Levers: three parts, three orders
A lever is a rigid bar turning about a pivot to move a load. The fulcrum is the fixed pivot, the load is the force moved, the effort the force you apply. Which part sits in the middle names the class: first order — fulcrum in the middle (see-saw); second order — load in the middle (wheelbarrow); third order — effort in the middle (tweezers, forearm). Name the class from the middle part, then give a real example.
MA is force, VR is movement
Two ratios describe how a machine multiplies force. Mechanical advantage (MA) is load to effort: MA = load / effort, a pure number; an MA above 1 lets a small effort move a bigger load. Velocity ratio (VR) is VR = effort distance / load distance, also a pure number. The trade-off: you never get something for nothing — a high MA means the effort moves a long way to move the load a short way (high VR).
Efficiency and why MA is below VR
In a perfect machine no energy is wasted, so MA would equal VR. Real machines lose energy to friction, so Efficiency = (mechanical advantage / velocity ratio) x 100 per cent. Because friction wastes some effort, MA is always less than VR, so efficiency is always below 100 per cent. It can also be found as (useful work out / work in) x 100 per cent. Designers raise it by cutting friction with bearings and lubrication.
Drawn from real examiner reports.
MA and VR muddled or vaguely defined
The key definition trap. Mechanical advantage is a FORCE ratio: load / effort. Velocity ratio is a MOVEMENT ratio: effort distance / load distance. Candidates define MA only vaguely ("being easier") instead of load / effort, and swap or invert the two. Remember MA is about forces, VR about distances; keep each division the right way round.
w23 P43 Q11a(ii)
Ratio stated the wrong way round
A ratio is often written upside down — a velocity ratio of 5 written as 1:5, or MA computed as effort / load. Fix the order first: MA = load / effort, VR = effort distance / load distance. If MA comes out below 1 for a machine meant to make a job easier, the division is inverted. Put the larger quantity on top where the machine multiplies force.
s22 Q11a(iii); w22 Q11c(iii)
A big lever gives force for free
The wrong belief: that a lever which multiplies force also moves the load as far as the effort, so you gain force at no cost. In fact a lever obeys a strict trade-off: a large mechanical advantage always comes with a large velocity ratio, so the effort must move a long way to move the load only a short way. Extra force is always paid for by extra movement.
A wheelbarrow is a first-order lever
The wrong belief: that a wheelbarrow is a first order lever because the wheel looks like a central pivot. In a wheelbarrow the fulcrum is the wheel at one end, the load sits in the middle, and the effort is at the handles at the other end. Because the load is in the middle, it is a second order lever. Judge by which part is in the middle.
Efficiency over 100 per cent
Because efficiency = (MA / VR) x 100 per cent and a real machine always loses effort to friction, MA is always LESS than VR, so efficiency is always BELOW 100 per cent. Candidates set MA equal to VR, or invert the division and quote, say, 120 per cent — impossible. Keep MA on top; a result above 100 means the ratio was inverted.
Effort round a pivot moves a circle
When a lever or handle turns about a pivot, the effort moves along a circle, so its distance per turn is the circumference = 2 x pi x radius, not the radius. Candidates use the radius alone, giving a velocity ratio about six times too small. Use the circumference: a handle of radius 60 mm moves 2 x pi x 60 = about 377 mm per turn.
s23 P42 Q11d(i)
Lever class guessed, not worked out
Candidates guess whether a lever is first, second or third order instead of working it out. The test is always which part is in the middle: fulcrum = first order (see-saw), load = second order (wheelbarrow), effort = third order (tweezers, forearm). Find which part actually sits between the other two, not where the pivot appears.
s23 P43 Q11a(iv); w23 Q4
Balancing a lever: equal moments
A lever balances when the load's moment equals the effort's moment about the fulcrum: moment = force x perpendicular distance from the fulcrum. Candidates forget to measure FROM the fulcrum, or mix mm and m so the answer is 1000 times out. Keep distances from the pivot in one unit, give the moment in newton-metres, then set the moments equal.
Show every stage, state the unit
Credit is given at each stage: write the formula, substitute, state the answer. Note where there is no unit — mechanical advantage, velocity ratio, efficiency and factor of safety are all pure ratios; a moment does carry a unit (newton-metres).
Distance round a turning pivot
When the effort turns a handle about a pivot, use the circumference (2 x pi x radius) for the distance moved, not the radius. If both effort and load move on circles, the 2 x pi cancels, so the velocity ratio is simply the ratio of the two radii.
Classify then calculate: the routine
Classify by which part is in the middle (fulcrum = first, load = second, effort = third). Calculate with MA = load / effort, VR = effort distance / load distance, efficiency = MA / VR x 100 per cent; substitute and keep ratios the right way round.
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