Respuesta :
With the concept of Law of Conservation Of Mechanical Energy the speed of sphere at the bottom of the swing is 2.182 m/s
What is Law conservation of Mechanical energy?
The sum of the Kinetic energy and the potential energy is known as the total Mechanical Energy
[tex]U_f +K_f=U_i+K_i[/tex]
Where,
[tex]U_f[/tex] and [tex]K_f[/tex] are final potential energy and kinetic energy respectively.
[tex]U_i[/tex] and [tex]K_i[/tex] are initial potential energy and kinetic energy respectively.
The total Mechanical energy of the system remains constant if the internal forces are conservative and the external forces do no work. This is called the Principle of conservation of energy.
Now, here in the question we have a sphere attached to a thread of length L=2.3 cm and is suspended from the ceiling. A uniform electric field deflects the pendulum setup upto a certain angle until it gets into an equilibrium state. We have been asked that if the electric field is suddenly turned off, what will be the speed of the sphere at the bottom.
So, as the electric field is turned off, then it just behaves like a simple pendulum.
Hence, using the Conservation of mechanical energy, in the pendulum, at the bottom the total energy is conserved and the kinetic energy and mechanical energy are equal.
Let the mass of the sphere be [tex]m[/tex] and velocity of the sphere be v,
Kinetic energy (K) = [tex]\frac{1}{2}mv^2[/tex]
Potential energy(P) = [tex]mgL[/tex]
[tex]g=9.8 m/s^2[/tex]
Equating both the energies,
K=P
[tex]\frac{1}{2}mv^2[/tex] = [tex]mgL[/tex]
[tex]v^2=2gL[/tex]
[tex]v=\sqrt{2gL}[/tex]
[tex]v=\sqrt{2*9.8*24*10^-3}[/tex]
[tex]v=2.182m/s[/tex]
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