Physics, asked by khushiprajapati563, 5 months ago

energy of a partical in free fall at different position of partical and explain conservation ij free fall​

Answers

Answered by Anonymous
0

Answer:

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Answered by Shivam273303
0

Answer:

Consider a mass $m$ which is falling vertically under the influence of gravity. We already know how to analyze the motion of such a mass. Let us employ this knowledge to search for an expression for the conserved energy during this process. (N.B., This is clearly an example of a closed system, involving only the mass and the gravitational field.) The physics of free-fall under gravity is summarized by the three equations (24)-(26). Let us examine the last of these equations: $v^2 = v_0^{ 2} - 2 g s$. Suppose that the mass falls from height $h_1$ to $h_2$, its initial velocity is $v_1$, and its final velocity is $v_2$. It follows that the net vertical displacement of the mass is $s=h_2-h_1$. Moreover, $v_0=v_1$ and $v=v_2$. Hence, the previous expression can be rearranged to give

\begin{displaymath}

\frac{1}{2} m v_1^{ 2} + m g h_1 = \frac{1}{2} m v_2^{ 2} + m g h_2.

\end{displaymath} (123)

The above equation clearly represents a conservation law, of some description, since the left-hand side only contains quantities evaluated at the initial height, whereas the right-hand side only contains quantities evaluated at the final height. In order to clarify the meaning of Eq. (123), let us define the kinetic energy of the mass,

\begin{displaymath}

K = \frac{1}{2} m v^2,

\end{displaymath} (124)

and the gravitational potential energy of the mass,

\begin{displaymath}

U = m g h.

\end{displaymath} (125)

Note that kinetic energy represents energy the mass possesses by virtue of its motion. Likewise, potential energy represents energy the mass possesses by virtue of its position. It follows that

E = K + U = Constant.

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