Question

A uniform plank of length 2.00 m and mass 32.0 kg is supported by three ropes as indicated by the blue vectors in the figure below. Find the tension in each rope when a 690 N person is d 0.475 m from the left end. Your response differs from the correct answer by more than 10%. Double check your calculations. N 40.0 Ts ?2.00 m Need Help?Read It

Answer 1

Given,

L = 2 m ; m = 32 kg ; W = 690 N d = 0.475 m

w = mg = 32 x 9.8 = 313.6 N

Consider the torques about left end

- 690 x 0.475 - 313.6 x 1 + T1 sin40 x 2 = 0

T1 x 1.286 = 641.35

T1 = 641.35/1.286 = 498.72 N

Hence, T1 = 498.72 N (= 499 N)

T2 = W + w - T1 sin40

T2 = 690 + 32 x 9.81 - 498.72 x sin40 = 683.3 N

Hence, T2 = 683.3 N (=683 N)

T3 = T1 cos40

T3 = 498.72 x cos40 = 382.36 N

Hence, T3 = 382.36 N (= 382 N)