Y11 Physics Induction Upthrust

Formulae & Terminology Density, ρ = m V Pressure, p = F A , for solids, liquids & gases Pressure in a liquid, p = hρg Weight of an object, W = mg Normal Contact Force Fluid Upthrust Archimedes’ Principle

AS Physics: Course Expectations High level of mathematical content You need to THINK! You must be ORGANISED & able to work independently. OCR syllabus A 50% Paper 1 (Breadth in Physics, 70 marks, 1½ hours) 50% Paper 1 (Depth in Physics, 70 marks, 1½ hours) + Practical Skills assessed throughout course – pass or fail

Density (g/cm3) = Mass (g) / Volume (cm3) Plasticene Take a blob of roughly 50g Find its mass Estimate or measure its volume Calculate density Density, ρ = m V Density (g/cm3) = Mass (g) / Volume (cm3)

Density (g/cm3) = Mass (g) / Volume (cm3) Plasticene Find its mass: (mine was 45.02g) Estimate or measure its volume: (Roughly cuboid - 2.7cm x 2.8cm x 3.0cm) = 22.7cm3 (Could have used a displacement can) Calculate density: 45g / 22.7cm3 = 2.0g/cm3 Density (g/cm3) = Mass (g) / Volume (cm3)

Does Plasticene Float? Density of water = 997.04 kg/m3 What is this in g/m3 to 2 decimal places? What is this in g/cm3 to 2 decimal places? Why does the plasticine sink?

Does Plasticene Float? Density of water = 997.04kg/m3 What is this in g/cm3 to 2 decimal places? 997.04kg/m3 = 997.04 x 1000 g/m3 = 997,040g/m3 997,040g/m3 = 997,040 / (100 x 100 x 100) g/cm3 = 0.99704 g/cm3 = 1.00 g/cm3 to 2 d.p. Why does the plasticine sink? 2g/cm3 > 1g/cm3

Weight (N) = mass (kg) x gravitational field strength (N/kg) Make a boat! Calculate the weight of the boat in N Weight (N) = mass (kg) x gravitational field strength (N/kg) [G.F.S. on Earth is 9.81N/kg] Draw a labelled force diagram when it is sitting on the desk. Are the forces balanced? How?

Weight (N) = mass (kg) x gravitational field strength (N/kg) Make a boat! Normal Contact Force Calculate the weight of the boat in N Weight (N) = mass (kg) x gravitational field strength (N/kg) Draw a force diagram when it is sitting on the desk. Are the forces balanced? How? Up and down forces balanced – no change in velocity, push from table (contact force) = weight Weight (N) = mass (kg) x 9.81N/kg = 0.045kg x 9.81N/kg = 0.44N Weight

Does it float? What is pushing the boat up now to counteract its weight? Why is this different to the table? Make sure it floats and then estimate the volume of water displaced. ? Weight

Does it float? What is pushing the boat up now to counteract its weight? Why is this different to the table? Water is pushing with an ‘upthrust’ force but water is a fluid that can flow. That makes it harder to support as liquid will be pushed out of the way. What is the volume of water displaced? (7.0cm x 3.5cm x 2.0cm) = 49.0cm3 [Again , I did this by marking the boat and estimating the volume submerged but you could use a displacement can.] Upthrust Weight

Weight of fluid displaced What is the mass of the water displaced (pushed out of the way) by the boat? Density (g/cm3) = Mass (g) / Volume (cm3) So, Mass (g) = Density (g/cm3) x Volume (cm3) [Density of water = 997.04kg/m3 or about 1g/cm3] What is the weight of the water displaced (pushed out of the way) by the boat? Weight (N) = mass (kg) x gravitational field strength (N/kg) [G.F.S. on Earth is 9.81N/kg]

Weight of fluid displaced What is the mass of the water displaced (pushed out of the way) by the boat? Volume of water = 49cm3 = 0.000049m3 Mass of water = Density x volume = 997.04kg/m3 x 0.000049m3 = 0.049kg What is the weight of the water displaced (pushed out of the way) by the boat? Weight of water displaced = 0.049kg x 9.81N/kg = 0.48N This is about the same as the weight of the boat (0.44N). Considering the error in our measurements, it is (and should be) exactly the same!

Upthrust & Archimedes’ Principle The upthrust (N) is the force exerted upwards on an object in a fluid. We have found that this ‘upthrust’ is equal to the weight of the water displaced by the object. This is called Archimedes’ Principle.

How will upthrust vary with mass? Build a paper or plasticene boat that is roughly cuboid in shape and capable of holding at least 50g. Remove all mass and mark the water level on the outside of the boat as it floats. Estimate the volume of water displaced and use this to calculate the mass and then weight of water displaced. (This is equal to the upthrust). Now add one 10g mass and repeat. You need at least 5 readings. Keep going until the boat sinks. Good luck! Mass added to the boat (g) Depth of boat (cm) Volume of water displaced (cm3) Mass of water displaced (g) [as density of water =1g/cm3] Weight of water displaced = Upthrust (mN) [Mass x 9.81] 10

Sample Results – Paper Boat Area of the base of my boat was 17.5 cm2 (3.5cm x 5.0cm) Mass added to the boat (g) Depth of boat (cm) Volume of water displaced (cm3) Mass of water displaced (g) [as density of water =1g/cm3] Weight of water displaced = Upthrust (mN) [Mass x 9.81] 0.2 3.5 34.3 10 0.5 8.75 85.8 20 0.7 12.25 120.1 30 1.0 17.5 171.7 40 1.3 22.75 223.2 50 1.7 29.75 291.8 60 2.2 38.5 377.7 70 2.7 47.25 463.5

Sample Results – Plasticene Boat Area of the base of my boat was 20.25 cm2 (4.5cm x 4.5cm) Mass added to the boat (g) Depth of boat (cm) Volume of water displaced (cm3) Mass of water displaced (g) [as density of water =1g/cm3] Weight of water displaced = Upthrust (mN) [Mass x 9.81] 1.6 32.4 317.8 10 2.2 44.55 437.0 20 2.6 52.65 516.5 30 3.0 60.75 596.0 40 3.5 70.88 695.3

Induction task – Part 1 (Graph) Use your results to plot a graph of upthrust in (milli)Newtons (on the y axis) against mass in grams (on the x axis) and draw a line of best fit. State & explain the relationship shown. Explain why your graph does not go through the origin. Sketch a graph to show what a graph of Upthrust (mN) against total mass of the boat (g) would look like. How well do your points fit the line of best fit? What were the main sources of uncertainty in the practical that may have caused any scatter?

Induction task – Part 2 (Research) Research Archimedes’ Principle & create a powerpoint presentation with the following slides. (Be ready to present it to the rest of the class.) Slide 1: what is upthrust? Slide 2: what is Archimedes’ Principle? Slide 3: information about Archimedes himself Slide 4: using p = F A , ρ = m V & W = mg, show that the pressure in a liquid can be given by the formula p = hρg Slide 5: use p = hρg to prove Archimedes’ Principle