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The cover for a 0.5 -m-diameter access hole in a water storage tank is attached to the tank with four equally spaced bolts as shown. Determine the additional force on each bolt due to the water pressure when the center of the cover is located 1.4 m below the water surface.

Physics 101 Mechanics

Chapter 9

Distributed Forces: Moments of Inertia

Section 2

Parallel-Axis Theorem and Composite Areas

Moment, Impulse, and Collisions

Cornell University

University of Michigan - Ann Arbor

University of Washington

Lectures

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

03:30

In physics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Given a force, F, applied for a time, t, the resulting change in momentum, p, is equal to the impulse, I. Impulse applied to a mass, m, is also equal to the change in the object's kinetic energy, T, as a result of the force acting on it.

02:45

A 4 -m-diameter water tank…

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The circular access port i…

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The tank is filled with wa…

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but told that the cover for 1/2 meter diameter access hole in a water storage tank It's attached to the tank with four equally space bolt shown determined additional force on each bolt through the water. Pressure from the center of the cover when the center of the cover is located 1.4 meters below the water surface. All right, so here is our the inside where the water, the pressure is acting. And then we have this outer flans here and then bolts attaching it to the tank. And so we know that the water level is 1.4 meters above the center of the circle, which is Excuse me, that's also the the central it from a measured from the surface of the water. Now we'll have to figure out what their center of pressure is, and it will be somewhere a little deeper because the pressure of what the pressure increases as we go down. So the result in force is the is is the density of water times gravity, um, or 9820 Newtons per meter. Uh, Cube. And we have That is the Times, the centrally times the area of this. So we have all those numbers so we can figure out what that result in force is. And that is 2696.7 Newtons. Now we need if we got where where that force acts so that it acts a position. Weiss api. So the center of pressure and we you can get that by using the formula were given. So the area moment about the X axis, which is the top of the is that the water level, um, divided by the distance to the sense right from the water level times the area over which the water is acting in that we get after we figure out what the area moment is about this axis. So that's the area moment about the central access plus the area times. Um, why bar squared, OK, so you can plug it. We have all these numbers, complete them all in, and we get 0.3 80 meters to the fourth. And so now we have everything. Um, everything here we have this, we have this and we have this and we can figure out the center of pressure is at 1.41 meters. So about what is that? 10 centimeters? A little bit low here, Um, so we have those things, and now we have to do the mechanics. And so we have to bolt here and two bolts here, the two bolts at this level are gonna have the same force value in the two bulls that the bottom will have the same force value. Because that same level, um, we have the result in force from the pressure here acting at a distance. Why P down here? Um, these bolter at at 45 degree angles Night. So, um, this distance here is our two times sign of pi over four. And then we know that the sum of thes two of these forces to f A plus two FC must equal this for this to be an equilibrium in the horizontal correction. We also know the moment Listen more months about well, give a given any point because it's an equilibrium on my pick point. A have to be zero. So that is, um has he here? This is distances to D times two FC is four dfc and clockwise is in the negative direction as I've defined it here and then this. We have their, um, resulting from the pressure. And now it acts at, um we need to figure out what it's the moment about the A but point a is, and so that is, um de my plus y p minus y bar. Okay, so So we have why bar, um and we Yeah, we subtract off. Basically, we get this piece plus this piece. So this is why p y my minus y bar. And this is D So that's what this that distances and we can plug in our values. And we took a moment about this point So FAA didn't show up in here so we can use fine FC. And it is 707.4 Newtons and it is also equal f d the bolt on the other, the other side at the same death. And once we know that we can't plug it back into here and we can find out that f A is 640.9 Newtons and this is what we'd expect that we we would expect that there needs to be that these bolts down the lower bolts would have would need to carry more load than the upper bolts

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