$8.$ A wheel$-$type tractor, operating in its second$-$gear range and at its full rated rpm$,$ is observed to maintain a steady speed of $1\mathrm{.}50$ mph when operating under the conditions described herein. Ambient air temperature is $60\backslash$deg F$,$ altitude is sea level. The tractor is climbing a uniform $6\mathrm{.}5\%$ slope with a rolling resistance of $65$ lb per ton, and it is towing a pneumatic$-$tired trailer loaded with fill material. The two$-$axle tractor has a total weight of $60,000$ lb$.,55\%$ of which is distributed to the power axle. The loaded trailer has a weight of $75,000$ lb$.$

a$.$ For the environmental conditions just described, manufacturer rates the tractive effort of the new tractor at $60$ rimpull horsepower. What percentage of this rated rimpull does the tractor actually develop? The $"20$ lb of rimpull required ton of weight per $\%$ of slope" approximation will be acceptable. Assume traction is not a limiting factor. $(87\mathrm{.}7\%)$

b$.$ What is the value of the coefficient of traction, if the drive wheels of the tractor are at the point of incipient slippage for the conditions just described? $(0\mathrm{.}4)$

$9.$ A wheel$-$type tractor unit, operating in its fourth$-$gear range and at its full rated rpm$,$ is observed to maintain a steady speed of $7\mathrm{.}50$ mph when operating under the conditions described herein. Ambient air temperature is $60\backslash$deg F$.$ Altitude is sea level. The tractor is climbing a uniform $5\mathrm{.}5\%$ slope with a rolling resistance of $55$ lb per ton, and it is towing a pneumatic$-$tired trailer loaded with fill material. The single$-$axle tractor has a operating weight of $66,000$ lb$.$ The loaded trailer has a weight of $48,000$ lb$.$ The weight distribution for the combined tractor$-$trailer unit is $55\%$ to the drive axle and $45\%$ to the rear axle.

a$.$ The manufacturer, for the environmental conditions described, rates the tractive effort of the new tractor at $330$ rimpull horsepower. What percentage of this rated rimpull hp does the tractor actually develop? The $"20$ lb of rimpull required per ton of weight per $\%$ of slope" approximation will be acceptable. Assume traction is not a limiting factor.

b$.$ What is the value of the coefficient of traction if the drive wheels of the tractor are at the point of incipient slippage for the conditions just described?