Chapter 11. Net force on an object due to a pressure difference (11-10)

Question

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{"title":"A pressure difference on two opposite sides of an object produces a net force.","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"3,4,27,42\"}]"} {"title":"Area of each side of the object","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"272,8,298,43\"}]"} {"title":"Lower pressure on the \perpher side of the object","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"195,33,199,34\"},{\"shape\":\"poly\",\"coords\":\"132,99\"},{\"shape\":\"rect\",\"coords\":\"199,12,233,53\"}]"} {"title":"High pressure on one side of the object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"118,15,147,52\"}]"}

Question

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{"title":"A pressure difference on two opposite sides of an object produces a net force.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"3,4,27,42\"}]"} {"title":"Area of each side of the object","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"272,8,298,43\"}]"} {"title":"Lower pressure on the \perpher side of the object","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"195,33,199,34\"},{\"shape\":\"poly\",\"coords\":\"132,99\"},{\"shape\":\"rect\",\"coords\":\"199,12,233,53\"}]"} {"title":"High pressure on one side of the object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"118,15,147,52\"}]"}

Question

c8v/wJ7B06y3Hygs/uFzwuPO6OUp2HU+uzUz5LsvNFlb6g10dstu4REOqmSdYNoBbRM7uNwLJRA=
{"title":"A pressure difference on two opposite sides of an object produces a net force.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"3,4,27,42\"}]"} {"title":"Area of each side of the object","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"272,8,298,43\"}]"} {"title":"Lower pressure on the \perpher side of the object","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"195,33,199,34\"},{\"shape\":\"poly\",\"coords\":\"132,99\"},{\"shape\":\"rect\",\"coords\":\"199,12,233,53\"}]"} {"title":"High pressure on one side of the object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"118,15,147,52\"}]"}

Question

ghPUVkki18HPTA+e/dRvdw80AzgVrQdOSZ1HPYn2yWw5r/W9OwUAjZqFQN8=
{"title":"A pressure difference on two opposite sides of an object produces a net force.","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"3,4,27,42\"}]"} {"title":"Area of each side of the object","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"272,8,298,43\"}]"} {"title":"Lower pressure on the \perpher side of the object","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"195,33,199,34\"},{\"shape\":\"poly\",\"coords\":\"132,99\"},{\"shape\":\"rect\",\"coords\":\"199,12,233,53\"}]"} {"title":"High pressure on one side of the object","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"118,15,147,52\"}]"}

Review

As a simple example of the force produced by a pressure difference, consider an object like a door with fluid on each side. The object has area \(A\), there is pressure \(p_1\) on one side of the object, and there is a greater pressure \(p_2\) on the \perpher side (Figure 11-10). By rearranging Equation 11-2, \(p = F_\perp /A\) we can calculate the magnitude of the force that each fluid exerts perpendicular to the object's surface:

Force on side 1: magnitude \(F_{\perp\ 1} = p_1A\)

Force on side 2: magnitude \(F_{\perp\ 2} = p_2A\)

Since \(p_2 >p_1\) the force \(F_{\perp\ 2}\) on side 2 is greater than the force \(F_{\perp\ 1}\) on side 1. These forces are in opposite directions, so the \(\textbf{net}\) force on the object has magnitude

\(F_{\mathrm{net}} = F_{\perp\ 2} - F_{\perp\ 1} = p_2A - p_1A\)

Equation 11-8 must be satisfied for a fluid to remain at rest, so this is also called the \(\textbf{equation of hydrostatic equilibrium}\).