Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.
Newton’s second law of motion, unlike the first law of motion pertains to the behavior of objects for which all existing forces are unbalanced. The second law of motion is more quantitative and is used extensively to calculate what happens in situations involving a force.
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:
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:
The equation shows that the direction of the total acceleration vector points in the same direction as the net force vector.
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.
2. For Constant Mass
The application of the second law of motion can be seen in identifying the amount of force needed to make an object move or to make it stop.
Following are a few examples that we have listed to help you understand this point:
Example 1: If there is a block of mass 2kg, and a force of 20 N is acting on it in the positive x-direction, and a force of 30 N in the negative x-direction, then what would be its acceleration?
Solution: To calculate its acceleration, we first have to calculate the net force acting on it.
Fnet = 20 N – 30 N = -10 N
Mass = 2kg
The negative acceleration indicates that the block is slowing and its acceleration vector is moving in an opposite direction directed opposite to the direction of motion.
Example 2: How much horizontal net force is required to accelerate a 1000 kg car at 4 m/s2?
Solution: Newton’s 2nd Law relates an object’s mass, the net force on it, and its acceleration. Therefore, we can find the force as follows:
Fnet = ma
Substituting the values, we get
1000 kg × 4 m/s2 = 4000 N
Therefore, the horizontal net force is required to accelerate a 1000 kg car at 4 m/s2 is 4000 N.
Newton’s second law is applied in daily life to a great extent. For instance, in Formula One racing, the engineers try to keep the mass of cars as low as possible. Low mass will imply more acceleration, and the more the acceleration, the chances to win the race are higher.