Inclined Planes, Wedges and Screws flashcards

$\text{IMA}=\frac{L}{h}$: sloped length divided by vertical rise (same units). An 800 N cart on a 6 m ramp rising 1.5 m needs an ideal 200 N push.

No. Lifting to height h always needs at least $W\times h$ of work. A longer ramp lowers the force but spreads the same work over more distance; friction can even add work.

$\text{IMA}=\frac{\text{length}}{\text{thickness}}$ at the wide end. A 15 cm long, 3 cm thick wedge has IMA 5. Long thin wedges give more advantage; blunt ones need more force.

$\text{lead}=\text{pitch}\times \text{starts}$: axial travel per full turn. A triple-start screw with 1.5 mm pitch advances 4.5 mm per turn. Single-start: lead equals pitch.

$\text{IMA}=\frac{2\pi r}{\ell }$: handle circle 2πr divided by lead ℓ (same units). A 0.25 m handle and 5 mm lead give about 314. Longer handle or finer lead raises IMA.

Friction always opposes motion. Raising: push = $W\sin \theta +{\mu }_{k}W\cos \theta$. Lowering at steady speed: hold back only $W\sin \theta -{\mu }_{k}W\cos \theta$. Normal force on a slope is $W\cos \theta$.

Low-efficiency screws (roughly below 50%) are self-locking: thread friction keeps the load from turning the screw back. Vibration or wear can still let it slip, so use jack stands.

$\text{efficiency}=\frac{\text{AMA}}{\text{IMA}}\times 100\%$, with AMA = load / actual effort. A 5 m ramp rising 1 m (IMA 5) needing 225 N for 900 N (AMA 4) is 80% efficient.