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Suppose the door of a room makes an airtight but frictionless fit in its frame. Do you think you could open the door if the air pressure on one side were standard atmospheric pressure and the air pressure on the other side differed from standard by 1%? Explain.

Short Answer

Expert verified

One could open the door, but he will face some difficulty.

Step by step solution

01

Given information

The given information is listed below,

  • Standard atmospheric pressure is applied on one side of the door
  • The difference between the pressure on another side of the door is 1% .
02

Significance of Pascal’s law

At rest, a surface in a fluid obeys Pascal's law. For this surface and fluid to remain at rest, the fluid must exert forces of equal magnitude in opposite directions on both sides of the surface.

03

Determination of the force acting on the door

The pressure varies with weather changes and with elevation.

According to Pascal鈥檚 law, the force can be given by,

F=pA1

Here, pis the atmospheric pressure on the object at a point whose value is 1.01105Paand A1is the area of the surface.

Let the door has an area (A) of 1 square meter. The new area can be given as,

A1=1%A=1%1100%A=0.01A

Substitute all the values in the above equation. The force on the door can be calculated as,

F=1.01105Pa0.011m21N/m21PaF=1010N

This force is approximately equal to the weight of 1 large man (about 102 kg).

Thus, one could push and open the door but with some difficulty.

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