Moments, Pressure & Hooke's Law
Calculate the turning effect (moment = force × perpendicular distance), explain how pressure is transmitted equally in liquids (Pascal's principle) and the concept of atmospheric pressure, and describe Hooke's Law (extension ∝ force up to the elastic limit)
What a learner can do afterwards
- Calculates the moment of a force and uses the principle of moments to solve lever problems
- Explains why hydraulic systems can multiply force (pressure transmitted equally)
- States Hooke's Law and plots force-extension graphs identifying the elastic limit
- Calculates spring constant k from a force-extension graph (k = F/x)
The lesson
You already know how a lever balances around a pivot. The turning effect a force has around that pivot is called a moment. To calculate it, multiply the force by the perpendicular distance from the pivot to the line of the force: moment = force × distance. Moments are measured in newton metres (Nm). A bigger force or a longer distance both make a bigger moment.
A mechanic pushes on a spanner 0.3 m from a bolt with a force of 40 N. Moment = 40 N × 0.3 m = 12 Nm. If she grips a spanner twice as long, 0.6 m, the same 12 Nm moment now needs only 20 N of force. That is why a longer spanner makes a tight bolt easier to turn.
Squeeze a liquid trapped in a closed container, and the pressure you create spreads out equally in every direction. This is Pascal's principle. Hydraulic systems use it: push a small piston with a small force, and the same pressure acts on a much bigger piston, producing a much bigger force. The air above you has weight too, and this creates a pressure called atmospheric pressure, pushing on you from every direction.
Hooke's Law only holds up to the elastic limit. Stretch a spring past that point, and it will not return to its original length, so the force-extension graph stops being a straight line.
Moments make things turn, pressure in a liquid pushes equally in every direction, and a spring's extension stays proportional to force until it passes the elastic limit.
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Where it sits
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Where this leads
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8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.