FORCES 2. Mass and the effect of gravity on it - weight
calculations and various phenomena explained, plus work done and GPE
Doc Brown's Physics Revision Notes
Suitable for GCSE/IGCSE Physics/Science courses or their equivalent
This page will answer questions such as ...
What is weight and how do we calculate it?
What is the difference between mass and weight?
Why does gravity vary from planet to planet?
Why can a feather and iron bar fall at the same rate in a vacuum?
Introduction to gravity
A gravitational attractive forces acts between all objects of any mass, no matter how close or far apart they are.
Gravity is universal and its force exists wherever there is mass.
You experience gravity it as you jump up vertically against it's force and are then pulled back down to earth by the same force.
Gravity makes everything fall towards the surface of an object e.g. like a planet, and it is gravity that gives everything 'weight' (explained below).
The force of gravitational attraction between two masses increases by two factors:
What is mass? What is weight and how do you calculate it?
Mass is the amount of matter in an object (all the atoms added together) and is constant unless you change the object in someway to remove atoms or add atoms.
One consequence of gravity is that you experience weight.
You should appreciate immediately that your mass is constant at a given instance in time wherever you are in the universe, but the same cannot be said for weight.
So what is weight? Why can it vary for a given mass?
Quite simply, weight is the force of gravity acting on an object of given mass. Weight is in effect the 'pulling' force an object experiences in a gravitational field e.g. you experience the Earth's gravitational field as your weight even if it says kg on your bathroom scales!
The formula to calculate this force, that is to calculate the weight of an object, is quite simple.
On the surface of planet Earth the force of gravity on objects is 9.8 N/kg (the Earth's 'g' value'), so a mass of 1 kilogram experiences an attractive force of about 10 newtons. However, on the surface of the moon, the gravitational field force is only 1.6 N/kg (the moon's 'g' value'), so 1 kg on the moon only experiences a force of 1.6 N. On the moon you would feel much lighter and could leap around with your Earth designed muscles to much greater heights - you may have seen how the astronauts on the moon had to be careful to not overdo things!
Although you would seem 'lighter' on the moon, your mass will be still the same! Weighing machines like bathroom scales are calibrated to the strength of the Earth's gravitational field so the spring action scale can be read in kg. Bathroom scales, or any other scales, would give a very false reading on the moon!
You can measure weight using a calibrated spring balance force meter (newtonmeter).
Some simple example calculations:
Other aspects of weight and gravity phenomena
Why does a feather and a hammer fall at the same velocity in vacuum?
What is the centre of mass of an object? How can be determine it by experiment?
For an irregular shaped object like yourself its a bit more tricky!
You should find that all the lines intersect at point G, the centre of mass.
The method works because when the object hangs freely, there is equal mass (weight) on either side of the plumbline and this is independent of the pin point.
You can determine the centre of mass of a teachers by pinning them up by the tips of their ears, fingers or toes!
APPENDIX weight, work and gravitational potential energy
Two types of calculations follow on from the 'weight and gravity' notes above.
You may encounter either of them before or after studying 'weight and gravity', but they are closely related and follow on from the notes above.
If you allow a weight to fall it can do work, because a raised weight is an energy store of gravitational potential energy (GPE).
The general formula for work done (energy transferred) is:
work done in joules = acting resultant force in newtons x distance through which the force acts in metres
W (J) = F (N) x d (m)
You can then apply this equation to calculate the energy stored as GPE on raising a weight (mass x gravitational force) a given height. You therefore have also calculated the energy that can be released (ignoring friction) if the weight is allowed to fall.
The force (F) involved will be the weight of material raised or lowered
In general an object or material possesses gravitational potential energy by virtue of its higher position and can then fall or flow down to release the GPE e.g. winding up the weights on a clock, water stored behind a dam that can flow down through a turbine generator. Any object falling or material flowing downwards is converting GPE into kinetic energy and any object raised in height gains GPE.
Since gravitational energy is a form of stored energy, it does nothing until it is released and converted into another form of energy.
The amount of gravitational potential energy gained by an object raised above ground level can be calculated using the equation:
GPE = mass × gravitational field strength × height, Egpe = m g h
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