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Mechanics

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17 Sep 2007 11:07:46 IST

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600

HC VERMA SUM NO 12

None

A MAN HAS INTO A DITCH OF WIDTH D AND 2 OF HIS FRIENDS ARE SLOWLY PULLING HIM UP USING A LIGHT ROPEWITH EQUAL FORCE EXERTED BY EACH FRND FIND D FORCE WEN MAN IS AT DEPTH H

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ramyani chakrabarty

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Joined: 22 Apr 2007

Posts: 2537

17 Sep 2007 11:43:01 IST

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forces acting on the man are :
1. tension T along the 2 strings in upward direction [at angle

with vertical imaginary line]
2.Mg downwards, M being the mass of man

applying Pythagorus theorem, we get,

T² = h² + d² /4
T=^{[ ]}

(h² + d² /4)
if

is the angle between the stringand the vertical, we get,

2 Tcos

- Mg=Ma

T= (Ma + Mg)/2cos

now as the man rises up,

increases and cos

decreases.as a result T      increases.

      when the man is at a depth h,a=0
         2T=Mg/cos

T= Mg

(h² + d² /4)/2h.

P.S after typing i found that i replaced H by h, and D by d
I cannot draw.so sorry for that

ramneek kakkar

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Joined: 10 Sep 2007

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17 Sep 2007 16:10:36 IST

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using angle 'a'

2tcosa=mg .....................................1

now cosa =

h / sqroot of
d^2/4 +h^2
filling value in 1
get t tis force

ramneek kakkar

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Joined: 10 Sep 2007

Posts: 8

17 Sep 2007 16:11:31 IST

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rate me if it is correct

Krishna Gopal Singh

Forum Expert

Joined: 29 Dec 2006

Posts: 5153

19 Sep 2007 23:37:49 IST

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Well done both ramayani and ramneek are correct

Piyush Khemka

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Joined: 22 Sep 2007

Posts: 10

22 Sep 2007 13:56:16 IST

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when the man is at a depth h,a=0
2T=Mg/cos
T= Mg (h 2 + d 2 /4)/2h.

Excue me.....but i didnt understand this part......How come u replaced cos Q with sumthing else??

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