1. Y11 Physics Induction
Upthrust

2. 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

3. 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

4. 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)

5. 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)

6. 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?

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

8. 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?

9. 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

10. 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

11. 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

12. 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 = kg/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]

13. Weight of fluid displaced
What is the mass of the water displaced (pushed out of the way) by the boat?
Volume of water = 49cm3 = m3
Mass of water = Density x volume = kg/m3 x m3 = 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!

14. 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.

15. 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

16. 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

17. Sample Results – Plasticene Boat
Area of the base of my boat was 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

18. 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?

19. 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