# The foot of a ladder rests against a wall and its top is held by a tie rope as shown in the figure below. The ladder weighs 100N, and centre of gravity is 0.40m length from the foot. A 150N child hangs from rung that is 0.20 of length from the top.determine the tension in the tie rope and the components of the force on the foot of the ladder.

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Completing Question : Length of ladder 1m

Angle made by ladder with the vertical is (theta) .

Final Answer :

160 \tan( \theta) \: units160tan(θ)units

Horizontal Component of force acting on the foot of ladder : = Tension of rope

Vertical Component : 250N

Steps and Understanding :

1) System is in Equilibrium,

So Net Torque about any point is 0 .

2) Let that point be Foot of ladder.

There are forced which are giving torque to ladder.

Tension

Force applied by Child

Gravitational force.

3) We will make out ne+ torque 0 to find the value of Tension.

For Calculation see pic.

Angle made by ladder with the vertical is (theta) .

Final Answer :

160 \tan( \theta) \: units160tan(θ)units

Horizontal Component of force acting on the foot of ladder : = Tension of rope

Vertical Component : 250N

Steps and Understanding :

1) System is in Equilibrium,

So Net Torque about any point is 0 .

2) Let that point be Foot of ladder.

There are forced which are giving torque to ladder.

Tension

Force applied by Child

Gravitational force.

3) We will make out ne+ torque 0 to find the value of Tension.

For Calculation see pic.

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