Simulation · Physics · Class 11
See-saw: balance the moments
From the lesson Principle of moments and centre of gravity in System of Particles and Rotational Motion. Change the values and watch what happens.
The idea behind it
NCERT §6.8.1, §6.8.2
- An ideal lever is a light rod pivoted at the fulcrum, like a see-saw or the beam of a balance. With load F₁ at distance d₁ and effort F₂ at d₂ from the fulcrum, the reaction there is R = F₁ + F₂.
- Principle of moments: d₁F₁ = d₂F₂, load arm × load = effort arm × effort. Anticlockwise moments are usually taken positive. It also holds when the parallel forces are not perpendicular to the lever.
- Mechanical advantage M.A. = F₁/F₂ = d₂/d₁. When the effort arm is longer than the load arm, M.A. > 1 and a small effort lifts a large load.
- The centre of gravity is the point about which the total gravitational torque on the body is zero; a cardboard balances horizontally on a pencil tip placed there.
- In uniform gravity Σmᵢrᵢ × g = 0 gives Σmᵢrᵢ = 0, so the centre of gravity coincides with the centre of mass. For a body so large that g varies across it, they differ; the centre of mass depends only on how the mass is distributed.
- A plate hung freely from a point settles with its centre of gravity on the vertical through that point. Two or three such verticals from different points cross at the centre of gravity.
- A 70 cm, 4.00 kg uniform bar on knife-edges 10 cm from each end carries 6.00 kg at 30 cm from one end. With g = 9.8 m/s², forces give R₁ + R₂ = 98.00 N and moments about the centre give R₁ − R₂ = 11.76 N: R₁ = 54.88 N and R₂ = 43.12 N, about 55 N and 43 N.
- A 3 m, 20 kg ladder rests against a frictionless wall with its foot 1 m out. Moments about the foot give the wall's push F₁ = W/(4√2) = 34.6 N; the floor supplies N = 196.0 N up and friction 34.6 N, a resultant of 199.0 N at about 80° to the horizontal.
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