Hi, this is Module 29 of an introduction engineering mechanics.

Today we're going to apply those 3D equilibrium equations to solve for another

problem where we want to find the force reactions and the moment reactions acting

on a body. We did that last module and we're going to

do another problem today. And so here's the problem.

We have a door, okay, it's homogeneous it weighs 50 pounds and it's lost its lower

hinge. So there's a missing hinge down here.

And to compensate, engineers are famous for using all kinds of ways to

jerry-rigged structures like this, and so, to compensate temporarily, we've used a

cable that has been attached from b to c. Luckily we used a cable instead of duct

tape. Duct tape is another thing that engineers

like to use a lot of. But we've got this cable from b to c and

we have a 15 pound force which is pulling on that, that door at point d here in the

x direction. The cable lies in this x z plane.

And we want to find the force and moment reactions at the hinge.

And we also want to find the tension in this cable.

And so go ahead and, and start the problem if you can and come on back when you've

figured out what you should do. Okay, now that you've thought about that,

what you should have thought about first to do, as always, is do a free body

diagram. And so in this case The, the freebody

diagram is, the body in question is the door, okay?

So we've sketched the door. We've put on our external forces and

moments, in this case, we've got a 15 pound force acting at d.

We've got the 50 pound force of the door itself.

The, the weight acting at its mass center. We've got the cable here that's got a

tension, so it's, and it's acting on a 3 on 4 slope in the x z plane.

And the last thing we needed to do was to put on the moment and force reactions at

the hinge. So on this hinge, you can see that the

hinge. Prevents motion in the x direction, it

would prevent motion in the y direction, and it would prevent motion in the z

direction. So we have our force reactions, Ax, Ay,

and Az. This hinge would prevent rotation about

the x axis, so we have a moment reaction about the x axis.

It would prevent rotation about the x axis, so we have a moment reaction about

the x axis. But it doesn't prevent motion around the z

axis, and so there is no moment reaction there because it's free to rotate.

And so, I have 5 reactions here at the hinge, 3 forced reactions and 2 moment

reactions. And so that's your complete free body

diagram. The last thing I had to do was add on the

dimensions. And so, what I'd like you to do, woops.

Is to now, solve this problem by applying the equations of the equilibrium.

So you're going to sum sources vectorially.

Set them equal to zero. Sum moments.

Vectorially, set them equal to zero. And you will find the tension in the cable

and these force and moment reactions. And I've included a PDF in your module

handouts so that you can see how well you did, and see if you got the solution.

And that's it for today's module, thanks.