A uniform plank of length 2.00 m and mass 31.5 kg is supported by three ropes, a

Question

A uniform plank of length 2.00 m and mass 31.5 kg is supported by three ropes, as indicated by the blue vectors in the figure below. Find the tension in each rope when a 715 N person is 0.500 m from the left end. magnitude of vector T 1 Incorrect: Your answer is incorrect. Your response differs from the correct answer by more than 10%. Double check your calculations. N magnitude of vector T 2 Incorrect: Your answer is incorrect. Your response differs from the correct answer by more than 10%. Double check your calculations. N magnitude of vector T 3 N

Explanation / Answer

Given that the mass of the plank is M = 31.5 kg
            Length of the board is L = 2.00m
             The weight of the person is W= 715 N
        -------------------------------------------------------------
                   
From the figure the distance
AB = 0.500m          
AC = 1.00 m ( weight of the rodat the center of the rod)
AD = 2.00
CD= 1.00 m
         -----------------------------------------------------------------------------------

Since the system is in equilibrium then the torque is zero about any point
   
Apply torque about the point A
       
-T2 * (0) - W(AB) - Mg(AC) +T1sin40*(AD) = 0
                                                   
T1sin40*(AD) = W(AB) + Mg(AC)
                                                   

T1=( W(AB) + Mg(AC) ) / (AD)sin40

= 518.212 N

Apply torque about the point D

-T2 * (AD) - W(BD) - Mg(CD) +T1sin400*(0) = 0

T2* (AD) = W(BD) + Mg(CD)
T2 = ( W(BD) + Mg(CD) ) / AD

= 690.6 N

Apply newtons law in horizontal direction then

T3 = T1 cos40    
    
= 396.973N

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