gravity and y is the position coordinate in the direction of g . Impulse We sometimes encounter examples where a large force acts for a very short duration producing a finite change in momentum of the body. For example, when a ball hits a wall and bounces back, the force on the ball by the wall acts for a very short time when the two are in contact, yet the force is large enough to reverse the momentum of the ball. Often, in these situations, the force and the time duration are difficult to ascertain separately.
However, the product of force and time, which is the change in momentum of the body remains a measurable quantity. This product is called impulse: Impulse = Force × time duration = Change in momentum ( . ) A large force acting for a short time to produce a finite change in momentum is called an impulsive force . In the history of science, impulsive forces were put in a conceptually different category from ordinary forces.
Newtonian mechanics has no such distinction. Impulsive force is like any other force – except that it is large and acts for a short time. Example . A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of m s – .
If the mass of the ball is . kg, determine the impulse imparted to the ball. (Assume linear motion of the ball) Answer Change in momentum = . × –(– .
× ) = . N s, Impulse = . N s, in the direction from the batsman to the bowler. This is an example where the force on the ball by the batsman and the time of contact of the ball and the bat are difficult to know, but the impulse is readily calculated.
⊳ . NEWTON’S THIRD LAW OF MOTION The second law relates the external force on a body to its acceleration. What is the origin of the external force on the body ? What agency provides the external force ?
The simple answer in Newtonian mechanics is