5.1.3 Gravity, weight and centre of mass

Weight and gravity

1. Weight is a force because gravity can pull on an object and change its motion or shape.
2. Close to the Earth, objects have weight because they sit in the Earth’s gravitational field.
3. A gravitational field is the region around a mass where another mass feels a force; near the Earth it pulls objects towards the centre of the Earth, which is why unsupported objects fall downwards.

Gravitational field strength

1. The weight of an object depends on the gravitational field strength at the point where the object is.
2. A larger $g$ means a stronger pull on each kilogram of mass, so the same object has a larger weight.
3. In any calculation the value of $g$ is given in the question, so you do not need to recall it.

Calculating weight

1. Weight is calculated with the equation $W=mg$.
   1. $W$ is weight in newtons ($N$).
   2. $m$ is mass in kilograms ($kg$).
   3. $g$ is gravitational field strength in newtons per kilogram ($N/kg$).
2. The equation shows that weight depends on both the object’s mass and the gravitational field strength.

Centre of mass

1. For many simple, regular objects the centre of mass is near the middle of the object.
2. On a force diagram, the weight arrow is drawn from the centre of mass, pointing vertically downwards, because weight acts towards the centre of the Earth.
3. This is a model: weight really acts on all parts of the object, but treating it as acting at one point makes diagrams and calculations simpler.

Weight and mass are directly proportional

1. Weight and mass are directly proportional, as long as the gravitational field strength is constant.
   1. If the mass doubles, the weight doubles.
   2. If the mass triples, the weight triples.
   3. If the mass is zero, the weight is zero.
2. The equation $W=mg$ shows this: if $g$ stays the same, $W$ changes in the same ratio as $m$.
3. A graph of weight against mass is a straight line through the origin; a steeper line means a larger gravitational field strength.

Measuring weight

1. Weight is measured using a calibrated spring-balance, also called a newtonmeter.
2. A newtonmeter contains a spring; when an object hangs from it, the object’s weight stretches the spring.
3. The scale is calibrated in newtons, so the weight can be read directly.
4. In a calculation, always give weight in newtons ($N$), not kilograms; kilograms are the unit of mass.