Below are some links and documents for the Researching Physics dealing with measurement of the acceleration due to gravity.
http://practicalphysics.org/measurement-g-using-electronic-timer.html
http://www.practicalphysics.org/acceleration-due-gravity.html
https://revisionworld.com/a2-level-level-revision/physics/fields-0/gravitational-fields-0
The information below is based on the material found from the website above. TBC!
Fields
A field is a region of space where forces are exerted on objects with certain properties. Three types of field are considered:
- gravitational fields affect anything that has mass
- electric fields affect anything that has charge
- magnetic fields affect permanent magnets and electric currents.
These three types of field have many similar properties and some important differences. There are key definitions and concepts that are common to all three types of field.
Gravitational fields
Newton realised that all objects with mass attract each other. This seems surprising, since any two objects placed close together on a desktop do not immediately move together according to Newton’s second law F=ma. The attractive force between them is tiny, and very much smaller than the frictional forces that oppose their motion.
Gravitational attractive forces between two objects only affect their motion when at least one of the objects is very massive. This explains why we are aware of the force that attracts us and other objects towards the Earth – the Earth is very massive. The mass of the Earth is about 6 × 1024 kg.
The diagram represents the Earth’s gravitational field.
The lines show the direction of the force that acts on a mass that is within the field.
This diagram shows that:
- gravitational forces are always attractive – the Earth cannot repel any objects
- the Earth’s gravitational pull acts towards the centre of the Earth
- the Earth’s gravitational field is radial; the field lines become less concentrated with increasing distance from the Earth.
The force exerted on an object in a gravitational field depends on its position. The less concentrated the field lines, the smaller the force. If the gravitational field strength at any point is known, then the size of the force can be calculated.
The gravitational field strength, g, at any point in a gravitational field is the force per unit mass at that point
g=F/m
Close to the Earth g has the value of 9.8 Nkg-1
Gravitational field strength is a vector quantity, its direction is towards the object that causes the field.
Universal gravitation
Newton concluded, during his work, that the gravitational attractive force that exists between any two masses:
- is proportional to each of the masses
- is inversely proportional to the square of their distances apart.
Newton’s law of gravitation describes the gravitational force between two points. It can be written as
F=(GMm)/r2
Where
G is the universal gravitational constant and is equal to 6.67 × 10-11 N m2 kg-2 . M and m are the magnitude of the masses and r is the separation between the centre of the masses.
A point mass is one that has a radial field, like the Earth as shown in the diagram above.
Although the Earth is a large object, on the scale of the Universe it can be considered to be a point mass. The gravitational field strength at its centre is zero, since attractive forces pull equally in all directions. Beyond the surface of the Earth, the gravitational force on an object decreases with increasing distance. When the distance is measured from the centre of the Earth, the size of the force follows an inverse square law; doubling the distance from the centre of the Earth decreases the force to one quarter of the original value. The two objects attract each other with equal sized forces and act in opposite directions. The variation of g with distance from the surface of the Earth is shown in the diagram.
g and G
Newton’s law of gravitation can be used to work out the value of the force between any two objects. It can also be used to calculate the strength of the gravitational field due to a spherical mass such as the Earth or the Sun.
F=(GMm)/r2
As the value of F is also the weight then we can equate these two quantities, so that g not only equals W/m but also g=(GM)/r2 as below
Gravitational field strength is a property of any point in a field. It can be given a value whether or not a mass is placed at that point. Like gravitational force, beyond the surface of the Earth the value of g follows an inverse square law.
Because the inverse square law applies to values of g when the distance is measured from the centre of the Earth, there is little change in its value close to the Earth’s surface. Even when flying in an aircraft at a height of 10 000 m, the change in distance from the centre of the Earth is minimal, so there is no noticeable change in g. The radius of the Earth is about 6.4 × 106 m, so you would have to go much higher than aircraft-flying height for g to change by 1%.
The same symbol g is used to represent:
- gravitational field strength
- free-fall acceleration.
These are not two separate quantities, but two different names for the same quantity. Gravitational field strength, g, is defined as the force per unit mass, g = F/m.
From Newton’s second law and the definition of the newton, free-fall acceleration, g, is also equal to the gravitational force per unit mass. The units of gravitational field strength, N kg–1, and free-fall acceleration, m s–2, are also equivalent.
