SITEMAP   School-college Physics Notes: Forces Section 2.2 Explaining mass and weight

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Forces 2: 2.2 Explaining what are mass and weight? - and how do you calculate weight?

Doc Brown's Physics exam study revision notes

2.2a What are mass and weight - how do you calculate weight?

This page will answer questions such as ... What is weight and how do we calculate it?  What is the difference between mass and weight?

Mass is the amount of matter in an object

That is all the atoms added together and is constant unless you change the object in someway to remove atoms or add atoms.

The standard unit of mass is the kilogram (kg), in chemistry or physics laboratory you often weigh things out as grams (1 g = 1 kg/1000). In chemistry calculations you tend to work in g, in physics calculations is often kg.

Mass is NOT the same as weight.

Mass is NOT a force, but the mass of an object is constant no matter where it is in the whole universe e.g.

you may be 40 kg here on Earth, in outer space, up in a satellite space station, on planet Mars or frozen on Pluto!

BUT your weight might be anything from 400 N on the Earth's surface, to zero in outer space - all will be explained!

One consequence of gravity is that you experience weight, which is always acts as a downward force due to a gravitational field effect and is always an attractive force.

Note :

Mass is a scalar measurement (just has size or magnitude).

Weight (or any force) is a vector measurement (it has both size and direction - always downwards for gravity).

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!

weight = a force in newtons

Weight varies with the mass of the object and the strength of the gravitational field at the point where the object is.

Weight is directly proportional to mass AND directly proportional to the gravitational field strength (gravitational acceleration) too. The formula to calculate this force, that is to calculate the weight of an object, is quite simple.

weight in newtons = mass of object in kilograms x gravitational field strength

W (N) = m (kg) x g (N/kg)

OR you may need to think in terms of:

force in newtons = mass of object in kilograms x gravitational acceleration

This expression is equivalent to F = ma, the equation of Newton's 2nd Law of Motion.

The general equation is easily rearranged:

W = m x g,    m = W ÷ g,    g = W ÷ m

(learn to rearrange, its better than using the triangle)

Notes:

(i) There are three are variables, W, m and g.

(ii) Weight is proportional to mass for a give g.

(iii) The gravitational field strength constant (g) varies from planet to planet because the mass of the planets varies.

On a massive planet like Jupiter, the gravitational field strength is much greater than that on Earth.

On a smaller planet or our Moon, with far less mass, the gravitational field strength is much less.

Examples of surface gravitational field strength constants:

which can be units of weight in N/kg, but also units of acceleration in m/s2

Our Moon 1.62, planets: Mercury 3.70, Earth 9.81, Jupiter 24.79. To put these objects in perspective, an extremely dense neutron star may have a gravitational acceleration of 7 x 1012 m/s2 and its even greater for a black hole. kapow !!!!

(iv) g also varies with the distance you are from the centre of a large body like a planet e.g. it decreases the further up you are from the Earth's surface e.g. on the top of a mountain.

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!

In travelling from the Earth to the Moon, you would seem to have lost a lot of weight!

Unless of course, you take Moon calibrated weighing scales!

You can measure weight using a calibrated spring balance, effectively a force meter or Newton meter.

Along side the spring is a scale calibrated in newtons, the unit of force.

You can use a balance that is calibrated in g/kg and multiply by 9.8 to get the weight of the object on the Earth's surface.

2.2b Some simple example weight calculations Note that it is better to be able to rearrange a formula than use a formula triangle

Q1 What is the weight of 70 kg adult on (a) the Earth, (b) the moon.

Using the gravitational field constants quoted above

On Earth the force of gravity on objects is 9.8 N/kg and  on the surface of the moon, the gravitational field force is only 1.6 N/kg

Q2 An astronaut on Mars found an object of mass 5.50 kg gave a reading on an electronic balance meter of 20.41 N. Calculate the strength of gravity on the surface of Mars.

Q3 The force of gravity on the dwarf (minor) planet Pluto is 0.710 N/kg.

What would be the mass of an object on Pluto that would experience a weight of 10.0 N?

Q4 Imagine an astronaut in a space station experiencing 'weightlessness'.

Suppose the astronaut pushes against the wall with a force of 30 N and moves backwards with an acceleration of 0.40 m/s2. What is the mass of the astronaut?

This is quite a trick problem to solve!

Keywords, phrases and learning objectives for forces

Know and be able to describe and explain the difference between mass and weight.

Know that mass is scalar quantity and weight is a vector quantity.

Know how to calculate weight and solve problems using the formula weight = mass x gravitational field constant g and use the correct units of newtons, kilograms and value of g

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Note that it is better to be able to rearrange a formula than use a formula triangle

Q1 What is the weight of 70 kg adult on (a) the Earth, (b) the moon.

Using the gravitational field constants quoted above

(a) W = m x gearth = 70 x 9.8 = 686 N

(b) W = m x gmoon = 70 x 1.6 = 112 N

Quite a difference!

Q2 An astronaut on Mars found an object of mass 5.50 kg gave a reading on an electronic balance meter of 20.41 N. Calculate the strength of gravity on the surface of Mars.

W = mg, so gmars = W/m = 20.41/5.50 = 3.71 N/kg

Note the value of the gravitational field strength is more than the moon (smaller mass) and not as large as on Earth (bigger mass). This is ignoring their different sizes and densities, its just a surface gravity comparison.

Q3 The force of gravity on the dwarf (minor) planet Pluto is 0.710 N/kg.

What would be the mass of an object on Pluto that would experience a weight of 10.0 N?

W = mg, so m = W/gpluto = 10/0.71 = 14.1 kg (3 sf)

Q4 Imagine an astronaut in a space station experiencing 'weightlessness'.

Suppose the astronaut pushes against the wall with a force of 30 N and moves backwards with an acceleration of 0.40 m/s2. What is the mass of the astronaut?

Here you have to think of the 'weight' equation as

force in newtons (N) = mass of object (kg) x acceleration (m/s2)

(of F = ma, if you have studied Newton's 2nd law of motion)

Substituting in the equation gives:

20 = mass x 0.40,  therefore mass of astronaut = 30 / 0.40 = 75 kg

Note that in this calculation, the acceleration does not have to be due to a gravitational field.

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