NEWTON'S SECOND LAW OF MOTION

1. Momentum

Momentum is defined as the mass of an object multiplied by its velocity. It is a vector quantity having the same direction as the velocity.

Momentum is given the symbol p, and has units kg·m·s-1 (or N·s as will be shown next).

2. Newton's second law of motion

Newton's Second Law of Motion
"The rate of change of momentum of a body is proportional to the net force applied to that body and in the direction of the force."

Alternatively:

Newton's Second Law of Motion
"When a resultant force is applied to a body it produces an acceleration that is directly proportional to the resultant force and inversely proportional to the mass of the body."

The second law enables one to calculate the magnitude of the resultant force either by measuring the rate of change in momentum of the object to which the force is applied or by measuring the mass and acceleration of the object.

Thus, from the second law, the average resultant force F


Units of force are chosen such that k = 1. The S.I. unit of force is the NEWTON, (N), which is the force which accelerates a mass of 1 kg at 1 m·s-2.

In a practical situation, the initial velocity, vi, the velocity, vf, after a time interval, Δt, and the mass, m, of the body are often known. Thus the average resultant force can be calculated using

3. Impulse

In some instances the duration of the force is not known. In such cases the IMPULSE, which is the product of a force and the time interval, Δt, during which it is applied, FΔt, may be calculated from the change in momentum:

Generally, the impulse is directly proportional to the applied force AND the time during which the force is applied. The units of impulse are N·s, i.e. the same as those for momentum, that is, N·s or kg·m·s-1. From the formula shown above, we can deduce that:

4. Inertial mass

The property of a body which determines its acceleration in response to a given force is its INERTIAL MASS, m, defined by

The unit of mass, the KILOGRAM, kg, is the mass of a certain block of platinum-iridium alloy known as the INTERNATIONAL PROTOTYPE KILOGRAM which is carefully preserved at the International Bureau for Weights and Measures at Sèvres, France.(Click here for more information on inertial mass.)

5. Weight

When a body is released near the surface of the earth, it falls towards the ground with an acceleration which is approximately 9.8 m·s-2.

This acceleration due to gravity, denoted g, is due to a force which has a magnitude mg and which is directed towards the centre of the earth, acting on the body, where m is the mass of the body.

This force is called the WEIGHT of the body, w:

The difference between weight and mass was discussed more fully in Grade 10 .

6. Additional questions


More information on inertial mass

The second law also gives us an insight into the concept of mass. In particular, masses can only be measured relative to other masses - there is no absolute scale of mass.

Imagine that we have two trolleys, of masses ma and mb, on a frictionless track coupled in such a way that a spring located between them is compressed:

When the coupling is broken the spring, will expand and both trolleys will receive oppositely directed impulses of equal magnitude which last until they separate. After separation, they will continue with constant velocities in opposite directions:

Because the trolleys received equal but oppositely directed impulses, their changes in momentum must also be equal but oppositely directed.

The International Prototype Kilogram

Thus by measuring the velocities va and vb it is possible to determine mb if ma is known. It is therefore necessary to define a particular object as having unit mass. This is why there exists an internationally agreed prototype kilogram.