Problem about finding tension of two vertical strings...

Question

a 2.0m long beam with a mass of 2.0kg is supported horizontally by two vertical strings at each end. if a load of 4.0kg is placed 0.50m from the left end, what are the tensions on the two vertical strings?

Answer 1

Let's call the forces on the left and right end FL and FR. The sum of the forces in the vertical direction has to be zero, so:

FR+FL=(Mbeam+Mload)g=(2+4)g=6g

FR+FL=6g

The sum of the moments at any point of the beam has to be zero. Let's choose that point to be the middle of the beam.

The distance from FL to the middle is 1m. The distance from FR to the middle is also 1m, but that force is counterclockwise, so negative. The force of the 4g is also counterclockwise, so negative, and the distance is 0.5m. We can ignore the weight of the beam, since we've chosen the center of the beam to calculate the moments around.

Mtot=0=FL*1-FR*1-4g*0.5

FL-FR=2g

We are left with two equations:

FL+FR=6g

FL-FR=2g

which resolves to FL=4g and FR=2g