Calculate the Latent Heat of Vaporization. (Please see picture attached)
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Both kinetic and gravitational potential energy can become zero at infinite distance from the Earth.
Consider an object of mass <em>m </em>projected from the surface of the Earth with a velocity <em>v. </em>
The total energy of the body on the surface of the Earth is the sum of its kinetic energy and gravitational potential energy
.
here, <em>M</em> is the mass of the Earth, <em>R</em> is the radius of Earth and <em>G</em> is the universal gravitational constant.
The gravitational potential energy of the object is negative since it is in an attractive field, which is the gravitational field of the Earth.
The energy of the object on the surface of the earth is given by,
As the object rises upwards, it experiences deceleration due to the gravitational force of the Earth. Its velocity decreases and hence its kinetic energy decreases.
The decrease in kinetic energy is manifested as an equal increase in potential energy. The potential energy becomes less and less negative as more and more kinetic energy is converted into potential energy.
At a height <em>h</em> from the surface of the Earth, the energy of the object is given by,
The velocity is less than <em>v</em>.
When h =∞, the gravitational potential energy increases from a negative value to zero.
If the velocity of projection is adjusted in such a manner that the velocity decreases to zero at infinite distance from the earth, the object's kinetic energy also becomes equal to zero.
Thus, it is possible for both kinetic and potential energies to be zero at infinite distance from the Earth. In this case, kinetic energy decreases from a positive value to zero and the gravitational potential energy increases from a negative value to zero.
Answer:
(a):
(b):
(c):
(d):
(e):
Explanation:
Given, the position of the particle along the x axis is
The units of terms and
should also be same as that of x, i.e., meters.
The unit of t is seconds.
(a):
Unit of
Therefore, unit of
(b):
Unit of
Therefore, unit of
(c):
The velocity v and the position x of a particle are related as
(d):
The acceleration a and the velocity v of the particle is related as
(e):
The particle attains maximum x at, let's say, , when the following two conditions are fulfilled:
Applying both these conditions,
For ,
Since, c is a positive constant therefore, for ,
Thus, particle does not reach its maximum value at
For ,
Here,
Thus, the particle reach its maximum x value at time