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Simple Machines - Screw

Grade 6ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A screw is essentially an inclined plane wrapped around a cylinder or a cone in the form of a spiral.

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The spiral ridges on the surface of a screw are called 'threads'.

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The distance between two consecutive threads is known as the 'pitch' of the screw, denoted as pp.

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A screw converts rotational motion (circular motion) into linear motion (straight-line motion).

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In one complete rotation of the screw head, the screw moves forward or backward by a distance equal to its pitch (pp).

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Mechanical Advantage (MAMA): A screw provides a very high mechanical advantage. A smaller pitch results in a higher MAMA but requires more rotations to cover the same distance.

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Common applications include wood screws, bolts, car jacks, and corkscrews.

📐Formulae

Distance moved by effort in one rotation=2πr\text{Distance moved by effort in one rotation} = 2\pi r

Distance moved by load in one rotation=Pitch (p)\text{Distance moved by load in one rotation} = \text{Pitch } (p)

MA=Distance moved by effortDistance moved by load=2πrpMA = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}} = \frac{2\pi r}{p}

💡Examples

Problem 1:

A screw jack has a pitch of 0.5 cm0.5\text{ cm}. If the radius of the handle used to turn the screw is 14 cm14\text{ cm}, calculate the Mechanical Advantage (MAMA). (Take π=227\pi = \frac{22}{7})

Solution:

Given: Radius r=14 cmr = 14\text{ cm}, Pitch p=0.5 cmp = 0.5\text{ cm}.\Using formula: MA=2πrpMA = \frac{2\pi r}{p} \MA=2×227×140.5MA = \frac{2 \times \frac{22}{7} \times 14}{0.5} \MA=2×22×20.5MA = \frac{2 \times 22 \times 2}{0.5} \MA=880.5=176MA = \frac{88}{0.5} = 176.

Explanation:

The Mechanical Advantage is 176176, which means the screw jack multiplies the effort applied by 176176 times to lift a heavy load.

Problem 2:

If a screw is rotated 1010 times and it penetrates 20 mm20\text{ mm} into a wooden block, what is the pitch of the screw?

Solution:

Total distance moved =20 mm= 20\text{ mm}\Total number of rotations =10= 10\Pitch (p)=Total distanceNumber of rotations\text{Pitch } (p) = \frac{\text{Total distance}}{\text{Number of rotations}}\p=20 mm10=2 mmp = \frac{20\text{ mm}}{10} = 2\text{ mm}.

Explanation:

The pitch is the distance the screw moves linearly in a single full rotation. Dividing total distance by total turns gives the distance per turn.

Screw - Revision Notes & Key Formulas | ICSE Class 6 Science