The first law refers to the simple case when the net external force on a body is zero. The second
law of motion refers to the general situation when there is a net external force acting on the body.
It relates the net external force to the acceleration of the body.
Momentum of a body is defined to be the product of its mass m and velocity v, and is denoted by p: p = m v
Momentum is clearly a vector quantity.
- The total momentum of an isolated system of interacting particles is conserved.
Suppose a light-weight vehicle (say a small car) and a heavy weight vehicle (say a loaded truck) are parked on a horizontal road. We all know that a much greater force is needed to push the truck than the car to bring them to the same speed in same time.
Similarly, a greater opposing force is needed to stop a heavy body than a light body in the same time, if they are moving with the same speed.
If two stones, one light and the other heavy, are dropped from the top of a building, a person on the ground will find it easier to catch the light stone than the heavy stone.
The mass of a body is thus an important parameter that determines the effect of force on its motion.
Speed is another important parameter to consider. A bullet fired by a gun can easily pierce human tissue before it stops, resulting in casualty. The same bullet fired with moderate speed will not cause much damage.
Thus for a given mass, the greater the speed, the greater is the opposing force needed to stop the body in a certain time. Taken together, the product of mass and velocity, that is momentum, is evidently a relevant variable of motion.
The greater the change in the momentum in a given time, the greater is the force that needs to be applied.
- Second Law of Motion: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
- F = ma (Force = mass × acceleration), Unit of Force is Newton.
In the second law, F = 0 implies a = 0. The second law is obviously consistent with the first law.
Suppose a stone is rotated with uniform speed in a horizontal plane by means of a string, the
magnitude of momentum is fixed, but its direction changes (Fig. 4.4). A force is needed to cause this change in momentum vector. This force is provided by our hand through the string.
Experience suggests that our hand needs to exert a greater force if the stone is rotated at greater speed or in a circle of smaller radius, or both. This corresponds to greater acceleration or equivalently a greater rate of change in momentum vector.
- Force not only depends on the change in momentum but also on how fast the change is brought about. A seasoned cricketer draws in his hands during a catch, allowing greater time for the ball to stop and hence requires a smaller force. - reduce the rate of change of momentum- less force - less hurt
