User:HJH3/A

Set A (Surfaces and Interfaces)

Hongyuan Jimmy He - December 2010

Short Knowledge
A1. What governs the contact angle between the edge of a water droplet and the surface it adsorbs to?

A2. What is the formula for Surface Energy?

Short Calculation
A3. Solve the f equation:

A3. Solve the f equation:

A4. Solve the $$\mu_{-\frac{1}{2}}$$ equation:
 * $$\begin{align}

ax^2 + bx + c = 0 \end{align}$$ Let
 * $$\begin{align}

a &= 3\\ b &= 6\\ 2c &= -7 \end{align}$$

A5. Solve the equation:
 * $$\begin{align}

ax^2 + bx + c = 0 \end{align}$$ Let
 * $$\begin{align}

a &= 3\\ b &= 6\\ 2c &= -7 \end{align}$$

Long Knowledge
$$ \begin{align} \int_0^1 P( m=7|r, n=10) \, f(r) \, dr & = \int_0^1 {10 \choose 7} \, r^7 \, (1-r)^3 \, 1 \, dr \\ & = {10 \choose 7} \left / {11 \choose 3,7,1} \right. = {10 \choose 7} \, \frac{1}{1320} \end{align} $$

Long Calculation
$$ \begin{align} \int_0^1 P( m=7|r, n=10) \, f(r) \, dr & = \int_0^1 {10 \choose 7} \, r^7 \, (1-r)^3 \, 1 \, dr \\ & = {10 \choose 7} \left / {11 \choose 3,7,1} \right. = {10 \choose 7} \, \frac{1}{1320} \end{align} $$