NAME:

PHYSICS 231
2nd Midterm, November 14, 1997, 5:30 pm - 6:45 pm
Instructor: P. Q. Hung

Do all problems (20 points each). READ them carefully. You have to EXPLAIN all your answers. DO NOT just write them down. ANSWERS WITHOUT EXPLANATION WILL BE GIVEN NO CREDIT.

Some formulas (not necessarily all useful):

x=x₀+v_0xt+(1/2)a_xt²

y=y₀+v_0yt+(1/2)a_yt²

v_x=v_0x+a_xt

v_y=v_0y+a_yt

$v = \omega r$

$R = (v_{0}^{2}/g) sin(2\theta_{0})$

$\sum {\vec{F}}_{i} = m \vec{a}$, $\vec{F}= -(G\,m\,M/r^2)\,\hat{r}$

$E= \frac{1}{2} m v^2 + U$

$U_{spring} = 1/2\:k x^2$, $U = -(G\,m\,M/r)+ U_0$

$\vec{p} = m\, \vec{v}$, $\vec{L} = I \vec{\omega}$

$x_{CM} = \frac{m_1 x_1 + m_2 x_2 +\cdots+m_N x_N}{m_1 + m_2 +\cdots +m_N}$

$\vec{L} = \vec{r}\times \vec{p}$, $\vec{\tau}= \vec{r} \times \vec{F}$

$v_{1f} = (\frac{m_1 - m_2}{m_1 + m_2}) v_{1i} + (\frac{2 m_2}{m_1 +m_2}) v_{2i}$

$v_{2f} = (\frac{2 m_1}{m_1 +m_2}) v_{1i} + (\frac{m_2 - m_1}{m_1 + m_2}) v_{2i}$

$K_{rot} = (1/2)\,I \omega^2$,

$\hat{\imath} \times \hat{\jmath} = \hat{k}$, $\hat{\jmath} \times \hat{k} = \hat{\imath}$

g=9.8m/s², $G = 6.67 \times 10^{-11} N-m^2/kg^2$

$M_{moon} = 7.35 \times 10^{22}$ kg, $R_{moon} = 1.74 \times 10^6$ m.