Mechanics: Weight

Definition of Weight in Mechanics

Under the influence of gravity, all objects possess a downward force that is directly proportional to their mass, this force is referred to as Weight.
It is important to differentiate between mass and weight: mass is a constant, defining the quantity of matter in a body, whilst weight is a force resulting from the effect of gravity on this mass.
It should be noted that weight is a vector quantity, meaning it has both magnitude and direction. In most common scenarios, the direction of the weight force is downwards towards the centre of the Earth.

Weight (W) can be expressed by the formula: W = m⋅g, where ‘m’ is the mass of the object and ‘g’ is the acceleration due to gravity.
The acceleration due to gravity (g) is approximately 9.81 m/s² on the surface of the Earth, but this value changes depending on the location in universe. For example, it is less on the Moon.

Since weight is mass acted on by acceleration due to gravity, the weight of an object will vary depending on where in the universe it is. This introduces the concept of weightlessness, such as that experienced by astronauts in space where acceleration due to gravity is almost zero.

The effect of weight is often seen in mechanics problems, such as those involving inclined planes, where the weight of the object is a crucial factor impacting its motion.
The weight force acts vertically downwards, but when dealing with inclined planes, it is often more useful to consider its components parallel and perpendicular to the plane. These components can be calculated using trigonometry if the angle of inclination is known.

When calculating weight, be aware of your units. If mass is given in kilograms and gravity in m/s², weight will be in Newtons (N).
Always ensure your inputs and outputs are in the correct SI units unless the question specifies otherwise.