Forces and equilibrium Simulations | AS & A Level Mathematics 9709

1 interactive lab · AS & A Level Mathematics 9709

Free-Body Diagram: Resolving Forces

4.1 Forces and equilibrium · Resolve the forces on a particle along axes you choose, then predict: at rest, limiting equilibrium (F = μR) or not in equilibrium?

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Resolve the forces on a particle along axes you choose, then predict: at rest, limiting equilibrium (F = μR) or not in equilibrium?

You will be able to

Resolve a force into components along and perpendicular to a plane, or horizontally and vertically, and write the equation for each direction (the components sum to zero).
Calculate the normal reaction R and the friction force F needed for equilibrium on a smooth or rough plane, using g = 10 m s⁻² and giving answers to 3 s.f.
Decide from F ≤ μR whether a particle is in equilibrium, in limiting equilibrium (about to slip) or not in equilibrium, and state which way friction acts.
Represent a contact force by its normal and frictional components, and state the equal and opposite force on the plane (Newton's third law).

Examiner's note. Draw the forces (weight mg, normal reaction R, friction F, the applied force) and resolve in two perpendicular directions. Axes along and perpendicular to the plane put R and F on the axes, so each equation has one unknown: perpendicular, R + P sin θ = mg cos α (R = mg cos α only when P has no perpendicular component); along the plane, F + P cos θ = mg sin α. Friction opposes the tendency to slip, so decide its direction first. F = μR only in limiting equilibrium (about to slip); otherwise F is whatever the equation gives and F ≤ μR, and if the F needed is greater than μR the particle is not in equilibrium. Show each equation with the numbers in, use g = 10, and give answers to 3 s.f. The classic slips are R = mg on a slope, F = μR every time, mg sin α and mg cos α the wrong way round, and leaving P out of the perpendicular equation.

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Forces and equilibrium