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Question 18N.3.HL.TZ0.10

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Date November 2018 Marks available [Maximum mark: 6] Reference code 18N.3.HL.TZ0.10
Level HL Paper 3 Time zone TZ0
Command term Calculate, Outline, Suggest Question number 10 Adapted from N/A
10.
[Maximum mark: 6]
18N.3.HL.TZ0.10
(a)

An ice cube floats in water that is contained in a tube.

The ice cube melts.

Suggest what happens to the level of the water in the tube.

[2]

Markscheme

ice displaces its own weight of water / OWTTE

OR

melted ice volume equals original volume displaced / OWTTE ✔

 

no change will take place ✔

A horizontal pipe is inserted into the cylindrical tube so that its centre is at a depth of 5.0 m from the surface of the water. The diameter D of the pipe is half that of the tube.

When the pipe is opened, water exits the pipe with speed u and the surface of the water in the tube moves downwards with speed v.

(b.i)

Outline why u = 4v.

[2]

Markscheme

continuity equation says v × A1 = u × A2 ✔

«and» A1 = 4A2 ✔

«giving result»

(b.ii)

The density of water is 1000 kg m–3. Calculate u.

[2]

Markscheme

Bernoulli:

« 1 2 ρ v 2 + ρ g H + P atm = 1 2 ρ u 2 + 0 + P atm » gives  1 2 × 1000 × u 2 16 + 1000 × 9.8 × 5.0 = 1 2 × 1000 × u 2  ✔

u = 10.2 «m s–1» ✔

 

Accept solving directly via conservation of energy.

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