Question

Draw an energy vs ht/ distance graph to prove law of conservation of energy for
1) Freely falling body
2) An elastic spring

It's urgent. Plzx​

Answer 1

To draw:

Energy vs ht/ distance graph to prove law of conservation of energy for

• Freely falling body

• An elastic spring

For a freely falling body , the kinetic energy decreases and proportionately the potential energy increases , such that the net mechanical energy remains constant.

Similarly , for a body on an elastic spring , the potential energy of the spring increases with proportionate decrease in the kinetic energy of the body. This leads to constant it net mechanical energy of the body.

Graph:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,6)\put(1,1){\vector(1,0){3}}\put(1,1){\vector(0,1){3}}\put(1,3){\line(1,0){2}}\put(4.5,1){h}\put(0.75,4.25){ E_{g} }\put(1,0.5){Energy\:of\:free\:falling\:body}\end{picture}}$

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,6)\put(1,1){\vector(1,0){3}}\put(1,1){\vector(0,1){3}}\put(1,3){\line(1,0){2}}\put(4.5,1){x}\put(0.75,4.25){ E_{s} }\put(1,0.5){Energy\:of\:body\:on\:Spring}\end{picture}}$

Equations:

For free-falling body in gravity:

$\boxed{\sf{\dfrac{1}{2}m{v}^{2}+mgh=constant}}$

For body on spring:

$\boxed{\sf{\dfrac{1}{2}m{v}^{2}+\dfrac{1}{2}k{x}^{2}=constant}}$