Newton’s second law of motion
It states that rate of change of momentum of a body is equal to the force applied on it, in terms of the magnitude as well as in the sense of direction. Here the momentum is defined as the product of mass and velocity i.e. .
Therefore we can write mathematically.
F = d(mv)/ dt, if ‘m’ remains constant then
Thus acceleration is rate of change of velocity.
Since direction of a is same as F, we can write
F = ma , which is mathematically Newton’s second law of motion.
Here, if F = 0 then we find a = 0. This reminds us of first law of motion. That is, if net external force is absent, then there will be no change in state of motion, that means its acceleration is zero.
Further we can extend second law of motion, (in fact its decomposition) to three mutually perpendicular directions as per our coordinate system.
If components in x,y, and z directions are Fx, Fy, & Fz respectively, the three accelerations produced when Fx, Fy, & Fz act simultaneously) in the body are , Now,
If we add three forces then resultant is called net external force.
Similarly
is called net acceleration produced in the body.
Illustrations
1. In Figure 3.1. Let us have M = 10 kg and a new net external force in the direction as shown in figure 3.2 is 150 N. Find its acceleration.
Sol.
