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A tractor pulls a sledge from the forest on an icy road at a uniform speed of 15km/hr. At what speed could the tractor pull such a sledge from the forest in the summer over a log road if the power developed by the motor in both cases is the same? The coefficient of friction when moving over the icy road is 0.01, and over the log road, 0.15. 

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Answer: 1km/hr.

Explanation:

Since the power of the motor in both cases is the same, then the following relation should hold:

N = F1v1 = F2v2  (1)

where F1 and v1 are the tractive force of the motor and the velocity at which the sledge is hauled over the icy road. F2 and v2 are the tractive force and the velocity over the log road. Since, for a constant velocity, the work done by the tractive force of the motor in both cases is expended in overcoming the forces of friction, then 

F1 = k1P and F2 = k2P (2)

where P is the weight of the sledge. From Equations (1) and (2) it follows that

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