Question

A uniform plank of length 2.00 m and mass 30.23 kg is supported by three ropes. A 700 N person is a distance, of 0.55 m from the left end. A) find the magnitude of the tension in the vertical rope on the left end. Give your answers in newtons. B) find the magnitude of the tension in the rope in the right end. Give your answers in newtons C) find the magnitude of the tension in the horizontal rope on the left end. Give your answers in newtons

Answer 1

a. The magnitude of the tension, T₂ in the vertical rope on the left end is T₂ = 655.62 N

b. The magnitude of the tension in the rope in the right end is T₁ = 530.4 N

c. The magnitude of the tension in the horizontal rope on the left end, T₃ is T₃ = 406.3 N

What is tension force?

Tension force refers to a pulling force that is exerted by a string or cable about an axis.

a. The magnitude of the tension, T₂ in the vertical rope on the left end is given as follows:

Taking moment about the vertical axis

T₂ = 30.23 * 9.81 + 700 - T₁ * Sin40°

Solving for T₁ by taking the left end as the pivot;

T₁ Sin 40° * 2.00 = 700 * 0.55 + (30.23 * 9.81) * 1.0

T₁ * 1.285 = 681.5563

T₁ = 530.4 N

Therefore;

T₂ = 30.23 * 9.81 + 700 - 530.4 * Sin 40°

T₂ = 655.62 N

b. From calculation, the magnitude of the tension in the rope in the right end is T₁.

T₁ = 530.4 N

c. The magnitude of the tension in the horizontal rope on the left end, T₃ is determined thus:

Taking moments about the left end in the horizontal direction;

T₃ = T₁ * cos 40°

T₃ =  530.4 N * cos 40°

T₃ = 406.3 N

In conclusion, the tension at the rope in the various ends is determined by taking moments about the left end.

Learn more about tension force at: https://brainly.com/question/187404

#SPJ1