Review Conceptual Example 14 before attempting this problem. The truck in that example is traveling at 27 m/s. The density of air is 1.29 kg/m³. By how much does the pressure inside the cargo area beneath the tarpaulin exceed the outside pressure?

Conceptual Example 14

A tarpaulin is a piece of canvas that is used to cover a cargo, like that pulled by the truck in Figure 11.30. Whenever the truck stops, the tarpaulin lies flat. Why does it bulge outward whenever the truck is speeding down the highway?

(a) The air rushing over the outside surface of the canvas creates a higher pressure than does the stationary air inside the cargo area.

(b) The air rushing over the outside surface of the canvas creates a lower pressure than does the stationary air inside the cargo area.

(c) The air inside the cargo area heats up, thus increasing the pressure on the tarp and pushing it outward.

Reasoning

When the truck is stationary, the air outside and inside the cargo area is stationary, so the pressure is the same in both places. This pressure applies the same force to the outer and inner surfaces of the canvas, with the result that the tarpaulin lies flat. When the truck is moving, the outside air rushes over the top surface of the canvas, and the pressure generated by the moving air is different than the pressure of the stationary air.

Answer (a) is incorrect. A higher pressure outside and a lower pressure in the cargo area would cause the tarpaulin to sink inward, not bulge outward.

Answer (c) is incorrect. A heating effect would not disappear every time the truck stops and reappear only when the truck is moving.

Answer (b) is correct. In accord with Bernoulli’s equation (Equation 11.12), the moving air outside the canvas has a lower pressure than does the stationary air inside the cargo area. The greater inside pressure generates a greater force on the inner surface of the canvas, and the tarpaulin bulges outward.

Equation 11.12

Tarpaulin is flat Stationary Tarpaulin bulges outward Moving