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A 22 kg person climbs up a uniform 139 N ladder. The upper and lower ends of the ladder rest on frictionless surfaces. The bottom of the ladder is fastened to the wall by a horizontal rope. The angle between the horizontal and the ladder is 42°.

Answer :

So, the tension in the horizontal rope is 354.6 N.

A person weighing 22 kg is climbing up a ladder with a weight of 139 N. The ladder is resting on frictionless surfaces and is fastened to a wall by a horizontal rope. The angle between the ladder and the horizontal is 42 degrees.
To solve this problem, we need to analyze the forces acting on the ladder. There are three forces involved: the weight of the person, the weight of the ladder, and the tension in the horizontal rope.
1. The weight of the person is given as 22 kg. We can find the weight force using the formula W = m × g, where m is the mass and g is the acceleration due to gravity. So, W_person = 22 kg × 9.8 m/s² = 215.6 N.
2. The weight of the ladder is given as 139 N.
3. The tension in the horizontal rope is the force that keeps the ladder in equilibrium. It acts in the horizontal direction. We can find the tension force using the formula T = W_person + W_ladder, where T is the tension force, W_person is the weight of the person, and W_ladder is the weight of the ladder.

So, T = 215.6 N + 139 N

= 354.6 N.
In conclusion, the tension in the horizontal rope is 354.6 N.
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