Ch-9. force and laws of motion
I. INERTIA II. TYPES OF INERTIA III. NEWTON’S SECOND LAW
Types of inertia Inertia of a body is of three types – Inertia of rest Inertia of motion Inertia of direction Inertia of rest - it is the inability of a body to change by itself, its state of rest. This means a body at rest remains at rest and cannot start moving on its own. For example - when we shake branch of a mango tree, the mangoes fall down. This is because the branch comes in motion and the mangoes tends to remain at rest . hence they get detached and fall down. Inertia of motion- it is the inability of a body to change by itself, its state of uniform motion. It means a body in uniform motion can neither accelerate nor retard on its own and come to rest. For ex- suppose we are standing in a moving bus, and driver sops the bus suddenly. We are thrown forward with a jerk. As the bus is suddenly stopped ,our feet due to friction which does not allow relative motion between the feet and the floor of the bus. But the rest of the body continues to move forward due to inertia. that is why we are thrown forward. Inertia of direction- it is the inability of a body to change by itself, its direction of motion. A body continues to move along the same straight line unless compelled by some external force to change it. For example-when a stone tied to one end of a string is whirled and the string breaks suddenly, the stone flies off along the tangent to the circle.
NEWTON’S SECOND LAW According to Newton’s second law of motion, the rate of change of linear momentum of a body is directly proportional to the external force applied on the body, and this change takes place always in the direction of the applied force.
Suppose two bodies of different masses are initially at rest, and a fixed force is applied on them for a certain interval of time. To start with, the lighter body picks up a greater speed than the heavier body. however at the end of time interval, observations shows that each body acquire the same linear momentum. It means that the same force applied for the same time causes the same change in linear momentum in bodies of different masses. As per Newton’s second law of motion, F = ma Where F is force applied on the body or force under consideration m is mass of the body on which force acts a is acceleration produced in the body due to force applied The above equation is a mathematical form of Newton’s second law Magnitude of force can be calculated by multiplying mass of the body and the acceleration produced in it. Hence the second law of motion gives the measure of force. UNIT OF FORCE SI unit of force is newton (N) 1 N = 1 kg × 1 ms -2 = 1 kg ms -2 One newton force is that much force which produces an acceleration of 1 ms -2 in a body of mass 1 kg.
No force is required to move a body uniformly along a straight line . Accelerated motion is always due to an external force. By knowing the mass of a body and measuring change in velocity in a particular time interval, force applied F can be calculated. Mass of a body is measure of inertia
MATHEMATICAL FORMULATION OF NEWTON’S SECOND LAW OF MOTION Consider a body of mass, m is moving along a straight line Let, Initial velocity of the body = u Final velocity =v Time interval = t Force applied for time, t = F Initial momentum, P 1 =mu Final momentum, P 2 = mv Change in momentum, P = final momentum- initial momentum = P 2 – P 1 The rate of change of linear momentum = change in momentum/ time taken = P 2 - P 1 t =( mv -mu)/t =m(v-u)/t As per Newton’s second law statement, Force applied α rate of change of linear momentum F α m(v-u)/t F = k m(v-u)/t where k is constant of proportionality F= kma a=( v-u)/t If k= 1 F = ma The above equation is mathematical form of Newton’s second law
APPLICATION OF NEWTON’S SECOND LAW A Cricket player lowers his hand backward while catching a cricket ball. He allows a longer time to stop the ball. By increasing the time of catch, the player has to apply a smaller force against the ball in order to stop it. the ball in turn exert smaller force on his hand and his hand are not injured. An athlete is advised to come to stop slowly. After finishing a fast race, so that time of stop increases and hence force experienced decreases.
The second law of motion is often seen in action in our everyday life. Have you noticed that while catching a fast moving cricket ball, a fielder in the ground gradually pulls his hands backwards with the moving ball? In doing so, the fielder increases the time during which the high velocity of the moving ball decreases to zero. Thus, the acceleration of the ball is decreased and therefore the impact of catching the fast moving ball (Fig. 9.8) is also reduced. If the ball is stopped suddenly then its high velocity decreases to zero in a very short interval of time. Thus, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for holding the catch that may hurt the palm of the fielder.
In a high jump athletic event, the athletes are made to fall either on a cushioned bed or on a sand bed. This is to increase the time of the athlete’s fall to stop after making the jump. This decreases the rate of change of momentum and hence the force.
The momentum, p of an object is defined as the product of its mass, m and velocity, v. That is, p = mv (9.1) Momentum has both direction and magnitude. Its direction is the same as that of velocity, v. The SI unit of momentum is kilogram- metre per second (kg m s-1). Since the application of an unbalanced force brings a change in the velocity of the object, it is therefore clear that a force also produces a change of momentum.