11–8 Consider a heavy car submerged in water in a lake with a flat bottom. The driver’s side door of the car is 1.1 m high and 0.9 m wide, and the top edge of the door is 10 m below the water surface. Determine the net force acting on the door (normal to its surface) and the location of the pressure center if (a) the car is well-sealed and it contains air at atmospheric pressure and (b) the car is filled with water.

Respuesta :

Answer:

Explanation:

position of centre of mass of door from surface of water

= 10 + 1.1 / 2

= 10.55 m

Pressure on centre of mass

atmospheric pressure + pressure due to water column

10 ⁵ + hdg

= 10⁵ + 10.55 x 1000 x 9.8

= 2.0339 x 10⁵ Pa

the net force acting on the door (normal to its surface)

= pressure at the centre x area of the door

= .9 x 1.1 x 2.0339 x 10⁵

= 2.01356 x 10⁵ N

pressure centre will be at 10.55 m below the surface.

When the car is filled with air or  it is filled with water , in both the cases pressure centre will lie at the centre of the car .

The net force acting on the door (normal to its surface) and the location of the pressure should be  [tex]2.01356 \times 10^5 N[/tex]

Calculation of net force & pressure location:

The position of center of mass of door from the surface of water should be

[tex]= 10 + 1.1 \div 2[/tex]

= 10.55 m

Now

Pressure on center of mass

= atmospheric pressure + pressure due to water column

[tex]= 10^5 + 10.55 \times 1000 \times 9.8\\\\= 2.0339 \times 10^5 Pa[/tex]

Now

the net force acting on the door (normal to its surface)

[tex]= .9 \times 1.1 \times 2.0339 \times 10^5\\\\= 2.01356 \times 10^5 N[/tex]

So,

pressure centre will be at 10.55 m below the surface.

Therefore,

When the car is filled with air or  it is filled with water , in both the cases pressure center should be lie at the centre of the car .

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