Tiêu đề TOPIC 7 PRESSURE - WazaElimu.com.pdf ✅

54 TOPIC 7: PRESSURE PRESSURE  This is the force per unit area. Pressure = Force Area SI-Unit of Pressure is N⁄M2 or Pascal (Pa)  Other units of pressure are: atmosphere (atm), millimeters of mercury (mmHg) and torr bar. 1 N⁄M2 = 1 Pa 1 atm = 760mmHg 1 atm = 101325 N⁄M2 1 atm = 1 bar 1 bar = 100000 Pa 1 atm = 101325 Pa NOTE:  For a given amount of force, the smaller the area of application, the greater the pressure exerted. PRESSURE DUE TO SOLIDS  The pressure in solids depends on the surface area of contact. A force (F) applied by a small area exert a higher pressure as compared to when it is applied by a large surface. Thus: Pressure = Force applied Area of contact Increase in area cause the decrease in pressure for the same amount of force. That is why:  Feet of elephant cannot sink into soft soil even though it is very heavy. This is due to large surface area over elephant feet.  Sharp edges of knife cut easily than blunt knife. This is because a sharp knife has a small surface area.  A tractor and other heavy truck works on soft ground cannot sink due to large surface area of the tyres (wide tyres).  We feel great pain if we carry a bucket of water with a thin handle than when we use a wide handle (enhanced handle). Questions 1. Explain why hitting an inflated balloon with a hammer will not cause it to burst but sticking it with a pin will burst. 2. Why are dams constructed thicker at the bottom than at the top? 3. A hole at the bottom of a ship is more dangerous than one near the surface. Explain. 4. The mass of a cuboid is 60kg. if it measures 50cm by 30cm by 20 cm. Calculate its maximum pressure. P = F A P= F A
55 Example 1 A tip of the needle has a cross-sectional area of 1x10-6 M2 . I f a doctor applies a force of 20N to a syringe that is connected to the needle, what is the pressure exerted at the tip of the needle? Solution Data given Area (A) = 1x10-6 M2 Force (F) = 20N Pressure (P) =? From P= F A = 20N 1 x 10−6M2 = 2 x 107 N M2 Pressure exerted at the needle = 2 x 107 N M2 Example 2 A rectangular block weighing 250N has dimensions 34cm by 25cm by 10cm. What is the maximum (greatest) pressure and minimum (least) pressure it can exert on the ground? Solution (a) The maximum pressure that the block can produce when resting on a horizontal floor occurs when it rest on its smallest face (area). i.e The smaller the area, the higher the pressure. The smallest surface area (A) = 0.25 m x 0.1m = 0.025m2 Then; P = F A = 250N 0.025 M2 = 10000 N M2 The maximum pressure = 10000 N M2 (b) The minimum pressure that the block can produce when resting on a horizontal floor occur when it rest on its largest face (area). i.e The larger the area, the least the pressure. Largest surface area (A) = 0.34 m x 0.1 m = 0.034 m2 . Then: P = F A ⁄ = 250N 0.034 M2 = 7352.9 N M2 The minimum pressure = 7352.9 N M2 APPLICATIONS OF PRESSURE DUE TO SOLIDS 1. Used in making different objects like screw, nails, pins, spears and arrows. These items are given sharp points to increase their penetrating power. 2. It helps some of living organisms for self-defense. Fish uses its sharp fins to protect itself 3. It helps in construction of railways. During the constructions of railways, wide wooden or concrete sleepers are placed below the railways tracks. This provides a larger surface area over which the weight of the train acts. This is a safety measure to train tracks. 4. Buildings are constructed with wide foundations to ensure that the weight of the building acts over the larger area. 5. When one walks on shoes with sharp pointed heels they exert greater pressure on the ground than when wearing flat shoes.
56 PRESSURE IN LIQUIDS The pressure exerted by liquid is due to the weight of the liquid. As the depth of the liquid increases, the liquid weight increases hence increase in pressure. From the figure above; P = F A But F = mg Then P = mg A but also mass (m) = density (ρ) x volume (V) Then P = ρVg A but also from the figure above, Volume (V) = Area (A) x depth/height (h) P = ρAhg A P = ρhg Therefore, Pressure in liquid is obtained by using the formula below: P = ρhg Where by: ρ = density of liquid h = height due to liquid column g = gravitational acceleration/acceleration due to gravity P = pressure in liquid FACTORS AFFECTING PRESSURE IN LIQUIDS The pressure at any point in a liquid at rest depends on the following factors: 1. Depth of the liquid 2. Density of the liquid CHARACTERISTICS OF PRESSURE IN LIQUIDS 1. Pressure in a liquid increase with depth. 2. Pressure in a liquid act equally in all directions. 3. Pressure in a liquid increase with increase in density of the liquid. NOTE:  Point number three (3) above explains the reason why Mercury exerts more pressure than an equal volume of water. It is simply because mercury is denser than an equal volume of water. Example 1 What will the pressure due to a column of water of height 4m be if the density of water is 1000g/m3 . (Take g = 9.8N/kg) Solution Data given h = 4m, ρ = 1000kg/m3 , g = 9.8N/kg, P =? From P = ρhg = 1000kg/m3 x 4m x 9.8N/kg = 39200 N⁄M2 ∴Pressure due to a column of water = 39200 N⁄M2 Question The pressure at the bottom of a wall is 98000N⁄M2. How deep is the well? (Take density of water = 1g/cm3 and g = 10N/kg)
57 VARIATION OF PRESSURE WITH DEPTH The pressure in liquid increase with depth, Consider below  Thus the holes of the container (can) that are at the same level will experience the same pressure and the liquid will spurt to the same distance. This is because pressure in a liquid acts equally in all directions. It is also equal at the same depth. Consider also the figure below:  The holes punched at different levels on the container will spurt the water to different distances.  The holes at the top have the least height of liquid above it. This means that the water spurt the shorter distance. This distance increases with an increase in the height above the hole.  Therefore, the hole at the bottom of the container will spurt water to furthest distance.  When water or other liquid is poured into a communicating vessel, it will attain the same level in all its tubes, no matter the different shapes of the tubes. This proves that for a given liquid, the pressure at a point within it varies only with depth. Therefore, Pressure at A, B, C and D is the same.