Second Newton Law. Concepts and Illustrative Exercises

Newton's Second Law can be summarized as follows: If F represents the net force applied to an object of mass m, then its acceleration has the same direction as the net force and its magnitude is proportional to the quotient F/m, i.e.

a represents the acceleration, m the mass and F the net force. By net force it is understood the resultant vector sum of all the forces acting on the body.

Let's see Newton's Second Law concepts of Mass, Inertia, Acceleration and Force and an access to exercises on this Law.

Definition of Mass, Inertia.

What is mass? Newton himself used the term mass as synonym of quantity of matter. This idea used by Newton is not very precise. With more precision we can say that the mass is a measure of the inertia of a body. The greater the mass of a body the harder is to change its state of movement. It is hard to get moving starting from rest, or to stop while moving, or to get moving to a side from a rectilinear trajectory. A truck has much more inertia than a tennis ball moving at the same speed, being very much harder to change the state of movement of the truck.

To measure the concept of mass a standard should be defined. In the International System Units, the mass unit is the kilogram. The present standard is a cylinder made of platinum conserved in the International Bureau of Weights and Measures near Paris, whose mass, by definition, is exactly equal to one kilogram. In cgs units, the mass unit is the gram (g) and 1g = 10-3 kg. In the English System, the unit of mass is called the Slug.

Mass should not be confused with weight. The mass is a property of a body, is a measure of its inertia or its quantity of matter. The weight is a force, the force that the Earth exerts on the body. To clarify the difference, suppose we take an object to the Moon. There it will weight a sixth of its weight on Earth, but its mass will remain the same.

Acceleration, Net Force

The First Newton Law states that in absence of a net force on a body, this body remains at rest, or if it is moving, continues moving with constant velocity (keeping magnitude and direction). But, ¿what happens if a force acts over a body? The velocity must change, that is, a net force produces an acceleration.

The relation between acceleration and force can be found in daily experiences. Let us think pulling a supermarket cart. The net force exerted on the cart is the force that I apply minus the friction force on the wheels. If the net force is F, the acceleration will be a, if the force is 2F, la acceleration will be 2a, and so on. Hence, the acceleration of a body is directly proportional to the net force applied. The acceleration depends also on the mass of the object. If I keep the net force F and the total mass is doubled, the acceleration will be a/2.

Then, we can affirm that

The unit of force is chosen in such a way that the constant of proportionality in , be 1, and so,

a = F/m

Notice that with this second law we can state a more precise definition of force: as an action able to accelerate an object.

When the mass is in kilograms and the acceleration in meters per second squared, la force unit is called Newton (N), 1 N = 1kgm/s2.

In the English System, the force unit is the pound. It is defined as the weight (a force) of a body whose mass is 0.45359237 kg on some place on the Earth where the acceleration of gravity is 32.1734 feet/s2.

Exercises, Newton's Second Law:
Second Newton's Law Exercises, Part One
Second Newton's Law Exercises, Part Two

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