# Which is heavier: 1 kg of lead or 1 kg of cotton?

Both 1 kg of lead and 1 kg of cotton have the same mass and, consequently, the same weight. However, the measurement on the scale shows otherwise.

**What are mass and weight?**

**Mass** is a physical quantity inherent in bodies – it measures the **amount ****of matter** contained in them. The unit of mass in the International System of Units is the kilogram (kg).

**Weight** is the **gravitational force of attraction** that two masses exert on each other. Bodies with large masses, such as planets and stars, have a large gravitational field and therefore attract other bodies around them with greater force. Two identical bodies on different planets will always have the same mass, but their weight may differ, depending on the value of local gravity .

The weight of a body of mass **m** , subjected to a gravitational acceleration **g** , can be calculated by the following equation:

Therefore, an object of mass **1 kg** in the Earth’s gravitational field, which is approximately **9.8 m/s²** , has a weight of **9.8 N:**

**Who is the heaviest?**

After all, if the weights of 1 kg of lead and cotton are the same, why can scales indicate that cotton is lighter?

This happens because the **scales do not directly measure the weight of bodies** , but the **reaction to compression** , called the **normal ****force** .

**If, when stepping** on the scale, someone leans on you, making a **downward ****force** , it will indicate a **greater ****mass** . However, the increase indicated by the balance is not related to an **increase ****in ****mass** , but to the increase in the **compression ****force applied ****to** it.

Similarly, when we place **1 kg of cotton** on a scale, it measures a smaller compressive force than that exerted by **1 kg of lead** . This is because all bodies that are inside a fluid such as **water** or **atmospheric ****air** are subject to a vertical force, which points upwards, called **buoyancy** .

The **buoyancy** arises on bodies that occupy space within a fluid as a result of the pressure difference (atmospheric or hydrostatic). Pressure, in turn, is closely related to height: **the greater the depth** , the **greater the influence of the pressure** exerted on the body – therefore, the **lower portions of a body suffer greater pressure** . If the resultant of the forces acting on the body points upward, it will float, just as bubbles of gas in a soda or a hot air balloon do.

Pressure on the lower parts of the body is greater than the pressure above, causing it to float

The **buoyancy** is a vector quantity that depends on the **density** of the fluid, the local **gravity** and the **volume** of displaced fluid, and can be calculated by the equation below:

The **resultant of the ****weight** and **buoyancy** forces is called the **apparent ****weight** . It is thanks to this net force that things **appear lighter** than they really are when they are in the water, for example. The **greater ****the volume** of the **body** , the **smaller** its **apparent weight** , which is precisely why **cotton will have ****a slightly smaller measurement** on the scale than lead. To have the **same mass** as **lead** , **cotton ****takes up a much larger volume .** , since its **density is low** . As a result, the **thrust** on it is much more significant than that exerted on **lead** .

**Calculating the buoyancy on cotton**

Let’s calculate the **apparent ****weight** of 1 kg of cotton, considering that: this cotton mass occupies a **volume** of **4.3 liters** ( 4.3 x 10 ^{-3} m³), the air density is approximately 1.29 kg/m³ and the local gravity is 9.8 m/s²:

As the apparent weight of 1 kg of cotton is 9.74 N, the balance would indicate a mass of 994.4 g of cotton.

Since it is **very dense** , lead occupies a **much smaller volume** – so the atmospheric buoyancy on it is almost negligible and hardly measured by conventional balances, which have low accuracy.