A crowbar is of length $3 m$ . Where should the fulcrum be placed along the length of the crowbar so that a boulder of $9 k g_{w t}$ , be lifted with it by applying an effort of $10 N$ ? $(g = 10 m s^{- 2})$ .

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Solution

Step 1: Given data
$L e n g t h o f c r o w b a r = 3 m W e i g h t o f b o u l d e r = 9 k g_{w t} e f f o r t = 10 N g = 10 m s^{- 2}$
Step 2: Finding the fulcrum be placed along the length of the crowbar
$W e i g h t o f t h e b o u l d e r = L o a d = 9 k g_{w t} = 9 \times 10 = 90 N$
Consider the fulcrum be at a distance $D$ from the boulder.
Thus, the distance from $e f f o r t = L e n g t h o f c r o w b a r - D = (3 - D) m$ .
$L o a d \times L o a d a r m = E f f o r t \times E f f o r t a r m$
$90 \times D = 10 (3 - D) 90 D = 30 - 10 D 100 D = 30 D = \frac{30}{100} = 0.3 m$
Thus, the fulcrum should be placed at a distance of $0.3 m$ from the boulder.

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