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Question
A pair of scissors is used to cut a piece of a cloth by keeping it at a distance 8.0 cm from its rivet and applying an effort of 10 kgf by fingers at a distance 2.0 cm from the rivet.
- Find:
- the mechanical advantage of scissors and
- the load offered by the cloth.
- How does the pair of scissors act: as a force multiplier or as speed multiplier?
Solution
(a) Load arm = distance of cloth from rivet = 8.0 cm
Effort arm = distance of effort, i.e., fingers from rivet = 2.0 cm
(i) Mechanical advantage = `"effort arm"/"load arm"`
= `2/8`
= `1/4`
= 0.25
(ii) Principles of machine
Effort × Effort arm = Load × Load arm
or `"Load"/"Effort" = "Effort arm"/"Load arm"`
`"W"/"E" = 2/8 = 1/4`
`"W"/(10 "kgf") = 1/4`
∴ Load W = `10/4`
= 2.5 kgf
∴ Load offered by cloth = 2.5 kgf
(b) A pair of scissors acts as a speed multiplier, as dL > dE.
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