-- Multiply each side of the formula by 2
-- Then divide each side by t
-- Then subtract V(i) from each side.
Answer:
it will take for the sphere to increase in potential by 1500 V, 503.71 s.
Explanation:
The charge on the sphere after t seconds is:
q = (1.0000049 - 1.0000000) t = 0.0000049 t
The voltage on the surface is
V = k *
= k 0.0000049 t / R
solve for t
t = (R*V) / (0.0000049 k) = (0.12 * 1500) / (0.0000049 *
) = 503.71 s
Answer:
The external force leads to an increase on gravitational and spring potential energies.
Explanation:
The system consists of a mass, resort and Earth. According to the Principle of Energy Conservation there is a potential energy as a consequence of the interaction between Earth and the mass and spring potential energy because of the spring deformation and, besides, the existence of work due to an external force:



![F\cdot \Delta r = G\cdot m \cdot M \cdot \left(\frac{1}{r_{o}-\Delta r}-\frac{1}{r_{o}} \right)+\frac{1}{2}\cdot k \cdot [(x_{o}+\Delta r)^{2} -x_{o}^{2}]](https://tex.z-dn.net/?f=F%5Ccdot%20%5CDelta%20r%20%3D%20G%5Ccdot%20m%20%5Ccdot%20M%20%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7Br_%7Bo%7D-%5CDelta%20r%7D-%5Cfrac%7B1%7D%7Br_%7Bo%7D%7D%20%20%20%5Cright%29%2B%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20k%20%5Ccdot%20%5B%28x_%7Bo%7D%2B%5CDelta%20r%29%5E%7B2%7D%20-x_%7Bo%7D%5E%7B2%7D%5D)
The external force leads to an increase on gravitational and spring potential energies.