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Question
Shows a uniform metre scale of weight W supported on a fulcrum at the 60 cm mark by applying the effort E at the 90 cm mark.
- State with reason whether the weight W of the scale is greater than, less than or equal to the effort E.
- Find the mechanical advantage in an ideal case.
Solution
Because the metre scale remains uniform
∴ Its mass per unit length is same and its wt. W acts at the 50 cm mark.
(a) ∴ W × (60 – 50) = E (90 – 60) 10W = 30 E
W = `(30 E) /10` = 3E
∴ The reason why the weight of the scale is larger than the effort is because the distance of the weight of the metre scale from the fulcrum F (10 cm) is less than the effort's (30 cm). As a result, the weight of the scale is greater than the effort.
(b) In this case,
Effort arm = (90 - 60) cm = 30 cm
Load arm = (60 - 50) cm = 10 cm
Ideal Mechanical advantage (M.A) = `"effort arm"/"load arm"`
= `(30 cm)/(10 cm)`
M.A. = 3 cm
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