Pleae help! A uniform 2m long plank is supported at each end by ropes. The plank has a mass of 300grams and a 1 kg weight is attached 0.5m from one end. Find the tension in each supporting rope.

Answer 1

The total of the tension on both ropes is the total weight of plank and load,
W = 1.3 kg * 9.8 m/s^2 = 12.74 N

Set the total moment about either end equal to zero and solve for the rope tension T on the opposite end. The tension will be higher on the cable nearest to the 1 kg weight. If moments are taken about the end closest to the mass, and the cable at the opposite end has tension T2, then

0 = T2*2m - 0.3*1.0*g - 1.0*0.5*g

Note that the 0.3 kg mass of the plank acts at the center or mass and has a lever arm of 1.0 meter.

Solve for T2 and then use T1 + T2 = 12.74 N to get T1.