A towed rigid wheel with a total weight W is to be rolled on a hard horizontal surface as well as up the slope on a hard surface inclined at an angle θ with the horizontal. The rolling resistance of the wheel on inclined surface as compared to that on the horizontal surface is __________.
Options:
(A) increased by W sinθ
(B) increased by W cosθ
(C) decreased by W sinθ
(D) decreased by W cosθ
Official Answer Key:
A
Step-by-Step Solution & Explanation
When the wheel is towed up an incline, the total resistance to motion comprises two parts:
The rolling resistance proper, arising from deformation at the wheel–surface contact.
The grade resistance — the component of the weight acting down the slope, equal to W sinθ.
The additional force the towing vehicle must supply, over and above the horizontal-surface case, is therefore W sinθ. This is the dominant and directly quantifiable increase, and it is what the question asks for.
Why not the others: W cosθ is the normal component (it governs the contact load and slightly reduces the rolling-resistance term, but the options do not ask for that second-order effect); a decrease in either form contradicts the physical fact that climbing demands more pull.
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