{"id":577,"date":"2017-10-27T16:30:17","date_gmt":"2017-10-27T16:30:17","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/pressure\/"},"modified":"2017-11-08T03:24:54","modified_gmt":"2017-11-08T03:24:54","slug":"pressure","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/pressure\/","title":{"raw":"Pressure","rendered":"Pressure"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Define pressure.<\/li>\n<li>Explain the relationship between pressure and force.<\/li>\n<li>Calculate force given pressure and area.<\/li>\n<\/ul>\n<\/div>\n<p id=\"import-auto-id3108381\">You have no doubt heard the word <span data-type=\"term\" id=\"import-auto-id1932275\">pressure<\/span> being used in relation to blood (high or low blood pressure) and in relation to the weather (high- and low-pressure weather systems). These are only two of many examples of pressures in fluids. Pressure [latex]P[\/latex] is defined as<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]P=\\frac{F}{A}[\/latex]<\/div>\n<p>where [latex]F[\/latex] is a force applied to an area [latex]A[\/latex] that is perpendicular to the force.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2616925\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Pressure<\/div>\n<p id=\"import-auto-id2929954\">Pressure is defined as the force divided by the area perpendicular to the force over which the force is applied, or<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]P=\\frac{F}{A}.[\/latex]<\/div>\n<\/div>\n<p id=\"import-auto-id1614126\">A given force can have a significantly different effect depending on the area over which the force is exerted, as shown in <a href=\"#import-auto-id3175803\" class=\"autogenerated-content\">(Figure)<\/a>. The SI unit for pressure is the <em data-effect=\"italics\">pascal<\/em>, where <\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-id1787110\">[latex]1 Pa=1\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}.[\/latex]<\/div>\n<p id=\"import-auto-id1995887\">In addition to the pascal, there are many other units for pressure that are in common use. In meteorology, atmospheric pressure is often described in units of millibar (mb), where<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-847\">[latex]\\text{100 mb}=1\u00d7{\\text{10}}^{5}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}&nbsp;.[\/latex]<\/div>\n<p id=\"import-auto-id1571004\">Pounds per square inch [latex]\\left({\\text{lb\/in}}^{2}\\phantom{\\rule{0.25em}{0ex}}\\text{or}\\phantom{\\rule{0.25em}{0ex}}\\text{psi}\\right)[\/latex] is still sometimes used as a measure of tire pressure, and millimeters of mercury (mm Hg) is still often used in the measurement of blood pressure. Pressure is defined for all states of matter but is particularly important when discussing fluids.<\/p>\n<p id=\"import-auto-id2673215\">\n<\/p><div class=\"bc-figure figure\" id=\"import-auto-id3175803\">\n<div class=\"bc-figcaption figcaption\">(a) While the person being poked with the finger might be irritated, the force has little lasting effect. (b) In contrast, the same force applied to an area the size of the sharp end of a needle is great enough to break the skin.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1487076\" data-alt=\"In figure a, the person is poked with a finger exerting a small pressure due to the large area of contact and, in b, he is poked with a syringe exerting a large pressure due to the small area of contact.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_03_01a.jpg\" data-media-type=\"image\/jpg\" alt=\"In figure a, the person is poked with a finger exerting a small pressure due to the large area of contact and, in b, he is poked with a syringe exerting a large pressure due to the small area of contact.\" width=\"375\"><\/span><\/p><\/div>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2601795\">\n<div data-type=\"title\" class=\"title\">Calculating Force Exerted by the Air: What Force Does a Pressure Exert?<\/div>\n<p id=\"import-auto-id1438842\">An astronaut is working outside the International Space Station where the atmospheric pressure is essentially zero. The pressure gauge on her air tank reads [latex]6\\text{.}\\text{90}\u00d7{\\text{10}}^{6}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex]. What force does the air inside the tank exert on the flat end of the cylindrical tank, a disk 0.150 m in diameter?<\/p>\n<p id=\"import-auto-id1863946\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1863947\">We can find the force exerted from the definition of pressure given in [latex]P=\\frac{F}{A}[\/latex], provided we can find the area [latex]A[\/latex] acted upon.<\/p>\n<p id=\"import-auto-id2599366\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id1863948\">By rearranging the definition of pressure to solve for force, we see that<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-914\">[latex]F=\\text{PA}.[\/latex]<\/div>\n<p id=\"import-auto-id2401938\">Here, the pressure [latex]P[\/latex] is given, as is the area of the end of the cylinder [latex]A[\/latex], given by [latex]A={\\mathrm{\\pi r}}^{2}[\/latex]. Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-775\">[latex]\\begin{array}{lll}F&amp; =&amp; \\left(6.90\u00d7{\\text{10}}^{6}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}\\right)\\left(3.14\\right){\\left(0.0750 m\\right)}^{2}\\\\ &amp; =&amp; 1.22\u00d7{\\text{10}}^{5}\\phantom{\\rule{0.25em}{0ex}}\\text{N.}\\end{array}[\/latex]<\/div>\n<p id=\"import-auto-id1326922\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id3175478\">Wow! No wonder the tank must be strong. Since we found [latex]F=\\text{PA}[\/latex], we see that the force exerted by a pressure is directly proportional to the area acted upon as well as the pressure itself.<\/p>\n<\/div>\n<p id=\"import-auto-id1004455\">The force exerted on the end of the tank is perpendicular to its inside surface. This direction is because the force is exerted by a static or stationary fluid. We have already seen that fluids cannot <em data-effect=\"italics\">withstand<\/em> shearing (sideways) forces; they cannot <em data-effect=\"italics\">exert<\/em> shearing forces, either. Fluid pressure has no direction, being a scalar quantity. The forces due to pressure have well-defined directions: they are always exerted perpendicular to any surface. (See the tire in <a href=\"#import-auto-id2055656\" class=\"autogenerated-content\">(Figure)<\/a>, for example.) Finally, note that pressure is exerted on all surfaces. Swimmers, as well as the tire, feel pressure on all sides. (See <a href=\"#import-auto-id3130778\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2055656\">\n<div class=\"bc-figcaption figcaption\">Pressure inside this tire exerts forces perpendicular to all surfaces it contacts. The arrows give representative directions and magnitudes of the forces exerted at various points. Note that static fluids do not exert shearing forces.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2446191\" data-alt=\"The forces inside a tire are shown by arrow lines. An inset shows an enlarged view of the valve in the tire. Air pressure in the tire keeps the valve closed.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_03_02a.jpg\" data-media-type=\"image\/jpg\" alt=\"The forces inside a tire are shown by arrow lines. An inset shows an enlarged view of the valve in the tire. Air pressure in the tire keeps the valve closed.\" width=\"300\"><\/span><\/p><\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id3130778\">\n<div class=\"bc-figcaption figcaption\">Pressure is exerted on all sides of this swimmer, since the water would flow into the space he occupies if he were not there. The arrows represent the directions and magnitudes of the forces exerted at various points on the swimmer. Note that the forces are larger underneath, due to greater depth, giving a net upward or buoyant force that is balanced by the weight of the swimmer.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2689097\" data-alt=\"A man swimming underwater has many arrows pointing toward him to represent the directions and magnitudes of the forces exerted on him at various points.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_03_03a.jpg\" data-media-type=\"image\/jpg\" alt=\"A man swimming underwater has many arrows pointing toward him to represent the directions and magnitudes of the forces exerted on him at various points.\" width=\"400\"><\/span><\/p><\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">PhET Explorations: Gas Properties<\/div>\n<p id=\"eip-id1323026\">Pump gas molecules to a box and see what happens as you change the volume, add or remove heat, change gravity, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other.<\/p>\n<div class=\"bc-figure figure\" id=\"eip-id3028052\">\n<div class=\"bc-figcaption figcaption\"><a href=\"\/resources\/a45ff8bc2a26690feda69c6d0fc5e5040d0e0682\/gas-properties_en.jar\">Gas Properties<\/a><\/div>\n<p><span data-type=\"media\" id=\"Phet_module_12.3\" data-alt=\"\"><a href=\"\/resources\/a45ff8bc2a26690feda69c6d0fc5e5040d0e0682\/gas-properties_en.jar\" data-type=\"image\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/PhET_Icon.png\" data-media-type=\"image\/png\" alt=\"\" data-print=\"false\" width=\"450\"><\/a><span data-media-type=\"image\/png\" data-print=\"true\" data-src=\"\/resources\/075500ad9f71890a85fe3f7a4137ac08e2b7907c\/PhET_Icon.png\" data-type=\"image\"><\/span><\/span><\/p><\/div>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id1997800\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id1570850\">\n<li id=\"import-auto-id2602098\">Pressure is the force per unit perpendicular area over which the force is applied. In equation form, pressure is defined as\n<div data-type=\"equation\" class=\"equation\">[latex]P=\\frac{F}{A}\\text{.}[\/latex]<\/div>\n<\/li>\n<li id=\"import-auto-id1228614\">The SI unit of pressure is pascal and [latex]\\text{1 Pa}=1\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}[\/latex].<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id3449531\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3149806\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3418059\">\n<p id=\"import-auto-id1390169\">How is pressure related to the sharpness of a knife and its ability to cut?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2615691\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3253764\">\n<p id=\"import-auto-id1600137\">Why does a dull hypodermic needle hurt more than a sharp one?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1034685\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1228592\">\n<p id=\"import-auto-id2680982\">The outward force on one end of an air tank was calculated in <a href=\"#fs-id2601795\" class=\"autogenerated-content\">(Figure)<\/a>. How is this force balanced? (The tank does not accelerate, so the force must be balanced.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id935474\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2446141\">\n<p id=\"import-auto-id2681028\">Why is force exerted by static fluids always perpendicular to a surface?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2590796\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1935393\">\n<p>In a remote location near the North Pole, an iceberg floats in a lake. Next to the lake (assume it is not frozen) sits a comparably sized glacier sitting on land. If both chunks of ice should melt due to rising global temperatures (and the melted ice all goes into the lake), which ice chunk would give the greatest increase in the level of the lake water, if any? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1429595\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2672592\">\n<p id=\"import-auto-id954471\">How do jogging on soft ground and wearing padded shoes reduce the pressures to which the feet and legs are subjected? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2382902\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1569315\">\n<p id=\"import-auto-id2588349\">Toe dancing (as in ballet) is much harder on toes than normal dancing or walking. Explain in terms of pressure.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3091727\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1434785\">\n<p id=\"import-auto-id3064179\">How do you convert pressure units like millimeters of mercury, centimeters of water, and inches of mercury into units like newtons per meter squared without resorting to a table of pressure conversion factors? <\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id981448\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2611366\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3122030\">\n<p id=\"import-auto-id2456066\">As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of [latex]1\\text{.}\\text{50}\\phantom{\\rule{0.25em}{0ex}}{\\text{cm}}^{2}[\/latex] and the woman\u2019s mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3201948\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2420502\">[latex]3.59\u00d7{\\text{10}}^{6}\\phantom{\\rule{0.25em}{0ex}}\\text{Pa}[\/latex]; or [latex]\\text{521}\\phantom{\\rule{0.25em}{0ex}}{\\text{lb\/in}}^{2}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2437545\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2663832\">\n<p id=\"import-auto-id3035903\">The pressure exerted by a phonograph needle on a record is surprisingly large. If the equivalent of 1.00 g is supported by a needle, the tip of which is a circle 0.200 mm in radius, what pressure is exerted on the record in [latex]{\\text{N\/m}}^{2}[\/latex]?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3051764\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2687586\">\n<p id=\"import-auto-id3090228\">Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of [latex]3\\text{.}\\text{00}\u00d7{\\text{10}}^{9}\\phantom{\\rule{0.25em}{0ex}}{\\text{N\/m}}^{2}?[\/latex](This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2950005\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2407588\">[latex]2.36\u00d7{\\text{10}}^{3}\\phantom{\\rule{0.25em}{0ex}}\\text{N}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id1818589\">\n<dt>pressure<\/dt>\n<dd id=\"fs-id1917140\">the force per unit area perpendicular to the force, over which the force acts<\/dd>\n<\/dl>\n<\/div>\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Define pressure.<\/li>\n<li>Explain the relationship between pressure and force.<\/li>\n<li>Calculate force given pressure and area.<\/li>\n<\/ul>\n<\/div>\n<p id=\"import-auto-id3108381\">You have no doubt heard the word <span data-type=\"term\" id=\"import-auto-id1932275\">pressure<\/span> being used in relation to blood (high or low blood pressure) and in relation to the weather (high- and low-pressure weather systems). These are only two of many examples of pressures in fluids. Pressure <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> is defined as<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9fb402c0c23577f5246dbeb3f4276a28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#70;&#125;&#123;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/div>\n<p>where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2510519bbe1660dfdffb4195c7287343_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> is a force applied to an area <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/> that is perpendicular to the force.<\/p>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" id=\"fs-id2616925\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">Pressure<\/div>\n<p id=\"import-auto-id2929954\">Pressure is defined as the force divided by the area perpendicular to the force over which the force is applied, or<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fc5872c39c73278c112a112379d47869_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#70;&#125;&#123;&#65;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/div>\n<\/div>\n<p id=\"import-auto-id1614126\">A given force can have a significantly different effect depending on the area over which the force is exerted, as shown in <a href=\"#import-auto-id3175803\" class=\"autogenerated-content\">(Figure)<\/a>. The SI unit for pressure is the <em data-effect=\"italics\">pascal<\/em>, where <\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-id1787110\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e0256431ec5a8db6e72b96615eac026c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#32;&#80;&#97;&#61;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"import-auto-id1995887\">In addition to the pascal, there are many other units for pressure that are in common use. In meteorology, atmospheric pressure is often described in units of millibar (mb), where<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-847\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4a9ae631fc1fd1042179d1ffe98bcb4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#48;&#32;&#109;&#98;&#125;&#61;&#49;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;&#32;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"142\" style=\"vertical-align: -1px;\" \/><\/div>\n<p id=\"import-auto-id1571004\">Pounds per square inch <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-24ac8ed3fc518e2a4c0ae3ea59936568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#98;&#47;&#105;&#110;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#115;&#105;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"108\" style=\"vertical-align: -12px;\" \/> is still sometimes used as a measure of tire pressure, and millimeters of mercury (mm Hg) is still often used in the measurement of blood pressure. Pressure is defined for all states of matter but is particularly important when discussing fluids.<\/p>\n<p id=\"import-auto-id2673215\">\n<div class=\"bc-figure figure\" id=\"import-auto-id3175803\">\n<div class=\"bc-figcaption figcaption\">(a) While the person being poked with the finger might be irritated, the force has little lasting effect. (b) In contrast, the same force applied to an area the size of the sharp end of a needle is great enough to break the skin.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1487076\" data-alt=\"In figure a, the person is poked with a finger exerting a small pressure due to the large area of contact and, in b, he is poked with a syringe exerting a large pressure due to the small area of contact.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_03_01a.jpg\" data-media-type=\"image\/jpg\" alt=\"In figure a, the person is poked with a finger exerting a small pressure due to the large area of contact and, in b, he is poked with a syringe exerting a large pressure due to the small area of contact.\" width=\"375\" \/><\/span><\/p>\n<\/div>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2601795\">\n<div data-type=\"title\" class=\"title\">Calculating Force Exerted by the Air: What Force Does a Pressure Exert?<\/div>\n<p id=\"import-auto-id1438842\">An astronaut is working outside the International Space Station where the atmospheric pressure is essentially zero. The pressure gauge on her air tank reads <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-827dff9b5cdeab6a34bbd9521e146c99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/>. What force does the air inside the tank exert on the flat end of the cylindrical tank, a disk 0.150 m in diameter?<\/p>\n<p id=\"import-auto-id1863946\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1863947\">We can find the force exerted from the definition of pressure given in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9fb402c0c23577f5246dbeb3f4276a28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#70;&#125;&#123;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/>, provided we can find the area <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/> acted upon.<\/p>\n<p id=\"import-auto-id2599366\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id1863948\">By rearranging the definition of pressure to solve for force, we see that<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-914\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f2becbb3a8cb71dc5ef71be8e84697ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#65;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"65\" style=\"vertical-align: -1px;\" \/><\/div>\n<p id=\"import-auto-id2401938\">Here, the pressure <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> is given, as is the area of the end of the cylinder <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/>, given by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f18df9cb15867739694108f0028121f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#92;&#112;&#105;&#32;&#114;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"62\" style=\"vertical-align: -1px;\" \/>. Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-775\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-72f58a31cc76fb5ae281948542ba1c7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#108;&#125;&#70;&#38;&#32;&#61;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#46;&#57;&#48;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#55;&#53;&#48;&#32;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#92;&#32;&#38;&#32;&#61;&#38;&#32;&#49;&#46;&#50;&#50;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#46;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"324\" style=\"vertical-align: -17px;\" \/><\/div>\n<p id=\"import-auto-id1326922\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id3175478\">Wow! No wonder the tank must be strong. Since we found <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1a752d913409fb71d27903bef8606b0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: -1px;\" \/>, we see that the force exerted by a pressure is directly proportional to the area acted upon as well as the pressure itself.<\/p>\n<\/div>\n<p id=\"import-auto-id1004455\">The force exerted on the end of the tank is perpendicular to its inside surface. This direction is because the force is exerted by a static or stationary fluid. We have already seen that fluids cannot <em data-effect=\"italics\">withstand<\/em> shearing (sideways) forces; they cannot <em data-effect=\"italics\">exert<\/em> shearing forces, either. Fluid pressure has no direction, being a scalar quantity. The forces due to pressure have well-defined directions: they are always exerted perpendicular to any surface. (See the tire in <a href=\"#import-auto-id2055656\" class=\"autogenerated-content\">(Figure)<\/a>, for example.) Finally, note that pressure is exerted on all surfaces. Swimmers, as well as the tire, feel pressure on all sides. (See <a href=\"#import-auto-id3130778\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2055656\">\n<div class=\"bc-figcaption figcaption\">Pressure inside this tire exerts forces perpendicular to all surfaces it contacts. The arrows give representative directions and magnitudes of the forces exerted at various points. Note that static fluids do not exert shearing forces.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2446191\" data-alt=\"The forces inside a tire are shown by arrow lines. An inset shows an enlarged view of the valve in the tire. Air pressure in the tire keeps the valve closed.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_03_02a.jpg\" data-media-type=\"image\/jpg\" alt=\"The forces inside a tire are shown by arrow lines. An inset shows an enlarged view of the valve in the tire. Air pressure in the tire keeps the valve closed.\" width=\"300\" \/><\/span><\/p>\n<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id3130778\">\n<div class=\"bc-figcaption figcaption\">Pressure is exerted on all sides of this swimmer, since the water would flow into the space he occupies if he were not there. The arrows represent the directions and magnitudes of the forces exerted at various points on the swimmer. Note that the forces are larger underneath, due to greater depth, giving a net upward or buoyant force that is balanced by the weight of the swimmer.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2689097\" data-alt=\"A man swimming underwater has many arrows pointing toward him to represent the directions and magnitudes of the forces exerted on him at various points.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_12_03_03a.jpg\" data-media-type=\"image\/jpg\" alt=\"A man swimming underwater has many arrows pointing toward him to represent the directions and magnitudes of the forces exerted on him at various points.\" width=\"400\" \/><\/span><\/p>\n<\/div>\n<div data-type=\"note\" class=\"note\" data-has-label=\"true\" data-label=\"\">\n<div data-type=\"title\" class=\"title\">PhET Explorations: Gas Properties<\/div>\n<p id=\"eip-id1323026\">Pump gas molecules to a box and see what happens as you change the volume, add or remove heat, change gravity, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other.<\/p>\n<div class=\"bc-figure figure\" id=\"eip-id3028052\">\n<div class=\"bc-figcaption figcaption\"><a href=\"\/resources\/a45ff8bc2a26690feda69c6d0fc5e5040d0e0682\/gas-properties_en.jar\">Gas Properties<\/a><\/div>\n<p><span data-type=\"media\" id=\"Phet_module_12.3\" data-alt=\"\"><a href=\"\/resources\/a45ff8bc2a26690feda69c6d0fc5e5040d0e0682\/gas-properties_en.jar\" data-type=\"image\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/PhET_Icon.png\" data-media-type=\"image\/png\" alt=\"\" data-print=\"false\" width=\"450\" \/><\/a><span data-media-type=\"image\/png\" data-print=\"true\" data-src=\"\/resources\/075500ad9f71890a85fe3f7a4137ac08e2b7907c\/PhET_Icon.png\" data-type=\"image\"><\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id1997800\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id1570850\">\n<li id=\"import-auto-id2602098\">Pressure is the force per unit perpendicular area over which the force is applied. In equation form, pressure is defined as\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4806981d738c55d8603bbd9313c090c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#70;&#125;&#123;&#65;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -6px;\" \/><\/div>\n<\/li>\n<li id=\"import-auto-id1228614\">The SI unit of pressure is pascal and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-636b9561f7101d8b7b1c138521463744_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#32;&#80;&#97;&#125;&#61;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"115\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id3449531\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3149806\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3418059\">\n<p id=\"import-auto-id1390169\">How is pressure related to the sharpness of a knife and its ability to cut?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2615691\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3253764\">\n<p id=\"import-auto-id1600137\">Why does a dull hypodermic needle hurt more than a sharp one?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1034685\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1228592\">\n<p id=\"import-auto-id2680982\">The outward force on one end of an air tank was calculated in <a href=\"#fs-id2601795\" class=\"autogenerated-content\">(Figure)<\/a>. How is this force balanced? (The tank does not accelerate, so the force must be balanced.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id935474\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2446141\">\n<p id=\"import-auto-id2681028\">Why is force exerted by static fluids always perpendicular to a surface?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2590796\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1935393\">\n<p>In a remote location near the North Pole, an iceberg floats in a lake. Next to the lake (assume it is not frozen) sits a comparably sized glacier sitting on land. If both chunks of ice should melt due to rising global temperatures (and the melted ice all goes into the lake), which ice chunk would give the greatest increase in the level of the lake water, if any? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1429595\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2672592\">\n<p id=\"import-auto-id954471\">How do jogging on soft ground and wearing padded shoes reduce the pressures to which the feet and legs are subjected? <\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2382902\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1569315\">\n<p id=\"import-auto-id2588349\">Toe dancing (as in ballet) is much harder on toes than normal dancing or walking. Explain in terms of pressure.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3091727\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1434785\">\n<p id=\"import-auto-id3064179\">How do you convert pressure units like millimeters of mercury, centimeters of water, and inches of mercury into units like newtons per meter squared without resorting to a table of pressure conversion factors? <\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id981448\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2611366\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3122030\">\n<p id=\"import-auto-id2456066\">As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2161454493309b3dcf005d176ec21723_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -1px;\" \/> and the woman\u2019s mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3201948\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2420502\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7cd770eed44cc5664fe278925bf69ebf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#53;&#57;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/>; or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c8381919efaba6942e553bbee866555e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#50;&#49;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#98;&#47;&#105;&#110;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"76\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2437545\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2663832\">\n<p id=\"import-auto-id3035903\">The pressure exerted by a phonograph needle on a record is surprisingly large. If the equivalent of 1.00 g is supported by a needle, the tip of which is a circle 0.200 mm in radius, what pressure is exerted on the record in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-19f3bf9fe53de788f3ffafe06bc6ad99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"44\" style=\"vertical-align: -4px;\" \/>?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3051764\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2687586\">\n<p id=\"import-auto-id3090228\">Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-836eef739b2fb982edfe57e80f67a330_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#57;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#47;&#109;&#125;&#125;&#94;&#123;&#50;&#125;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"114\" style=\"vertical-align: -4px;\" \/>(This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2950005\" data-element-type=\"problems-exercises\">\n<p id=\"import-auto-id2407588\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-05780cfd63c5a21f62e79843a14470e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#51;&#54;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id1818589\">\n<dt>pressure<\/dt>\n<dd id=\"fs-id1917140\">the force per unit area perpendicular to the force, over which the force acts<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":211,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"all-rights-reserved"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-577","chapter","type-chapter","status-publish","hentry","license-all-rights-reserved"],"part":562,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/577","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/users\/211"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/577\/revisions"}],"predecessor-version":[{"id":578,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/577\/revisions\/578"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/parts\/562"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/577\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/media?parent=577"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=577"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/contributor?post=577"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/license?post=577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}