A tornado rips off a 1000-ft^2 roof with a mass of 2000 lbm. What is the minimum vacuum pressure

step 1 So let's start with the given data, right? So we have the math that is equal to 2 ,000 pounds ma

A tornado rips off a 1000-ft^2 roof with a mass of 2000 lbm....

Key Concepts

Force Equilibrium

Force equilibrium involves setting the upward force (due to the pressure acting over the area) equal to the downward gravitational force (the weight of the roof). This principle is used to determine the minimum pressure needed to lift the roof. Essentially, the pressure times the area must equal or exceed the weight of the roof.

Vacuum Pressure

Vacuum pressure refers to a condition where the pressure on one side of a surface is lower than the atmospheric pressure on the other side, creating a net force. In this problem, a vacuum is applied above the roof so that atmospheric pressure on the underside provides the lifting force. The key idea is that by reducing the pressure above the roof (creating a vacuum), one can generate an effective pressure differential capable of overcoming the weight.

Pressure

Pressure is the force applied per unit area. In problems like these, the pressure differential (here provided by a vacuum) creates an upward force over a given area, which must overcome the downward force of gravity acting on the object. Understanding pressure is key because it directly relates to how much force is exerted on every square foot of the roof.

Weight and Gravitational Force

The weight of an object is the gravitational force acting on its mass. It is calculated using the object's mass and the acceleration due to gravity. In this context, converting the mass (in lbm) to weight (in lbf) is essential in balancing the forces, so that the upward pressure-generated force can be compared directly with the downward gravitational force.

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