an excess torque of $10$ per cent of that at full speed, calculate the acceleration possible, assuming that efficiency and rail friction values remain unaltered.

$($U$.$ Lond.$)$