Evan's Space

Wonders of Physics


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Manometer – mercury levels difference changes with different density of liquid used

The pressure of a gas is measured using a manometer as shown in the diagram.

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The mercury in the manometer is replaced with a liquid which is less dense. How does the value of h change?

A It becomes zero.

B It decreases, but not to zero.

C It stays the same.

D It increases.

Solutions: Option D

The pressure to be measured remains constant. Since P = pgh, where p is the density of the liquid used in the manometer. If a liquid of lower density is used, height h of the liquid (level difference) will be greater. The gravitational field strength g remains constant.


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2013 Nov Sci Phy P2 Q9 – Pressure and Moment

CaptureSolutions:

(a) (i) A bigger force than F can be obtained due to the level system and hydraulic system.
Level system: Applying principle of moments, the anticlockwise moment by the F is equal to the clockwise moment by the force on piston A (note that the handle is pushing the piston down, but the piston A is pushing on the handle upwards – action = reaction). As the perpendicular distance from F to the pivot is greater than the perpendicular distance of the force by piston to the pivot, the force on the piston A is greater than F at handle.
Hydraulic system: As the pressure transmitted in the liquid is the same, pressure at piston A = pressure at piston B. As P = F/A and area of piston A is smaller than area of piston B, a larger force is obtained in piston B. 
Hence these two systems allow the force on piston B to be greater than F at the handle.

(a) (ii) Both liquid and gas molecules are in a continuously random motion. But in liquid, the molecules are closely packed together and able to slide around one another. There is very little empty space between the molecules hence liquid is not compressible. Gas molecules are far apart from one another, hence gas can be easily compressed.

(b) P = F/A = 12000 / 0.060 = 200 000 Pa

(c) Velocity is the vector quantity while speed is a scalar. As the car goes round the bend, the direction of the car changes. Hence velocity is changing even though speed is constant.

Likewise, as the velocity is changing, the car is considered to have an acceleration (not in the sense of increasing speed though).


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Liquid pressure – U-tube

A U-tube with 30 cm of water is set up vertically and 12 cm of olive oil is poured carefully into the left-hand limb of the tube as shown below. It is observed that water will be pushed up in the other limb. The density of water and olive oil are 1000 kg m-3 and 920 kg m-3 respectively.

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Given A is at same level as the boundary between olive oil and water.a) What is the length of water column above point A?b) A further 6 cm of olive oil is added into the left-hand limb. How much further will the water level rise in the right limb?

Solutions: View video tutorial for part (b)a)

 

Poil = Pwater above A

ρgh = ρgh920 x 10 x 12 = 1000 x 10 x h

h = 11.04 cm

 

b)                       Pressure of water = pressure of olive oil

1000 x 10 x (2x + 11.04)/100  = 920 x 10 x 18/100

x = 2.76 cm