Newton's second law is perhaps the most famous among the three laws of classical mechanics, which was postulated by an English scientist in the middle of the 17th century. Indeed, when solving problems in physics with the motion and equilibrium of bodies, everyone knows what the product of mass and acceleration mean. Let us consider in more detail the features of this law in this article.
Place of Newton's second law in classical mechanics
Classical mechanics is based on three pillars - the three laws of Isaac Newton. The first of them describes the behavior of a body if external forces do not act on it, the second describes this behavior when such forces arise, finally, the third law is the law of interaction of bodies. No wonder the second law holds a central place, since it connects the first and third postulates into a single and harmonious theory - classical mechanics.
Another important feature of the second law is that it offers a mathematical tool for the quantitative description of the interaction — this is the product of mass and acceleration. The first and third laws use the second law to obtain quantitative information about the process of action of forces.
Impulse of power
Further in the article, the formula of Newton’s second law will be presented, which appears in all modern physics textbooks. Nevertheless, initially the creator of this formula himself brought it in a slightly different form.
When postulating the second law, Newton was based on the first. It can be mathematically written in terms of the momentum p¯. It is equal to:
p¯ = m * v¯.
The momentum is a vector quantity that is associated with the inertial properties of the body. The latter are determined by the mass m, which in the above formula is a coefficient relating the velocity v¯ and the momentum p¯. Note that the last two characteristics are vector quantities. They are directed in the same direction.
What will happen if a certain external force F¯ begins to act on a body with a momentum p¯? That's right, the momentum will change by dp¯. Moreover, this value will be the greater in magnitude, the longer the force F¯ acts on the body. This experimentally established fact allows us to write the following equality:
F¯ * dt = dp¯.
This formula is Newton's 2nd law, presented by the scientist himself in his works. An important conclusion follows from it: the vector of change in the momentum is always directed in the same way as the vector of the force that caused this change. In this expression, the left side is called a momentum of force. This name has led to the fact that the magnitude of the momentum itself is often called an impulse.
Strength, Mass, and Acceleration
Now we get the generally accepted formula of the considered law of classical mechanics. To do this, substitute the quantity dp¯ in the expression in the previous paragraph and divide both sides of the equality by the time dt. We have:
F¯ * dt = m * dv¯ =>
F¯ = m * dv¯ / dt.
The time derivative of velocity is the linear acceleration a¯. Therefore, the last equality can be rewritten in the form:
F¯ = m * a¯.
Thus, the external force F¯ acting on the body under consideration leads to the appearance of linear acceleration a¯. Moreover, the vectors of these physical quantities are directed in one direction. This equality can be read the other way around: mass on acceleration is equal to the force acting on the body.
The solution of the problem
Let us show by the example of a physical problem how to use the considered law.
Falling down, the stone for every second increased its speed by 1.62 m / s. It is necessary to determine the force acting on the stone if its mass is 0.3 kg.
By definition, acceleration is the speed of a change in speed. In this case, its module is equal to:
a = v / t = 1.62 / 1 = 1.62 m / s 2 .
Since the product of mass and acceleration will give us the desired force, we get:
F = m * a = 0.3 * 1.62 = 0.486 N.
Note that the considered acceleration has all the bodies that fall on the moon near its surface. This means that the force we found corresponds to the force of lunar attraction.