NAME:

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

Do all problems . 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.

I) A cord is used to vertically lower an initially stationary block of mass m at a constant downward acceleration of g/4. When the block has fallen a distance d, find (a) the work done by the cord's force on the block (7 pts), (b) the work done by the weight of the block (3 pts), (c) the kinetic energy of the block (7 pts), and (d) the speed of the block (3 pts)

II) A 0.55 kg projectile is launched from the edge of a cliff with an initial kinetic energy of 1550 J and its highest point is 140 m above the launch point. (This is a projectile motion.) (a) What was the vertical component of its velocity just right after launch? (10 pts). What is the horizontal component of its velocity? (10 pts)

III) A 0.63 kg ball is thrown up with an initial speed of 14 m/s and reaches a maximum height of 8.1 m. How much energy is dissipated by the air drag acting on the ball during the ascent? (10 pts). How much higher would it have gone were the air drag negligible? (10 pts).

IV) A body of mass 2.0 kg makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed. What is the mass of the struck body? (15 pts). What is the speed of the center-of-mass of the system if the initial speed of the 2.0 kg body was 4.0 m/s? (5 pts).