newton's second law of motion- definition and derivation
Answers
Answer:
Newton’s second law states that the acceleration of an object depends upon two variables – the net force acting on the object and the mass of the object. The acceleration of the body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body. This means that as the force acting upon an object is increased, the acceleration of the object is increased. Likewise, as the mass of an object is increased, the acceleration of the object is decreased.
Acceleration is directly proportional to the net force and inversely proportional to the mass.
Newton’s second law can be formally stated as,
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
This statement is expressed in equation form as,
a=Fnetm
The above equation can be rearranged to a familiar form as
F=ma
Since force is a vector, Newton’s second law can be written as
F⃗ =ma⃗
The equation shows that the direction of the total acceleration vector points in the same direction as the net force vector.
Deriving Newton’s Second Law
Force is equal to the rate of change of momentum
For Changing Mass
Let us assume that we have a car at a point (0) defined by location X0 and time t0. The car has a mass m0 and travels with a velocity v0. After being subjected to a force F, the car moves to point 1 which is defined by location X1 and time t1. The mass and velocity of the car change during the travel to values m1 and v1. Newton’s second law helps us determine the new values of m1 and v1 if we know the value of the acting force.
Taking the difference between point 1 and point 0, we get an equation for the force acting on the car as follows:
F=m1v1−m0v0t1−t0
Let us assume the mass to be constant. This assumption is good for a car because the only change in mass would be 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 car, especially if we only look at small changes in time. Meanwhile, if we were discussing the flight of a bottle rocket, then the mass does not remain constant and we can only look at changes in momentum.
For Constant Mass
For a constant mass, Newton’s second law can be equated as follows:
F=mv1−v0t1−t0
We know that acceleration is defined as the change in velocity divided by the change in time.
The second law then reduces to a more familiar form as follows:
F=ma
The above equation tells us that an object will accelerate if it is subjected to an external force and the amount of force is directly proportional to the acceleration and inversely proportional to the mass of the object.
Explanation:
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According to Newton's Second law of motion force applied on a body is directly proportional to the rate of change in linear momentum.
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