Question

10) A body executes SHM of time period 8s.If its mass be 0.1kg,its velocity 1s
after it passes through its mean position be 4m/s, find its i)K.E ii) P.E iii) T.E???​

Answer 1

Given:

body executes SHM of time period 8s.If its mass be 0.1kg,its velocity 1 sec after it passes through its mean position be 4m/s.

To find:

• KE , PE and TE at that point ?

Calculation:

First of all , latest find out the amplitude of the SHM trajectory :

$\therefore \: v = a \omega \cos( \omega t)$

$\implies \: 4 = a \times \dfrac{2\pi}{T} \times \cos( \dfrac{2\pi}{T} \times t )$

$\implies \: 4 = a \times \dfrac{2\pi}{8} \times \cos( \dfrac{2\pi}{8} \times 1 )$

$\implies \: 4 = a \times \dfrac{\pi}{4} \times \cos( \dfrac{\pi}{4} )$

$\implies \: 4 = a \times \dfrac{\pi}{4} \times \dfrac{1}{ \sqrt{2} }$

$\implies \: a = \dfrac{16 \sqrt{2} }{\pi} \: m$

$\implies \: a \approx \: 7.2 \: m$

Now, displacement from the mean position at the time be "x" :

$\therefore \: x = a \sin( \omega t)$

$\implies \: x = \dfrac{16 \sqrt{2} }{\pi} \times \sin( \dfrac{2\pi}{8} \times 1)$

$\implies \: x = \dfrac{16 \sqrt{2} }{\pi} \times \sin( \dfrac{\pi}{4} )$

$\implies \: x = \dfrac{16 \sqrt{2} }{\pi} \times \dfrac{1}{ \sqrt{2} }$

$\implies \: x = 5.09 \: m$

Now, let potential energy be PE :

$\therefore \: PE = \dfrac{1}{2} m { \omega}^{2} {x}^{2}$

$\implies \: PE = \dfrac{1}{2} \times 0.1 \times {( \dfrac{\pi}{4}) }^{2} \times {(5.09)}^{2}$

$\implies \: PE = \dfrac{1}{2} \times 0.1 \times \dfrac{ {\pi}^{2} }{16} \times 25.9$

$\implies \: PE = 0.08 \times {\pi}^{2}$

$\boxed{ \implies \: PE = 0.78 \: J}$

Now, kinetic energy be KE :

$\therefore \: KE = \dfrac{1}{2} m { \omega}^{2} ( {a}^{2} - {x}^{2} )$

$\implies \: KE = \dfrac{1}{2} \times 0.1 \times \dfrac{ {\pi}^{2} }{16} \times \{{(7.9)}^{2} - {(5.9)}^{2} \}$

$\implies \: KE = \dfrac{1}{2} \times 0.1 \times \dfrac{ {\pi}^{2} }{16} \times 27.6$

$\boxed{ \implies \: KE = 0.86 \: joule}$

So, total energy :

$\boxed{ \therefore \: TE = 0.86 + 0.78 = 1.64 \: joule}$

Answer 2

Explanation:

Qᴜᴇꜱᴛɪᴏɴ⤵

10) A body executes SHM of time period 8s. If its mass be 0.1kg, its velocity Is after it passes through its mean position be 4m/s, find its

K.E

P.E

T.E??

ᴀɴꜱᴡᴇʀ⤵

1.ᴋᴇ✔