The mass of a body is the quantity of matter it contains. so-i) Under what condition the mass of the body is generally referred to be constant? ii) Why did Newton define mass as inertial mass in...

The mass of a body is the quantity of matter it contains. so-

i) Under what condition the mass of the body is generally referred to be constant?
ii) Why did Newton define mass as inertial mass in Newton's second law?

Asked on by itssnigdha

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krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

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Mass is defined as the amount of matter contained in a given body. Unless the matter in the body is added or removed there will not be change in the mass of the body. This mass is different from the weight or the force exerted by gravity on the body. This force may vary slightly from place to place on the earth as the force of gravity itself changes. For example the gravitational pull reduces as the altitude of the object increase. The changes in the gravitational force can be substantial when we consider the entire universe.

I am not so sure that Newton's Second Law Motion defines mass at all. The second law states that "the rate of change of momentum is directly proportional to the impressed force and takes place in the same direction in which the force acts. Though Newton's first Law of Motion does relate to inertia when it states that "every body continues in its state of rest or of uniform motion in a straight line, unless acted upon some external force", as inertia is is defined as that property of matter, by virtue of which  a body cannot move itself nor change the motion imparted to it.

Although Newton did not recognize this fact, matter can be converted in energy and energy into matter. In this way when a body, by virtue of its motion gains kinetic energy, the increase energy actually increases the mass of the body. However at the speeds that we normally encounter, this change in mass is too insignificant to be considered.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

i)

Generally we treat mass as constant. Mass is the amount of matter that is contained in an object. By the 2nd law of motion Newton gave us the definitionof force , F =ma or mass is the force divided by acceleration. So in order to measure the mass we have to exert a measured force on a rigid body and the find the generated acceleration and find the ratio. We can as well measure the force generated on a body under gavitational acceleration and find its mass as The gravitational force divided by the gravitational acceleration. Under all the cicumstance the mass found do agree with each other except for our experimental error or approximations. However, mass, looking like constantincreases if the the relative velocity of the object increses very high.

ii)

The specific term inertial mass, therefore, has a specific significance. Consider the mass of body at m at 1/2  of light speed, when m = m0/sqrt{1- (1/2)^2} , where m0 is the inertial mass or when the relative velocity of the object is 0.

So m = m0/sqt(.75) = 1.1547m0. But for all our practical speed or velocity, it is a very very small ratio compared with the velocity of light. So the mass looks constant. So the inertial mass has a very special meaning.

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