It is easier to draw up a wooden block along a smooth inclined plane than to haul it vertically, principally b

Question

It is easier to draw up a wooden block along a smooth inclined plane than to haul it vertically, principally because:

Accepted Answer

1. **Vertical Lifting:** To lift a block of mass $m$ vertically upwards, the applied force $F_{vertical}$ must oppose the full force of gravity (weight). Thus, $F_{vertical} = mg$.
2. **Inclined Plane:** On a smooth inclined plane making an angle $	heta$ with the horizontal, the weight $mg$ is resolved into two components:
   - Perpendicular to the plane: $mg \cos 	heta$ (balanced by normal reaction).
   - Parallel to the plane: $mg \sin 	heta$ (opposing upward motion).
3. **Comparison:** The force required to pull the block up the smooth incline is $F_{incline} = mg \sin 	heta$ [Source 72].
4. **Conclusion:** Since $\sin 	heta < 1$ for any acute angle, $F_{incline} < F_{vertical}$. The effort is reduced because only the component (part) of the weight ($mg \sin 	heta$) needs to be overcome, not the entire weight ($mg$). Mass and $g$ remain constant.

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