Mass and weight

Understanding the difference between mass and weight, and how gravity affects objects, is essential in physics. This section will explain the concepts of mass, weight, and gravitational field strength, and how they are related to each other.

Mass

• Mass is a measure of the quantity of matter in an object. 

• It is a scalar quantity, which means it has only magnitude and no direction.

• Mass is measured in kilograms (kg), and it is the same regardless of an object's location. 

  • This means an object's mass is constant whether it is on Earth, the Moon, or anywhere else in the universe.

Weight

• Weight is the gravitational force exerted on an object that has mass. 

• Unlike mass, weight depends on the gravitational field strength at the object's location.

• Weight is a vector quantity, which means it has both magnitude and direction. 

• It always acts towards the center of the gravitational field, which, in most cases, is the center of a planet like Earth.

• The weight of an object is measured in newtons (N).

Gravitational field strength

• The gravitational field strength (g) is defined as the force per unit mass exerted by gravity. It tells us how strong the gravitational field is at a particular location.

• The formula for gravitational field strength is:

• Where:

  • g is the gravitational field strength (in newtons per kilogram, N/kg).

  • W is the weight (in newtons, N).

  • m is the mass (in kilograms, kg).

• On the surface of the Earth, g is approximately 9.8 N/kg, which means that each kilogram of mass experiences a force of 9.8 N due to gravity.

• This value of g is also equivalent to the acceleration of free fall for an object near the Earth's surface, meaning that objects in free fall accelerate at 9.8 m/s².

Measuring weight and mass

• The weight and mass of objects can be compared using a balance. 

• A balance measures mass by comparing an object to known standard masses. Since weight is proportional to mass, balances can also provide an indication of weight if used in a consistent gravitational field.

• On Earth, where g is constant, weight is often used interchangeably with mass in everyday language. However, it is important to understand that they are not the same thing scientifically.

The effect of gravitational field on mass

• Weight is caused by the gravitational pull of a massive object, like a planet, acting on an object's mass. The gravitational field strength determines how much an object will weigh.

• For example:

  • On Earth, the gravitational field strength is 9.8 N/kg, so an object with a mass of 10 kg has a weight of: