Q1.
On the other end of the scale, place one eraser. Does the stapler lift up? If not, add one more eraser.
Answer
With one or two erasers the far end of the scale goes down and the heavy stapler is lifted — even though a stapler weighs several times as much as an eraser.
The scale is a lever, the pencil is the fulcrum.
Balance condition: effort × effort arm = load × load arm (Eq. 7.15)
Say the pencil is 5 cm from the stapler end and 25 cm from the eraser end:
load arm = 5 cm, effort arm = 25 cm
Mechanical advantage = effort arm / load arm = 25 cm / 5 cm = 5
So an eraser weighing 0.2 N can lift a stapler weighing up to 5 × 0.2 N = 1 N
Balance condition: effort × effort arm = load × load arm (Eq. 7.15)
Say the pencil is 5 cm from the stapler end and 25 cm from the eraser end:
load arm = 5 cm, effort arm = 25 cm
Mechanical advantage = effort arm / load arm = 25 cm / 5 cm = 5
So an eraser weighing 0.2 N can lift a stapler weighing up to 5 × 0.2 N = 1 N
Why it happens: the eraser end is far from the pencil, so it sweeps through a large distance; the stapler end is close to the pencil and moves only a little. Work done at one end is passed to the other end, F1d1 = F2d2. A small force moving far can therefore deliver a large force moving a short way.
Try This: slide the pencil towards the middle of the scale. The mechanical advantage falls, and now the erasers cannot lift the stapler. Slide it closer to the stapler and even one eraser is enough. The lever's power lies entirely in where the fulcrum sits.