ALCANCE PARCIAL DE COMPLEMENTACIÓN ECONÓMICA COLOMBIA - ARGENTINA

Therefore, we conclude that everybody continues in its state of rest or of uniform motion in a straight line unless and until it is compelled by some unbalanced force to change that state. This is the statement of Newton’s First Law of Motion. So, Newton’s first law of motion may be used to define force. It also defines another concept called inertia. The property of a body by virtue of which it is unable to change its state of rest or of uniform motion in a straight line is called inertia. You can do another activity to understand the concept of inertia.

ACTIVITY 8.1

Aim: To study Newton’s first law of motion and inertia. What is required ? Two books and a smooth sheet of paper.

What to do? (i) Place the sheet of paper on the table with some part of it coming out of the edge of the table. Now stack two books on the paper. (ii) Remove the paper with a jerk and see the effect on books.

What do you observe? When the paper is removed with a jerk from below the books, the books do not change their position (Fig. 8.3).

Fig 8.3 Paper being removed with a jerk from below the books

What do you infer? We find that the books remain in their position unless something external is done. Even removal of paper from below them with jerk does not change their position.

ACTIVITY 8.2

Aim: To study the inertia of rest

What is required? A coin, talcum powder, a table with sunmica top or glass top. What to do? (i) Strike the coin on a smooth floor and note the distance travelled by it. (ii) Now, sprinkle talcom powder on the floor and again strike the coin from the same place with the same force and note the distance travelled by it again. The distance travelled by the coin in straight line is different in the two situations.

What do you infer? We find that coin travels through much longer distance along a straight line on the floor when powder is sprinkled. The floor exerts a resistive force on the motion of the coin. But this resistive force is much less when powder is sprinkled on the floor, so coin travels much farther. If we imagine a completely smooth floor which offers no resistive force, the coin will continue to move on it with constant velocity unless some net external force is applied to stop it.

Inertia is a property common to all bodies in nature. You must have experienced that it is difficult to move a heavy body than a lighter one e.g., pushing a loaded box is more difficult than to push an empty box because heavy box has more inertia. So inertia of a body is characterized by the quantity called mass of the body. Thus, it can be said that the mass of a body is a measure of its inertia.

Some illustrations of first law of motion

(a) Why do you tend to fall while getting off a moving bus or why are you thrown forward when the moving bus stops suddenly and you are not cautious. What actually happens is that when a moving bus suddenly stops, your feet in contact with the bus are suddenly brought to rest while the rest of your body, which has acquired the same velocity as the bus, due to inertia of motion tends to move forward even after the bus has stopped.

sometimes the loaded goods fall from it. This is due to the inertia of motion of the goods. When the trolley stops suddenly, it comes at rest immediately. But because of inertia of motion, the goods placed in it try to remain in motion. Hence they fall from it. Now think, why does the ink comes out of a fountain pen when it is given a jerk?

Newton's second law of motion

You have seen that force changes or tends to change the state of motion of a body. When you throw a piece of stone in the air, you apply a force. Greater the force with which you throw the stone, the farther it goes, i.e., the greater the force, the greater is the change in motion of a particular body. But how does the motion of a body change when you apply some external force? To establish a relationship between the force and the acceleration produced in a body, Newton formulated his second law of motion. If you kick a football, it moves, but if you kick it very hard, it moves faster than before. Kicking harder means applying more force due to which football gains more acceleration and hence moves faster. It is seen that acceleration of a body is directly proportional to the force applied on the body.

Fig. 8.4 Passenger falling forward as the bus stops suddenly

The mass of the football is greater than that of the plastic ball. For the same force the acceleration produced in the plastic ball is greater than the acceleration produced in the football. So it can be said that the acceleration produced in a body depends on its mass and is inversely proportional to the mass.

Hence, we have, a = F/m ... 8.1

Where, ‘a’ denotes the acceleration produced in a body of mass ‘m’ when a force ‘F’ is applied on it. Now, you know acceleration is a vector quantity and force is also a vector quantity, so the equation (8.1) may be expressed in the vector form as

Fig 8.5 Motion of (a) foot ball (b) plastic ball when the same force is applied on them This shows that acceleration produced in a body is in the same direction as the applied force. Equation (8.2) represents Newton’s second law of motion which may be stated as the acceleration produced in a body is directly proportional to the unbalanced force acting on it and is inversely proportional to its mass. The direction of the acceleration is the same as that of the force.

Unit of force:

You can use equation (8.1) to define the unit of force. Equation (8.1) may be written as,

F = ma ... 8.3

In SI system of units, if m = 1 kg and a = 1 ms-2 then, F = (1 kg *1 m)/1s2 = 1kgm/s2

1kgm/s2

is called as 1 Newton whose symbol is N. Hence, the SI unit of force is Newton.1 Newton force is that force which on acting on a body of mass 1 kg produces in it an acceleration of 1 ms-2

i.e., 1N = 1 kg ms-2

You must note that equation (8.3) can be used to find out the acceleration or force applied or mass of a body provided any two of the three quantities namely force, mass and acceleration are known. If you put F = 0 in equation (8.3), you will get, ma = 0 But, mass m of a body can never be zero. Therefore, or a = v – u = 0 or v = u i.e., a moving body continues to move with the same velocity if no force acts on it. This is nothing but the first law of motion. So first law can be derived from the second law. Let us solve some problems using Newton’s Law of motion.

Example 8.1: What force accelerates a 50 kg mass at 4m/s-2?

Solution: Newton’s second law gives F = ma Here m = 50kg and a = 4ms-2 Therefore, F = 50 kg x 4ms-2 = 200 kg ms-2 = 200N (since 1N = 1kg ms-2 )

Example 8.2: If a force of 50 N acts on a body of mass 10 kg. then what is the acceleration produced in the body?

Here, F = 50 N = 50 kg ms-2 and m = 10 kg a= 50kgms-2

* 1/10 kg = 5ms-2 Momentum

You know that a moving body always has a mass and a velocity. These two quantities help us to define a new quantity called momentum. Thus, the momentum of a moving body is defined as the product of its mass and velocity, and its direction is same as that of its velocity.

So, we can say that all moving bodies have momentum. i.e. Momentum = Mass x Velocity

p = m x v = mv

You know, velocity is a vector quantity, so momentum is also a vector quantity directed along the velocity.

In vector notation, p = mv

Momentum plays an important role in the motion of bodies. We know that the acceleration of a body is defined as rate of change of its velocity.

v = Final velocity, u = Initial velocity and t = Time Newton’s second law of motion gives.

F = ma

Substituting (8.4) in the above equation we have, F = ( Final momentum – Initial momentum ) / Time (according to the definition of momentum)

or F = ( Change in momentum ) / Time = Rate of change of momentum

Hence the rate of change of momentum of a body is equal to the force acting on the body and is in the same direction.

This is another way of stating Newton’s second law of motion.

Unit of momentum: By definition, momentum is the product of mass and velocity. In SI units, the unit of mass is kg and that of velocity is m/s. Therefore, the unit of momentum is kg m/s or kgms-1

or Ns