Answer to Question #151585 in Mechanics | Relativity for Viccy

Question

What is newton second law

Answer 1

The second law of Newton defines a force to be equal to the change in momentum with a change in time. Momentum is defined to be the mass m of object times its velocity V.

Let us assume that we have an airplane at a point "0" defined by its location X₀ and time t₀. The airplane has a mass m₀ and travels at velocity V₀. The airplane is subjected to an external force F and moves to a point "1", which is described by a new location X₁ and time t₁. The mass and velocity of the airplane change during the flight to values m₁ and V₁. Newton's second law can help us determine the new values of V₁ and m₁ if we know how big the force F is. Let us just take the difference between the conditions at point "1" and the conditions at point "0".

$$F= \dfrac{m_1*V_1-m_0*V_0}{(t_1-t_0)}$$

Newton's second law talks about changes in momentum (m * V) so, at this point, we can't separate out how much the mass changed and how much the velocity changed. We only know how much product (m * V) changed.

Let us assume that the mass stays a constant value equal to m. This assumption is pretty good for an airplane, the only change in mass would be for the fuel burned between point "1" and point "0". The weight of the fuel is probably small relative to the weight of the rest of the airplane, especially if we only look at small changes in time. If we were discussing the flight of a baseball, then certainly the mass remains a constant. But if we were discussing the flight of a bottle rocket, then the mass does not remain a constant and we can only look at changes in momentum. For a constant mass m, Newton's second law looks like this:

$$F= \dfrac{m(V_1-V_0}{(t_1-t_0)}$$

The change in velocity divided by the change in time is the definition of the acceleration a. The second law then reduces to the more familiar product of a mass and acceleration:

$$F=m*a$$

Remember that this relation is only good for objects that have a constant mass. This equation tells us that an object subjected to an external force will accelerate and that the amount of the acceleration is proportional to the size of the force. The amount of acceleration is also inversely proportional to the mass of the object; for equal forces, a heavier object will experience less acceleration than a lighter object. Considering the momentum equation, a force causes a change in velocity; and likewise, a change in velocity generates a force. The equation works both ways.

The velocity, force, acceleration, and momentum have both a magnitude and a direction associated with them.