I need this please and thank you A Ladder of mass M = 20.0 KG and the length L =

Question

I need this please and thank you

A Ladder of mass M = 20.0 KG and the length L =10.0 m rests against a frictionless vertical wall and on a frictionless horizantal surface. A rope , holding the ladder in static equilibrium , is attached to the bottom of the ladder and fixed to the vertical wall at the horizantal surface . The ladder makes an angle theata = 60 degree with respect to the horizontal

1- Find the force of the wall on the ladder ?
2-Find the tension T in the rope ?

3 An 80 kg worker plans to do some work on the wall and climb the ladder
what will the new tension in the rope be if he will be on the top of the ladder ?

4 The rope is rated at 450 N . Should the wworker be worried ? Explain ?

Explanation / Answer

1)let the normal reaction from the wall be N

and weight acting from mid point of ladder vertically downwards

as the system is in equilibrium total moment with respect to bottom of ladder = 0

taking g as 10 m/s2

10 sin 60 x N = 20 x10 x 5 cos 60

=> N =57.74 N

2) Since net horizontal force along the ladder = 0

therefore tension in the string = N acting on the opposite direction from the wall = 57.74 N

3)when worker climbs at top of ladder weight of worker acts vertically downwards

as the system is in equilibrium total moment with respect to bottom of ladder = 0

taking g as 10 m/s2

10 sin 60 x N = 20 x10 x 5 cos 60 + 80 x 10 x 10 cos 60

=> N = 519.62 N

as T = N = 519.62 N

d) as T > 450 N the worker needs to worry

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