Equilibrium/physics

Question

A 10.5 kg board 6.00 m long is

supported by two sawhorses, one

at each end. A 4.45 kg saw sits on

The board 1.80 m from the left end.

Find the upward force that the

LEFT sawhorse exerts on the

Board.

Can someone please answer this thourghly?

Answer 1

Remember that for an object to be in equilibrium, the net force and net torque on it must be 0. Also recall that we can take examine the torque about ANY point and this will be true, and that careful selection of the point to use can often simplify problems significantly.

Take this problem for example. There are many forces acting on the board; the left sawhorse, the right sawhorse, the weight of the saw placed on it, and the weight of the board itself. Of these, we do not know the force of the left or right sawhorse. But the problem is only asking us for one of those two, the left sawhorse. If we choose the location to measure our torques as the spot where the right sawhorse contacts the board, then the right sawhorse will contribute 0 torque (because it will be a distance 0 away from the pivot point), which will give us an equation that depends only on the left sawhorse, which is what we're trying to find.

So let's do that! Call the length of the board L, the distance from the saw to left edge of the board d, the mass of the board M, the mass of the saw m, and the force by the left sawhorse F. Take our pivot point to be the right edge of the board. Then, here's the contribution each of the forces gives to the torque on the board:

Right Sawhorse: 0

Left Sawhorse: -FL

Saw: mg(L-d)

Board: 1/2 MgL

Take note that the left sawhorse gets a negative toque because that force serves to cause a clockwise (CW) rotation, while the other two try to cause a counter-clockwise (CCW) rotation. We could define either CW or CCW to be positive, but CCW is the standard. If you're having trouble seeing where each of these factors come from, make sure you've got a good sketch of the system, and carefully label the distances.

That the net torque is 0 (because, again, the board is in equilibrium) means that

-FL+mg(L-d)+1/2 MgL=0

Which we can easily solve for F, our unknown force from the left sawhorse

FL=mg(L-d)+1/2 MgL

F=mg(1-d/L)+1/2Mg

F=82.06N