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The ladder shown in figure has negligibl...

The ladder shown in figure has negligible mass and rests on a frictionless floor. The crossbar connects the two legs of the ladder at the middle. The angle between the two legs is `60^0`. The fat person sitting on the ladder with a mas of 80 kg. Find the contact force exerted by the floor on each leg and the tension in the cross bar.

Text Solution

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The forces acting on different parts are shown in figure. Consider the vertical equilibrium of the ladder plus the person system. The forces acting on this system are its weight (`80 kg`) `g` and the contanct force `N+N=2N` due to the floor.

Thus, `2N=(80kg)g` or `N(40 kg)(10 m//s^(2))=400N` Next consider the equlibrium of the left leg of the ladder. Taking torques of the forces acting on it about the upper end,
`N(2m)tan30^@=T(1m)`
or `T=N2/(sqrt(3))=(400N)xx2/(sqrt(3))=80/(sqrt(3))N`
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