Parallelogram Law of Forces
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flagWhat you'll discover
- arrow_forwardState the parallelogram law of vector addition
- arrow_forwardSet up equilibrium of three concurrent forces on Gravesand’s apparatus
- arrow_forwardCompute the resultant √(P² + Q² + 2PQcosγ) and compare it with R
- arrow_forwardExplain when three given forces cannot balance (triangle rule)
The law being tested
If two forces acting at a point are drawn as the adjacent sides of a parallelogram, their resultant is the diagonal from that point — in magnitude AND direction. Numerically the diagonal is R = √(P² + Q² + 2PQcosγ), where γ is the angle between the forces.
Gravesand’s apparatus tests this physically: strings over two frictionless pulleys carry weights P and Q, while a third weight R hangs straight down from the same knot. The knot drifts until the three pulls cancel. At equilibrium the resultant of P and Q must be exactly equal and opposite to R — vertical, with magnitude R.
Procedure on the board
Hang known slotted weights on all three hangers and let the junction settle. Put a mirror-backed paper behind the strings and mark each string’s direction by sighting dots with no parallax, then remove the paper and draw the lines to a scale such as 1 cm = 50 g-wt.
Construct the parallelogram on P and Q, measure its diagonal, and compare with the weight R (don’t forget hanger weights!). Agreement within 2-3% verifies the law. In the simulation, drag the knot away and release it — watching it return to the same spot shows that equilibrium is genuine, not an accident of friction.
Why some weights can never balance
Three forces at a point can only balance if each one is smaller than the sum of the other two — the same rule as triangle sides, because balanced forces drawn head-to-tail must close into a triangle. Load R = 400 g against P = Q = 100 g and the knot simply crashes into the pulleys: no geometry can make 200 g of pull hold up 400 g.
Error sources for your report: pulley friction (tap the board so strings settle to their true directions), stretching strings, hanger weights forgotten in P, Q, R, and parallax while marking string directions. NEB examiners often ask: "Why must the board be vertical?" — because only then do the weights act parallel to the board’s plane.