Question
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.
Answers
drwls
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.
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.