Pressure Objectives: 1. define pressure and apply definition 2. relate the pressure at a point in a fluid to its depth and the density 3. Apply Archimedes’ principle to predict whether a body would float or sink in a given fluid Complete either or both of the following activities below! Activity A Activity B Lean against a wall Fill a balloon with water. 1. With the flat of the palm of your Tie the upper end of balloon. hand pressing against the wall (holding up your body weight) then Make several holes on the balloon’s surface. The water will start dropping down. Make observations about the speed and amount of 2. Using sing your forefinger to support your body weight. water flowing through the holes. Squeeze the balloon, make observations about the speed and volume of water flowing through the holes. After completing either activity answer the following questions: • Activity A • Describe the sensation felt when your body weight was being supported through your palm on the wall versus when your body weight was being supported by your forefinger. • Is there a difference in sensation between both cases? If yes, what causes this difference? • Is there a difference in the speed and volume of water flowing through the holes poked in the balloon before you squeezed the balloon and while you squeezed the balloon? If so, what causes the difference? What is pressure? • When a force acts on an object it exerts pressure. • The pressure acts at a right-angle to the object itself, and its strength depends on the amount of force and the area over which it is applied. When we apply a force on a body then according it has two effects: • When force applied on small area, it gives high pressure e.g. force applied on the sharp edge of a knife produces a high pressure due to which we cut things easily. • When force is applied over a large area it gives low pressure, e.g. camels have wide feet to spread their weight on the sand which lowers the pressure and allows them to walk on sand without sinking in sand. Defining pressure mathematically • Pressure is the force exerted on a unit area. Mathematically, it is represented as P=F/A, where F=force, A=area and P=pressure. • Pressure is measured in Pascal’s (Pa). It is a pressure of one newton per meter square Pressure! • A girl stands on soft sand in flat shoes. A girl stands on soft sand in highheeled shoes. How would the marks in the sand be different? • A boy presses his thumb on the flat top of a drawing pin. A boy presses his thumb on the point of the drawing pin. What difference would his thumb feel? What would be more painful? Being trodden on by a 55kg woman wearing stiletto heels? Or being trodden on by a 3 tonne elephant? The woman’s foot in the stiletto heel! The whole of the woman’s weight is concentrated on a very small area, whereas the elephant’s weight is much more spread out – it exerts less pressure! Calculating Pressure • 1. A box on the floor has a weight of 250 newtons. The area that the box rests on is 0.25m2. calculate the pressure under the box. Pressure = F A = 250/0.25 = 1000N/m2 Pressure in a liquid • https://www.youtube.co m/watch?v=Cvp6mLW bgaM Explaining an increase in pressure with depth • • Pressure = h * ρ * g shows that the pressure in a liquid is constant at a particular depth (height) as long as the density of the liquid is the same throughout. • At very great depths the pressure is so high that the liquid is compressed and the density increases slightly. Calculating pressure in a liquid • Pressure in gases • The earth’s atmosphere is a deep layer of gages reaching beyond 100 km above the earth’s surface. • Our atmosphere could be described as a sea of air. All of that air piled on top of us is pulled down by gravity. • In fact, the air pushes against us in all directions. • As you go higher in elevation, less air is pushing down, so the air pressure is less. • At sea level the pressure is approximately 100kPa which is the same as one atmosphere (1 atm). If you climbed to a height of 2.2 km above sea level you would experience an air pressure of 80 kPa or 0.8 atm. • As water is much denser air, travelling to a depth of 10 meters in water the pressure acting on you will increase to 2 atm. Let’s Think About it! • When you step into a bathtub full of water what happens to the water in tub? • What happens to the level of water in the tub? Why? • What causes some objects to float while others sink? It’s bath time! Can you identify with reason which of the objects would sink/float in your bathtub? Archimedes’ principle Eureka! • https://www.youtube.com/watch?v=_p-hwElkrlk • Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. • Submerged objects will displace a volume of water qual to their own volume. • When you get in a bath full of water you will notice the water level rise. The weight of the displaced water will be the same as the upthrust you feel. Floating objects • An object will float as long as the upthrust (buoyancy) is equal to the weight of the object. • Solid objects with a density greater than that of water will always weigh more than the water they displace and so will sink. • Ships are built from steel which has a much higher density than water. They float because they contain large volumes of air and this reduces their average density to much lower than the density of water. For the ship to float it must displace the same weight of water as it weighs. Sinking Objects • Loading up the ship with cargo will increase the weight of the ship and therefore the weight of water displaced. This means the ship will sink lower into the water. • If too much cargo is added to the cargo then it will sink too low in the sea. If the ship is damaged and water enters into the ship then the weight of the ship increases and it sinks lower into the water until, eventually, it sinks. The average density of the ship as a whole becomes greater than the density of water. Submerged Objects • When an object is beneath the surface of a fluid Archimedes’ principle tells us there will be an upthrust force acting on the object equal to the weight of the fluid displaced. The upthrust force will seem to reduce the weight of the of the object by decreasing the resultant force. • Submarines • Alter their average density by allowing water tanks to fill with water. This increases its weight which makes it sink in the water. • To gain buoyancy the water can be pushed out of the tanks using compressed air, this decreases the weight of the submarine. • Balloons/ Airships • Are submerged in a fluid, air. This means there is a force acting upwards on the balloon/ airship equal to the weight of the air which has been displaced. This buoyancy allows balloons and airships to float as long as the upthrust is greater than their weight. Summary video on pressure, density and floating • https://www.youtube.com/watch?v=Cvp6mLWbgaM Worked Example • Example 2 • A hydrogen balloon has a total mass of 40 kg and a volume of 40 m^3. If the surrounding air has a density of 1.225 kg m^-3, how large is upwards force acting on the balloon? • Find the mass of air displaced: • • Mass = density * volume 49 kg = 1.225 kg m^-3 * 40 m^3 Weight of air displaced = mass * gravity 49 kg * 10 = 490 N Weight of balloon = 40 * 10 = 400 N • Resolve the vectors • Upwards force = upthrust – weight • 90 N = 490 N – 400 N
