Question

A uniform plank of mass 5.00 kg and length 3.60 m is supported by vertical ropes at its ends as in the figure below. A 60.0-kg painter is located 0.500 m to the left of the center and an 8.00 kg bucket is 1.00 m to the right of the center. Find the tensions ?1 and ?2 in the ropes.

Answer 1

Here,

for the tension T1

balacning the torque about the right end

-5 * 9.8 * 1.8 - 8 * 9.8 * 1 - 60 * 9.8 * (3.6 - 0.50) + T1 * 3.6 = 0

solving for T1

T1 = 552.61 N

the tension T1 is 552.61 N

Now, balancing the vertical forces

T1 + T2 - total weight = 0

552.6 + T2 = (60 + 5 + 8)* 9.8

T2 = 162.8 N

the tension T2 is 162.8 N