A 50-story building is being planned. It is to be 190.0m high with a base 46.0m

Question

A 50-story building is being planned. It is to be 190.0m high with a base 46.0m by 66.0m . Its total mass will be about 2.2

A 50-story building is being planned. It is to be 190.0m high with a base 46.0m by 66.0m . Its total mass will be about 2.2?107kg , and its weight therefore about 2.2?108N . Suppose a 200km/h wind exerts a force of 880N/m2 over the 66.0m wide face(Figure 1) Calculate the magnitude of the torque about the potential pivot point, the rear edge of the building (where F? E acts in the figure). Assume the total force of the wind acts at the midpoint of the building's face, and that the building is not anchored in bedrock. [Hint: F? E in the figure represents the force that the Earth would exert on the building in the case where the building would just begin to tip.] Express your answer using two significant figures.

Explanation / Answer

distance from pivot to line of weight force= 46/2=23m

torque from the weight=2.2*108*23 Nm in clockwise direction ---(1)

distance from pivot to line of wind pressure force=190/2=95m

force from wind= Pressure*A=880*190*66

So, torque from that force= 880*190*66*95 in anticlockwise direction---(2)

From (1 ) and (2)

net torque= 5.06*109- 1.05*109 =4.01*109 Nm in clockwise direction

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