Respuesta :
Answer:
75%
[tex]\dfrac{A}{\sqrt{2}}[/tex]
Explanation:
x = Displacement of spring = [tex]\dfrac{1}{2}A=\dfrac{A}{2}[/tex]
k = Spring constant
Total energy of the spring is
[tex]E=\dfrac{1}{2}kA^2[/tex]
Elastic potential energy is given by
[tex]U=\dfrac{1}{2}kx^2\\\Rightarrow U=\dfrac{1}{2}k(\dfrac{A}{2})^2\\\Rightarrow U=\dfrac{1}{2}k\dfrac{A^2}{4}\\\Rightarrow U=\dfrac{1}{4}\times \dfrac{1}{2}kA^2\\\Rightarrow U=\dfrac{1}{4}E[/tex]
Total energy is given by
[tex]E=U+K\\\Rightarrow K=E-U\\\Rightarrow K=E-\dfrac{1}{4}E\\\Rightarrow K=\dfrac{3}{4}E\\\Rightarrow \dfrac{K}{E}=0.75[/tex]
The percentage will be
[tex]\dfrac{K}{E}=0.75\times 100\%\\\Rightarrow \dfrac{K}{E}=75\%[/tex]
The required percentage is 75%
According to the given condition
[tex]\dfrac{E}{2}=\dfrac{1}{2}kx^2\\\Rightarrow \dfrac{\dfrac{1}{2}kA^2}{2}=\dfrac{1}{2}kx^2\\\Rightarrow \dfrac{1}{2}kA^2=kx^2\\\Rightarrow x=\sqrt{\dfrac{1}{2}A^2}\\\Rightarrow x=\dfrac{A}{\sqrt{2}}[/tex]
So, the energy is half when displacement is [tex]\dfrac{A}{\sqrt{2}}[/tex]
- At 75% ,the energy is kinetic energy.
- At [tex]\frac{A}{\sqrt{2} }[/tex] a fraction of A, the energy half kinetic and half potential.
Let x be the displacement of spring which is given to be [tex]\frac{1}{2} A=\frac{A}{2}[/tex]
k= spring constant
Total energy of the spring is:
[tex]E=\frac{1}{2} kA^2[/tex]
Elastic potential energy is given as:
[tex]U=\frac{1}{2} kx^2[/tex]
Now on substituting the value of x in above equation:
[tex]U=\frac{1}{2} k\frac{A^2}{4}[/tex]
It can also be written as:
[tex]U=\frac{1}{4} *\frac{1}{2} kA^2 \\\\U=\frac{1}{4} E[/tex] (∵[tex]E=\frac{1}{2} kA^2[/tex])
Total energy can be written as:
E=U+K
⇒K=E-U
⇒K=E-1/4 E
⇒K=3/4 E
⇒[tex]\frac{K}{E} =0.75[/tex]
(i) Now, we need to calculate the percentage of kinetic energy:
[tex]\frac{K}{E} =0.75*100=75\%[/tex]
The percentage of kinetic energy is 75%.
(ii) In second it is asked at what displacement, as a fraction of A, is the energy half kinetic and half potential?
∴[tex]\frac{E}{2} =\frac{1}{2} kx^2[/tex]
On substituting the value of E in above equation we will get:
[tex]x=\sqrt{\frac{1}{2} A^2} \\\\x=\frac{A}{\sqrt{2} }[/tex]
So, the energy is half when displacement is [tex]\frac{A}{\sqrt{2} }[/tex] .
Learn more:
brainly.com/question/12337396
