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Review Conceptual Example 7 before starting this problem. A uniform plank of length 5.0 m and weight 225 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 385 N walk on the overhanging part of the plank before it just begins to tip?

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lublana

Answer:

0.82 m

Explanation:

We are given that

Weight,[tex]w_1[/tex]=225 N

Length,l=5 m

d=1.1 m

We have to find the distance x  for which person weighs 385 N walk on the overhanging part of the plank before it just begins to tip.

Half length=[tex]\frac{l}{2}=\frac{5}{2}=2.5 m[/tex]

[tex]r=\frac{l}{2}-d=2.5-1.1=1.4 m[/tex]

[tex]w_2=385 N[/tex]

When system in equilibrium then

[tex]w_1r=w_2 x[/tex]

[tex]225\times 1.4=385\times x[/tex]

[tex]x=\frac{225\times 1.4}{385}[/tex]

[tex]x=0.82 m[/tex]

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