figure 3.1 shows a rectangular concrete slab of weight 18000N. It rests on a brick wall and is the roof of a bus shelter. The concrete slab is 3.0 m wide.
The wall is 2.5 m from the front of the concrete slab and 0.50 m from the back. The cables behind the shelter pull downwards and stop the slab toppling forward.
The concrete slab is of uniform thickness and density. Determine the perpendicular distance between the wall and the centre of mass of the slab?
State the principle of movement?
Calculate the total downward force exerted by the cables on the slab?
A) Since the centre of mass is always in the middle 3.0÷2=1.5
So, the centre of mass is (1.5m - 0.50=) 1.0m away from the wall
B) i) Principle of moment states that for a body to be in equilibrium anticlockwise is equal to clockwise moment
ii) F1 × F1 = F2 × D2
18000 × 1.0 = F × 0.5
18000÷0.5
F = 36000 N
Any questions?
center of mass of slab is in the center, so it is at1.5 m from the front, or from the wall, 1.0m
now to balance it,
Fc=force cables are pulling downward
Fw=force on the wall downward
sum forces=0
18000-Fc+Fw=0
moments about any point is zero, choose the wall point
1.0*18000=Fc*0.5
Fc=36000
fw=18000
where are the other answers
When we say D2 why didnt we choose 1m instead of 0.5 arent we going to take the distance from the centre of mass?
Well, well, well, it sounds like this rectangular concrete slab is having quite the adventure on top of that bus shelter! Let me calculate that perpendicular distance for you.
To find the distance between the wall and the center of mass, we need to take into account the weight distribution of the slab. Since the slab is of uniform density, we can assume that the center of mass is located at the geometric center of the rectangle.
The slab is 3.0 m wide, so the distance from the wall to the center of mass would be half of that, which is 1.5 meters. Ta-da!
Now, as for the principle of movement, the one that comes to mind in this case is the good ol' principle of stability. This principle states that an object will be stable if the line of action of the weight force falls within its base of support. In other words, as long as that slab's weight force stays within the area defined by the base (the rectangle in this case), it won't topple over like a clumsy circus clown.
Lastly, to determine the total downward force exerted by the cables on the slab, we need to consider that the cables are preventing the slab from toppling forward. Since the slab is in equilibrium, the magnitude of the total downward force exerted by the cables must be equal to the weight of the slab, which is given as 18000N. Voilà!
I hope my clownish explanations brought some smiles to your face while answering your questions. If you have any other inquiries, feel free to throw them my way!
To determine the perpendicular distance between the wall and the center of mass of the slab, we need to find the location of the center of mass of the slab.
Given that the slab is rectangular and of uniform thickness and density, its center of mass will be located at the geometrical center of the slab.
In this case, the slab is 3.0 m wide, so the center of mass will be located at a distance of 1.5 m from either side of the slab. Since the wall is 2.5 m from the front and 0.50 m from the back, the perpendicular distance between the wall and the center of mass can be calculated as follows:
Distance from wall to center of mass = (2.5 m - 0.50 m) = 2.0 m
Therefore, the perpendicular distance between the wall and the center of mass of the slab is 2.0 m.
The principle of movement in this scenario is likely the principle of equilibrium.
To calculate the total downward force exerted by the cables on the slab, we need to consider the fact that the slab is in static equilibrium. This means that the sum of the downward forces (weight of the slab) and the upward forces (tension in the cables) must equal zero for the slab to remain in balance.
Since the weight of the concrete slab is given as 18000N, the total upward force exerted by the cables must also be 18000N in order to achieve equilibrium.
Therefore, the total downward force exerted by the cables on the slab is 18000N.