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Home > News > News Archive > Newton's Laws of Motion part one. The difference between weight and mass

Newton's Laws of Motion part one. The difference between weight and mass

Title page of 'Principia', first edition (1687)
 The title page of Newton's Principia, first edition (1687)

Newtons laws of motion come in pretty handy for engineers engaged in the business of moving things, and  in this article we're going to take a look at them and get back to first principles by getting to grips with the difference between mass and weight.

Newton described three laws of motion that form the basis of classical mechanics. The first states that every object remains in a state of rest or constant velocity unless acted upon by a force.

The second law states that a mass (m) acted upon by a force (F) will undergo acceleration (a) in the same direction as the force with a magnitude that is directly proportional to the force and inversely proportional to mass. Therefore F = ma.

The third law states that the forces of action and reaction are equal and opposite. When a body exerts a force (F) on another body, it in turn exerts a force (-F) on the actor. F and -F are equal in magnitude but opposite in direction.

And this is why a good understanding of the difference between mass and weight is essential for engineers doing calculations about moving stuff. Imagine if we were on a space ship in weightless orbit. Now imagine that one of your colleagues throws you a spanner. When you catch it you apply a force sufficient to decelerate it, but once it has stopped accelerating it will feel weightless, and that's because of the absence of another force – gravity.

Back here on earth, if the same colleague throws you a spanner you will have to use force to decelerate it, but then you'll need to use more force to hold it, because now gravity is acting upon it.

This force we call weight and is the result of acceleration caused by the force of gravity acting upon a mass. It is expressed in kg(m/s2) or newtons (N). Weight is incorrectly thought of in terms of kilograms because the kilogram is the SI unit of mass and the newton is the SI unit of force. When we 'weigh' something, the reading on the scale is the mass and the force in the spring is the weight.

When labels tell you that something is so many kilograms, the information is actually telling you the mass of the object, even if it says weight, as it often does.

So it's pretty important to know the difference between mass and weight, and whether to put g into an equation or take it out. Mass is an unchanging factor of a body, whereas weight varies in accordance with the gravitational field. If there's no gravitation then there's no weight, regardless of the mass of the body. However, as we have seen above, even without gravity a force will be required to stop a body that has been set in motion, but once it has been stopped it will feel weightless.

The SI unit of mass is the kilogram (kg), distance is the metre (m), time is the second (s) and force is the newton (N).

Weight is the vertical force generated by mass, and gravity is measured in newtons. 1N is the force of earth's gravity on a body with a mass of approximately 102g, such as an apple for instance. In engineering it is quite common to see forces expressed in kilonewtons (kN), where 1kN = 1,000N.

When we consider movement, physically in any way, the factors involved are the mass of the body and whatever acceleration is required to achieve the desired result. The acceleration is either horizontal, vertical or rotational. What we have to factor is the dimension and direction of the force required to move a body in the desired way, and force is mass times acceleration. The direction of movement determines whether g is involved or not. If the motion is frictionless and purely horizontal or rotational then g is not involved.

Sometimes it may seem as if Newton's laws are wrong. For instance, imagine a horizontal conveyor moving a large box of apples. Once the conveyor has reached the desired speed then Newton's first law states that the box will remain in motion until a force acts upon it to cause deceleration.

Wouldn't it be great if we could get in our cars, accelerate to 30 miles an hour (OK, some of you might want to go faster) and then switch the engine off! Imagine how much fuel we'd save! According to Newton's first law we could carry on driving without power from the engine until we reached a hill or applied the brakes.

The fact of the matter is that the conveyor does require constant power as, unfortunately, do our cars because there are forces at work all the time that are opposing motion. These forces include rolling resistance, friction and, particularly in the case of our cars, wind resistance.

Watch out for our next article in which we'll take a look at practical engineering, the forces involved, and the calculations required, to achieve linear or rotational acceleration of a body.