Understanding Physics Topics is essential for solving complex problems in many fields, including engineering and medicine.

## Differences and Relation between Thurst and Pressure

If we push hard on a piece of wood with our thumb, the thumb does not go into the wood [see Figure]. But if we push a drawing pin into the wood with the same force of our thumb, the drawing pin goes into the wood [see Figure], These observations can be explained as follows :

Our thumb does not go into the wood because the force of thumb is falling on a large area of the wood due to which the ‘force per unit area’ (or pressure) on the wood is small. The drawing pin goes into the wood because due to the sharp tip of the drawing pin, the force of thumb is falling on a very small area of the wood due to which the ‘force per unit area’ (or pressure) on the wood becomes very large. It is clear from this example that pressure is the force acting on a unit area of the object (here wood). The force of thumb produces small pressure when it acts on a large area of wood but the same force of thumb’produces much greater pressure when it acts on a very small area of wood through the tip of drawing pin. Thus, the effect

of a force depends on the area of the object on which it acts.

Please note that the weight of a body is also a force. And it always acts in the downward direction.

We will now discuss the pressure exerted by a brick on the ground in two different positions—in the lying position and in the standing position.

In above Figure, two similar bricks (having the same weight) are placed in two different positions on the ground. The brick in Figure is in the lying position whereas the brick in Figure is in the standing position. The two bricks exert the same force on the ground because they have the same weight. But the two bricks exert different pressures on the ground because their areas in contact with the ground are different.

(i) The brick A is in the lying position so its area in contact with the ground is large [see Figure], S0, in this case the force of the weight of brick falls on a larger area of the ground and ‘the force per unit area’ (or pressure) on the ground is small (or less). Thus, the brick A in the lying position exerts smaller pressure on the ground.

(ii) The brick B is in the standing position so its area in contact with the ground is small [see Figure], In this case the force of the weight of brick falls on a smaller area of the ground, and ‘the force per unit area’ (or pressure) on the ground becomes large. Thus, the brick B in the standing position exerts a greater pressure on the ground.

From the above discussion we conclude that the pressure depends on two factors :

- Force applied, and
- Area over which force acts.

The same force can produce different pressures depending on the area over which it acts. For example, when a force acts over a large area of an object, it produces a small pressure. But if the same force acts over a small area of the object, it produces a large pressure.

We can now define pressure as follows : Pressure is the force acting perpendicularly on a unit area of the object. To obtain the value of pressure, we should divide the force acting on an object by the area of the object on which it acts. So, the formula for calculating pressure is :

Pressure = \(\frac{\text { Force }}{\text { Area }}\)

This formula gives the relation between pressure, force and area. We will now give the units in which pressure is measured. The SI unit of measuring force is newton (N), and the SI unit of measuring area is ‘square metre’ (m^{2}), therefore, the SI unit of measuring pressure is ‘newtons per square metre’ (N/m^{2} or N m^{-2}) which is also called pascal (Pa). Thus,

1 pascal = 1 newton per square metre

or 1 Pa = 1 N/m^{2}

In the above formula for pressure, if we put the value of force in newtons (N) and the value of area in square metres (m^{2}), then we will get the value of pressure in newtons per square metre (N/m^{2}) or pascals (Pa). Please note that whether we express the pressure in the units of N/m^{2} or Pa, it means the same thing.

We will now solve some numerical problems based on pressure.

**Example Problem 1.**

A force of 100 N is applied to an object of area 2 m^{2}. Calculate the pressure.

**Solution.**

Here, Force = 100 N

And, Area = 2 m^{2}

Now, putting these values in the formula :

Pressure = \(\frac{\text { Force }}{\text { Area }}\)

Pressure = \(\frac{100 \mathrm{~N}}{2 \mathrm{~m}^2}\)

= 50 N/m^{2} (or 50 Pa)

Thus, the pressure is 50 newtons per square metre or 50 pascals.

**Example Problem 2.**

A woman is wearing sharp-heeled shoes or pencil- heeled shoes (called stilettos). If the mass of this woman is 50 kg and the area of one heel is 1 cm^{2}, calculate the pressure exerted on the ground when the woman stands on just one heel, (g = 10 m/s^{2}).

**Solution.**

In this case the force will be the weight of woman which is given by m × g (where m is the mass of woman and g is the acceleration due to gravity). So,

Force = m × g

(Weight of woman) = 50 × 10 N

= 500 N

And Area = 1 cm^{2}

= \(\frac{1}{10000}\) m^{2}

Now, Pressure = \(\frac{\text { Force }}{\text { Area }}\)

= \(\frac{500 \times 10000}{1}\)

= 5000,000 N/m^{2} (or 5000,000 Pa)

Thus, the pressure exerted by a 50 kg woman wearing sharp-heeled shoes and standing on only one heel of area 1 cm^{2} is 5000,000 Nm^{2} (which is a very, very large pressure).

**Example Problem 3.**

A rectangular wooden block has mass of 4 kg. The length, breadth and height of this wooden block are 50 cm, 25 cm and 10 cm, respectively. Find the pressure on the table top :

(a) when the wooden block is kept with its surface measuring 50 cm × 25 cm on the table.

(b) when the wooden block is kept with its surface measuring 25 cm × 10 cm on the table.

(Assume : Acceleration due to gravity, g = 10 m/s^{2})

**Solution.**

Here, Mass of wooden block, m = 4 kg

Acceleration due to gravity, g = 10 m/s^{2}

So, Weight of wooden block, W = m × g

= 4 × 10 = 40 N

Since weight is a force, so we can say that the force exerted by the wooden block on the table top is 40 N. We will now calculate the pressure in the two cases.

(a) In the first case : Force = 40 N (Calculated above)

And, Area = 50 cm × 25 cm

= \(\frac{50}{100}\)m × \(\frac{25}{100}\)m

= 0.5 m × 0.25 m

= 0.125 m^{2}

Now, Pressure = \(=\frac{\text { Force }}{\text { Area }}\)

= \(\frac{40}{0.125}\)

= 320 N m^{-2} (or 320 Pa)

Thus, the pressure exerted by the wooden block on table top when kept on its face measuring 50 cm × 25 cm is 320 N m^{2} or 320 pascals (see above Figure).

(b) In the second case : Force = 40 N (Same as above)

And, Area = 25 cm × 10 cm

= \(\frac{25}{100}\)m × \(\frac{10}{100}\)m

= 0.25 m × 0.1 m

= 0.025 m^{2}

Now, Pressure \(=\frac{\text { Force }}{\text { Area }}\)

= \(\frac{40}{0.025}\)

= 1600 N m^{-2} (or 1600 Pa)

Thus, the pressure exerted by the wooden block on table top when kept on its face measuring 25 cm × 10 cm is 1600 N m^{-2} or 1600 pascals (see Figure).

Please note that the SI unit of pressure is pascal whose symbol is Pa. Actually, pascal is a very small unit of pressure, so many times a bigger unit of pressure called ‘kilopascal’ (kPa) is used.

We have just defined pressure in terms of force. Pressure can also be defined in terms of ‘thrust’. The force acting on a body perpendicular to its surface is called thrust. Actually, thrust is the total force acting on the surface of a body. So, we can also define pressure as follows : Thrust per unit area is called pressure. That is :

Pressure \(=\frac{\text { Thrust }}{\text { Area }}\)

The unit of thrust is the same as that of force. That is, the SI unit of thrust is newton (N). Actually, for most of the purposes, the terms ‘force’ and ‘thrust’ are used in the same sense. So, we will be using the term ‘force’ in all our discussions. The students are, however, free to use the term ‘thrust.’

### Explanation of Some Everyday Observations on the Basis of Pressure

We have just studied that ‘pressure is the force per unit area’. This definition of pressure can be used to explain many observations of our daily life. An important point to be kept in mind in this regard is that the same force produces less pressure if it acts on a large area but it can produce high pressure if it acts on a small area.

1. Why School Bags have Wide Straps. A school bag has wide strap made of thick cloth (canvas) so that the weight of bag may fall over a large area of the shoulder of the child producing less pressure on the

shoulder. And due to less pressure, it is more comfortable to carry the heavy school bag. On the other

hand, if the school bag has a strap made of thin string, then the weight of school bag will fall over a small area of the shoulder. This will produce a large pressure on the shoulder of the child and it will become very painful to carry the heavy school bag.

2. Why a Sharp Knife Cuts Better than a Blunt Knife. A sharp knife has a very thin edge to its blade.

A sharp knife cuts objects (like vegetables) better because due to its very thin edge, the force of our hand falls over a very small area of the object producing a large pressure. And this large pressure cuts the object easily. On the other hand, a blunt knife has a thicker edge. A blunt knife does not cut an object easily because due to its thicker edge, the force of our hand falls over a larger area of the object and produces lesser pressure. This lesser pressure cuts the object with difficulty.

3. Why the Tip of a Needle is Sharp. The tip of a sewing needle is sharp so that due to its sharp tip, the needle may put the force on a very small area of the cloth, producing a large pressure sufficient to pierce the cloth being stitched. A nail has a pointed tip, so that when it is hammered, the force of hammer falls on a very small area of wood (or wall) creating a large pressure which pushes the nail into wood (or wall).

4. Why the Pressure on Ground is More when a Man is Walking than when He is Standing. When a

man is walking, then at one time only his one foot is on the ground. Due to this, the force of weight of man falls on a smaller area of the ground and produces more pressure on the ground. On the other hand, when the man is standing, then both his feet are on the ground. Due to this the force of weight of the man falls on a larger area of the ground and produces lesser pressure on the ground.

5. Why the Depression is Much More when a Man Stands on the Cushion than when He lies Down on it. When a man stands on a cushion then only his two feet (having small area) are in contact with the cushion. Due to this the weight of man falls on a small area of the cushion producing a large pressure. This large pressure causes a big depression in the cushion. On the other hand, when the same man is lying on the cushion, then his whole body (having large area) is in contact with the g cushion. In this case the weight of man falls on a much larger area of the cushion producing much smaller pressure. And this smaller pressure produces a very little depression in the cushion.

The tractors have broad tyres so that there is less pressure on the ground and the tyres do not sink into comparatively soft ground in the fields. A wide steel belt is provided over the wheels of army tanks so that they exert less pressure on the ground and do not sink into it. Wooden sleepers (or concrete sleepers) are kept below the railway line so that there is less pressure of the train on the ground and railway line may not sink into the ground. The snow shoes have large, flat soles so that there is less pressure on the soft snow and stop the wearer from sinking into it.

It is easier to walk on soft sand if we have flat shoes rather than shoes with sharp heels (or pencil heels). This is because a flat shoe has a greater area in contact with the soft sand due to which there is less pressure on the soft sand. Due to this the flat shoes do not sink much in soft sand and it is easy to walk on it. On the other hand, a sharp heel has a small area in contact with the soft sand and so exerts a greater pressure on the soft sand. Due to this greater pressure, the sharp heels tend to sink deep into soft sand making it difficult for the wearer to walk on soft sand.

From the above discussion we conclude that in some everyday situations, the effect of force has to be increased whereas in other situations, the effect of force has to be decreased. For example, the effect of force is increased in tools like knives, axes, nails and pins, etc., by decreasing the area on which the force acts (so that the pressure is more). On the other hand, the effect of force is decreased in laying the foundations of buildings and dams by increasing the area on which the force acts (so that the pressure is less). For example, the foundations of buildings and dams are laid on a larger area of ground so that the weight of the building or dam (to be constructed) produces less pressure on ground (and the building or dam may not sink into the ground).