Inclined Planes, Wedges and Screws

Three of the six simple machines are one machine seen from three angles, which is why they share a lesson. Learn the inclined plane and the other two follow.

The inclined plane

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A ramp lets you raise a load with less force, over a longer distance.

Mechanical advantage = length of the slope / height.

In the figure, 12 feet of slope for 3 feet of height gives an advantage of 4. A 400-pound crate needs 100 pounds of push.

Longer and gentler means more advantage. Doubling the ramp's length for the same height doubles the advantage and doubles the distance you push.

The height is the vertical rise, not the horizontal base. A question giving both is checking which you use, and the answer is always the rise.

A ramp 20 feet long rises 4 feet. What is its advantage, and what force moves a 600-pound load?

20 over 4 is 5. And 600 divided by 5 is 120 pounds.

Check the work: 120 pounds over 20 feet is 2,400 foot-pounds; 600 pounds over 4 feet is 2,400 foot-pounds. Equal, as always.

The wedge

A wedge is an inclined plane that moves. Instead of an object sliding up a fixed ramp, the ramp drives into the object.

Mechanical advantage = length / thickness.

A wedge 6 inches long and 1 inch thick at its back has an advantage of 6.

Long and thin splits more easily than short and fat. That is why a splitting axe is different from a felling axe, why a chisel is ground thin, and why a doorstop works at all.

A wedge converts a downward force into sideways splitting forces, which is what the figure's outward arrows show. The force you apply goes in one direction and comes out in two others, much larger.

Examples: axe, chisel, knife, nail, doorstop, the point of a plow. A nail is a wedge, which surprises people and is asked.

The screw

A screw is an inclined plane wrapped around a cylinder. Unwrap a thread and you have a long shallow ramp.

Pitch is the distance between adjacent threads, and it is marked in the figure.

Closer threads mean a longer wrapped ramp for the same length of screw, so:

• Finer pitch, threads closer together: more advantage, more turns, less force per turn.
• Coarser pitch, threads further apart: less advantage, fewer turns, more force per turn, faster travel.

A fine-threaded screw is harder to strip and easier to turn but slower to drive. That trade-off is a question.

Examples: screws and bolts, a jackscrew, a vise, a car jack, a screw-top lid, a drill bit's flutes, an auger.

A screw plus a lever is a very large advantage, which is what a vise or a bottle jack is: the handle is a lever multiplying your force before the screw multiplies it again.

Friction matters more here

These machines lose more to friction than levers and pulleys do, because they work by sliding rather than pivoting or rolling.

That is not only a cost. A screw's friction is what stops it unwinding under load, which is why a jack holds a car up rather than lowering itself. A frictionless screw would be useless as a fastener.

So the actual advantage of a screw is far below its ideal value, and the difference is doing a job.

What you can skip

Across the 107 questions on this topic in our bank:

• Lead against pitch. Lead comes up once; the screw questions use pitch, the distance between threads, and single-thread screws where the two are equal.
• Trigonometry on ramps. No question uses sines or angles to find a force. The ramp questions use length over height.

Where people lose points

Using the ramp's horizontal base instead of its vertical rise.

Thinking a steeper ramp is easier. Steeper means less advantage and more force.

Saying a short thick wedge splits better. Long and thin does.

Thinking coarse threads give more advantage. Fine threads do.

Not recognizing a nail, a chisel or a knife as a wedge.

Expecting a screw to reach its ideal advantage. Friction is large here and is partly wanted.

Work one in under a minute

Two ramps rise to the same loading dock. One is 15 feet long and the other is 30 feet. Which requires less force to push a crate up, and by how much?

Both rise the same height, so the 30-foot ramp has twice the advantage and needs half the force.

The cost is that the crate is pushed twice as far.

Note that the height was never given and was never needed: the ratio of the two advantages is just the ratio of the two slope lengths, since the height is common to both.

Where this leads

These three complete the simple machines, and the screw's combination with a lever is the basis of the jack in the hydraulics lesson.