Question

# A ladder leans against a wall making a 55.0° angle to the floor. The ladder is...

A ladder leans against a wall making a 55.0° angle to the floor. The ladder is 4.50 m long, and weighs 415 N. The wall is frictionless and so is the floor. A horizontal wire is attached to the base of the ladder and attached to the wall. (a) What is the tension in the wire? (b) A person who weighs 655 N stands on a rung of the ladder located 2.00 m from its lower end. What is the new tension in the wire? {145 N, 349 N}

Solution:-

A diagram would be required for the solution so i am uploading a diagram.

Rest of the equations are :-

For first situation you can see the Tension is balanced by the Normal reaction. So

N = T ........................ (1)

Now take torques about point A and metion the inward torques negative and outward torques positive. therefore

T x 0 - 415 x 2.25 x sin (35) + N x 4.5 x Sin (55) = 0

which gives N = 145.23 newton therefore Tension in the string is 145 newtons approx.

Now for secnod situation you can see one extra torque of the Person would be counted therefore

agian writing the torque balance equations

T x 0 - 415 x 2.25 x sin (35) - 655 x 2 x sin (35) + N x 4.5 x Sin (55) =0

which gives the value of N this time as 349.18 N which is approx 349 N. thanks

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