Question

The pressure on the tyres of a sedan car is P. The contact surface of each tyre with the floor is A. Find the new contact surface of each tyre when air is released from the tyre and the pressure of the car is reduced to 1.25P.

Answer 1

Hint: For the above problem we will define pressure as; a group of forces acting upon an area is called pressure.
$P = \dfrac{F}{A}$ (Force is F and A is the area)
For a car having four tyres area will become four times because the car has four tyres.
Using the above methodology we will find the new contact area of each tyre of the car.

Complete step by step solution:
Let’s discuss a few points about pressure first then we will proceed for the calculation part:
Pressure is the specific amount of force applied at right angles to the surface area of an object. The SI unit of pressure is pascal (Pa). Pressure is also described as the potential to work (for the quantity which is under pressure). When pressure is measured under water it is expressed in decibars. We have various other pressures like fluid pressure , pressure due to air, stagnation pressure( pressure required to stop the moving fluid), surface pressure and surface tension , pressure due to an ideal gas etc.
Now we will calculate the surface area of the contact of the tyre:
We have:
$ \Rightarrow F = P \times A$ (Pressure P and area A are given in the question)
$ \Rightarrow F = P \times 4A$(Area becomes 4 times because of four tyres)..................(1)
When pressure gets reduced to 1.25 P then equation becomes:
$ \Rightarrow F = 1.25P \times 4A'$ (Area A’ is the new surface area)..............(2)
On equating equation one and two
$
   \Rightarrow 1.25P \times 4A' = P \times 4A \\
   \Rightarrow A' = \dfrac{A}{{1.25}} \\
 $(Cancelling the common terms)
New surface area will be 0.8A.

Note: We will have many other applications where pressure has different effects for example a sharp knife cuts easily while blunt knife take much force in cutting, when we stand on our feet pressure is more than we lay down, sharp needle is easily able to pierce the skin rather than a dull needle, camel can easily walk on sand than human beings because area of feet of camel is larger than human being.