F~1/r²
doubling the distance r, Decreases the force by ¼
Given:
The given value is
.
To find:
The value of the given expression by using the Binomial approximation.
Explanation:
We have,
![(1.0004)^{\frac{1}{2}}](https://tex.z-dn.net/?f=%281.0004%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
It can be written as:
![(1.0004)^{\frac{1}{2}}=(1+0.0004)^{\frac{1}{2}}](https://tex.z-dn.net/?f=%281.0004%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%281%2B0.0004%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
![[\because (1+x)^n=1+nx]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%281%2Bx%29%5En%3D1%2Bnx%5D)
![(1.0004)^{\frac{1}{2}}=1+0.0002](https://tex.z-dn.net/?f=%281.0004%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D1%2B0.0002)
![(1.0004)^{\frac{1}{2}}=1.0002](https://tex.z-dn.net/?f=%281.0004%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D1.0002)
Therefore, the approximate value of the given expression is 1.0002.
The potential energy of an object is defined by the equation: PE = mgh, where m = the mass of the object, g = the gravitational acceleration and h = the object's height above the ground.
<span>Melting of ice is an endothermic process, meaning that energy is absorbed. When ice spontaneously melts, ΔH (change in enthalpy) is "positive". ΔS (entropy change) is also positive, because, becoming a liquid, water molecules lose their fixed position in the ice crystal, and become more disorganized. ΔG (free energy of reaction) is negative when a reaction proceeds spontaneously, as it happens in this case. Ice spontaneously melts at temperatures higher than 0°C. However, liquid water also spontaneously freezes at temperatures below 0°C. Therefore the temperature is instrumental in determining which "melting" of ice, or "freezing" of water becomes spontaneous. The whole process is summarized in the Gibbs free energy equation:
ΔG = ΔH – TΔS</span>