Keith Mack
Newton's second law of motion is one of three laws formulated by Isaac Newton in his work 'Philosophiæ Naturalis Principia Mathematica' (Mathematical Principles of Natural Philosophy), published in 1687. The second law of motion is quantitative and is used to calculate what happens in situations involving a force. Newton's second law can be expressed mathematically as F = ma, where F is the force, m is the mass of the object, and a is the acceleration of the body. This law explains how force can change the acceleration of an object and how the acceleration and mass of the same object are related.
| Characteristics | Values |
|---|---|
| Law Number | Second Law |
| Mathematical Expression | F = ma |
| Variables | F (force), m (mass), a (acceleration) |
| Force | Product of mass and acceleration |
| Acceleration | Directly proportional to force, inversely proportional to mass |
| Momentum | Mass x velocity |
| Velocity | Has magnitude and direction |
| Direction | Vector quantity |
| Application | Used to predict motion of an object experiencing a net force |
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What You'll Learn
Force equals mass times acceleration
Newton's second law of motion, unlike the first law, pertains to the behaviour of objects with unbalanced forces. It is more quantitative and is used to calculate what happens in situations involving a force. Newton's second law states that the acceleration of an object depends on two variables: the net force acting on the object and the mass of the object.
The law is often referred to as the law of force and acceleration. According to the law, force is equal to the mass of an object multiplied by its acceleration. This relationship can be expressed mathematically as F = ma, where F is force, m is mass, and a is acceleration. For example, if a force of 50 N (Newtons) is applied to an object with a mass of 10 kg (kilograms), the acceleration will be 5 m/s^2 (metres per second squared).
The second law also explains how force can change the acceleration of an object. As the force acting on an object is increased, the acceleration of the object increases, and as the mass of an object is increased, its acceleration decreases. This means that for two people walking, the heavier person will walk slower because the acceleration of the lighter person is greater.
In a car crash, the force of the impact depends on either the mass or the acceleration of the car. As the mass or acceleration of the car increases, the force of the crash will also increase. Similarly, in the case of a rocket, the greater the thrust (force), the greater the acceleration. However, the acceleration also depends on the rocket's mass, with lighter rockets accelerating faster.
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Acceleration is inversely proportional to mass
Newton's second law of motion, unlike the first law, pertains to the behaviour of objects with unbalanced forces. This law is more quantitative and is used extensively to calculate what happens in situations involving a force. Newton's second law states that the acceleration of an object depends on two variables: the net force acting on the object and the mass of the object.
The relationship between the motion of an object and the forces acting on it is described by Newton's second law:
$$\\vec F=m\\vec a$$
Where $\\vec F$ is the force acting on the object, m is the mass of the object and $\\vec a$ is the object's acceleration. This can also be written as:
$$\\vec a=\\frac{\\vec F}{m}$$
This means that if the same force is applied to two objects with different masses, the object with the smaller mass will have a greater acceleration. In other words, the more "stuff" there is in an object, the more difficult it is to accelerate it. So, as the mass of an object increases, its acceleration decreases, and vice versa.
For example, among two people walking, if one is heavier than the other, the heavier person will walk slower because the acceleration of the lighter person is greater. Similarly, in the case of a car crash, as the acceleration or mass of the car increases, the force with which the crash takes place will also increase.
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Force is the dot product of mass and acceleration
Newton's three laws of motion were first stated in his Philosophiæ Naturalis Principia Mathematica, originally published in 1687. Newton's second law of motion pertains to the behaviour of objects for which all existing forces are unbalanced. The second law is quantitative and is used to calculate what happens in situations involving a force.
Newton's second law of motion states that force is the product of mass and acceleration. When a force is applied to an object, it is termed thrust. The greater the thrust, the greater the acceleration. Acceleration is also dependent on the mass of the object, i.e., the lighter the object, the faster the acceleration.
The second law can be mathematically formulated as:
- F=m(v1-v0)/(t1-t0)
- F=ma
Where F is force, m is mass, a is acceleration, and v and t are velocity and time, respectively.
The above equations tell us that an object will accelerate if it is subjected to an external force. The amount of force is directly proportional to the acceleration and inversely proportional to the object's mass. Newton's second law can be used to identify the amount of force needed to make an object move or stop. For example, when we kick a ball, we exert force in a specific direction. The harder the ball is kicked, the more force is applied, and the further away it will travel.
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Force equals the rate of change of momentum
Newton's three laws of motion were first stated in his Philosophiæ Naturalis Principia Mathematica, published in 1687. The concepts invoked in Newton's laws of motion—mass, velocity, momentum, and force—were built upon by later scholars. Newton's work was unique in that he approached natural philosophy with mathematics in a novel way.
Newton's second law of motion states that force equals the rate of change of momentum. This means that the change in the momentum of an object is the product of the force acting on the object and the time for which that force acts. This relationship can be expressed mathematically as F = dp/dt.
Newton's second law can also be used to explain how force changes an object's acceleration and how acceleration and mass are related. Force is the product of mass and acceleration. Therefore, as the force acting on an object increases, so does its acceleration. Conversely, as the mass of an object increases, its acceleration decreases.
The relationship between force and momentum can be better understood by examining the quantity of momentum. For example, consider an object with an initial momentum of 20 kg⋅m/s that comes to rest due to an average force of 2.5 N. Using the quantity of momentum, we can determine the time interval that the force must act on to bring the object to rest.
It is important to note that only the net force, or the vector sum of all forces acting on an object, can be considered equal to the rate of change of momentum. In most applications, simple forces are considered, so force is simply the push or pull, and the rate of change of momentum is left out of the calculation.
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The relationship between force, mass, and acceleration
Newton's second law of motion is a quantitative description of the behaviour of objects for which all existing forces are unbalanced. The law states that the acceleration of an object depends on two variables: the net force acting on the object and the mass of the object.
For a constant mass, as the force acting upon an object is increased, the acceleration of the object is increased. Conversely, as the mass of an object is increased, the acceleration of the object is decreased. This relationship can be observed in a car crash, where the force of the impact depends on either the mass or the acceleration of the car. As the acceleration or mass of the car increases, the force of the crash will also increase.
Newton's second law can also be applied to understand the motion of a rocket. As a rocket burns fuel and exhausts it to propel itself, the mass of the rocket changes. As a result, the same propulsion force can lead to increasing acceleration values over time. This is because the acceleration of an object is inversely proportional to its mass. Therefore, as the mass of the rocket decreases, the acceleration increases for the same amount of thrust.
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Frequently asked questions
Newton's second law of motion is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.
Newton's second law can be mathematically represented as F = ma, where F is the force and a is the acceleration. This formula tells us that an object subjected to an external force will accelerate and that the amount of acceleration is proportional to the force applied.
Newton's first law states that an object at rest will remain at rest, and an object in motion will continue moving with a constant velocity unless acted upon by an external force. The second law, on the other hand, focuses on the behaviour of objects with unbalanced forces and provides a quantitative description of how these forces affect the motion of the objects.
