Question

1. 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 center of gravity is 0.40m length from the foot. A 150N Child hangs from a 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.

Answer 1

Question #78426, Physics / Molecular Physics | Thermodynamics

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 center of gravity is 0.40m length from the foot. A 150N Child hangs from a 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.

Solution

The system is in equilibrium. Thus, net torque about the foot of the ladder is zero:

$$T \cos 37 L - 100 \sin 37 (0.4 L) - 150 \sin 37 (L - 0.2 L) = 0$$ $$T \cos 37 = \sin 37 (40 + 0.8(150))$$

The tension in the tie rope is

$$T = 160 \tan 37 = 120 \, N.$$

The net force is zero, so

$$N_x - 120 = 0$$ $$N_y - 100 - 150 = 0$$

The horizontal component of the force on the foot of the ladder is

$$N_x = 120 \, N.$$

The vertical component of the force on the foot of the ladder is

$$N_y = 250 \, N.$$

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