A uniform plank of length 2.00 m and mass 29.0 kg is supported by three ropes, a

Question

A uniform plank of length 2.00 m and mass 29.0 kg is supported by three ropes, as indicated by the blue vectors in the figure below. Find the tension in each rope when a 700 N person is 0.500 m from the left end. magnitude of vector T 1 541.2914 Incorrect: Your answer is incorrect. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N magnitude of vector T 2 N magnitude of vector T 3 T1 is at a 40 degree angle above horizontal, T2 is at a 90 degree angle above horizontal and T3 is at 0 degrees

Explanation / Answer

The rod is in equilibrium.
We must use principle of moments.

Let's choose the left point of the rod as a pivotal point.

Then M1 + M2 = M3, where

M1 = F1 * d, moment of the man's weight force.

M2 = m * g * d2, moment of the rod's weight, d2 = L/2 - distance to the center of mass of the rod.

M3 = T1 sin 40 * L, moment of the T1 rope tension force.

So,

F1 * d + m * g * d2 = T1 sin 40 * L

T1 = (F1 * d + m * g * d2)/(sin 40 * L) = (700*0.500 + 29* 9.8 * 1)/(2 * 0.588) =539.28N

To find T2:

T2 + T1 sin 40 = m * g + W

T2 = m * g + W - T1 sin 40 = 29 * 9.8 + 700 - 498 * 0.588 = 691.37 N

To find T3:

T3 = T1 cos 40 = 498 * 0.81 = 403 N

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