Acceleration = (final velocity - initial velocity) / time
= (35-65)/10
= -3 m/s2
Answer:
Explanation:
change in flux = no of turns x area of loop x change in magnetic field
= 1 x π 65² x 10⁻⁶ x ( 650 - 350 ) x 10⁻³
= 3.9 x 10⁻³ weber .
rate of change of flux = change of flux / time
= 3.9 x 10⁻³ / .10
= 39 x 10⁻³ V
= 39 mV .
Since the magnetic flux is directed outside page and it is increasing , induced current will be clockwise so that magnetic field is produced in opposite direction to reduce it , as per Lenz's law.
As we know that KE and PE is same at a given position
so we will have as a function of position given as
![KE = \frac{1}{2}m\omega^2(A^2 - x^2)](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm%5Comega%5E2%28A%5E2%20-%20x%5E2%29)
also the PE is given as function of position as
![PE = \frac{1}{2}m\omega^2x^2](https://tex.z-dn.net/?f=PE%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm%5Comega%5E2x%5E2)
now it is given that
KE = PE
now we will have
![\frac{1}{2}m\omega^2(A^2 - x^2) = \frac{1}{2}m\omega^2x^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dm%5Comega%5E2%28A%5E2%20-%20x%5E2%29%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm%5Comega%5E2x%5E2)
![A^2 - x^2 = x^2](https://tex.z-dn.net/?f=A%5E2%20-%20x%5E2%20%3D%20x%5E2)
![2x^2 = A^2](https://tex.z-dn.net/?f=2x%5E2%20%3D%20A%5E2)
![x = \frac{A}{\sqrt2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7BA%7D%7B%5Csqrt2%7D)
so the position is 0.707 times of amplitude when KE and PE will be same
Part b)
KE of SHO at x = A/3
we can use the formula
![KE = \frac{1}{2}m\omega^2(A^2 - x^2)](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm%5Comega%5E2%28A%5E2%20-%20x%5E2%29)
now to find the fraction of kinetic energy
![f = \frac{KE}{TE} = \frac{A^2 - x^2}{A^2}](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7BKE%7D%7BTE%7D%20%3D%20%5Cfrac%7BA%5E2%20-%20x%5E2%7D%7BA%5E2%7D)
![f = \frac{A^2 - (\frac{A}{3})^2}{A^2}](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7BA%5E2%20-%20%28%5Cfrac%7BA%7D%7B3%7D%29%5E2%7D%7BA%5E2%7D)
![f_k = \frac{8}{9}](https://tex.z-dn.net/?f=f_k%20%3D%20%5Cfrac%7B8%7D%7B9%7D)
now since total energy is sum of KE and PE
so fraction of PE at the same position will be
![f_{PE} = 1 - f_k](https://tex.z-dn.net/?f=f_%7BPE%7D%20%3D%201%20-%20f_k)
![f_{PE} = 1 - (8/9) = 1/9](https://tex.z-dn.net/?f=f_%7BPE%7D%20%3D%201%20-%20%288%2F9%29%20%3D%201%2F9)
Answer:
A substance made of two or more types of atoms
Explanation: