Question

(i)State the law of motion, having mathematical form :
1/t (mv - mu) F
[ where the symbols have usual meaning ]
(ii) Under what condition, the above sign of proportion changes to the sign
of equality

Answer 1

Explanation:

The first law of motion indicates that when an unbalanced external force acts on an object, its velocity changes, that is, the object gets an acceleration. We would now like to study how the acceleration of an object depends on the force applied to it and how we measure a force. Let us recount some observations from our everyday life. During the game of table tennis if the ball hits a player it does not hurt him. On the other hand, when a fast moving cricket ball hits a spectator, it may hurt him. A truck at rest does not require any attention when parked along a roadside. But a moving truck, even at speeds as low as 5 m s-1, may kill a person standing in its path. A small mass, such as a bullet may kill a person when fired from a gun. These observations suggest that the impact produced by the objects depends on their mass and velocity. Similarly, if an object is to be accelerated, we know that a greater force is required to give a greater velocity.

In other words, there appears to exist some quantity of importance that combines the object's mass and its velocity. One such property called momentum was introduced by Newton

Answer 2

(i) Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v. Here we see that, the initial momentum

p1 = m*u

The final momentum

p2 = m*v

The change in momentum can be written as

p2 – p1= m*v – m*u = m(v-u)

As we know, the rate of change of momentum with respect to time is proportional to the applied force. The applied force

F proportional to  m(v-u)/t

Or,

F proportional to  m*a

as acceleration (a) = rate of change of velocity with respect to time.

(ii) The sign of proportion changes to = when a constant is placed on the right hand side. Like F= kma

But in this case k = 1