Physics 131-2 Test 3

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Questions (10 pts. apiece) Answer in complete, well-written sentences WITHIN the spaces provided.

1. University of Richmond President Bill Cooper stands on the Whitehurst clock tower and drops water balloons on passing students. He chooses his origin to be the position of his hand when he drops the water balloon. A student/target picks the the top of their head to be the origin. If they calculate the value of a water balloon's mechanical energy, will the get the same value? Explain.

2. What packs a bigger wallop, a clay ball or a superball? Assume each object has the same mass and velocity. Explain.

3. A tractor trailer with velocity $\vec {\bf v}$ bumps into a car stopped at a stop light. How does the magnitude of the force exerted on the tractor trailer compare with the magnitude of the force exerted on the car? What is your evidence?

4. What is the parallel axis theorem? Describe each component in the expression.

5. Three uniform solids with identical masses are shown below (a square ring, a disk, and a circular ring). Which one has the greatest rotational inertia about an axis through its center of mass and perpendicular to its cross section? Explain.

   

Problems. Clearly show all reasoning for full credit. Use a separate sheet to show your work.

1.	15 pts.	The figure shows a ball of mass $m$ attached to the end of a thin rod with length $L$ and negligible mass. The other end is pivoted so it can move in a vertical circle. The rod is held in the horizontal position shown and given a downward push so it swings down and around and comes to a stop just as it reaches the vertical position. What initial speed is given to the ball in terms of $m$, $L$, and any other constants?
2.	15 pts.	A lead nucleus (mass 282 u) experiences an elastic, head-on collision with a nitrogen nucleus (mass 14 u) that is originally at rest. The initial speed of the lead nucleus is $v_0 = 1.0\times 10^6~m/s$. What is the final velocity of the nitrogen nucleus?
3.	20 pts.	Consider a rotating disk with a fixed axis of rotation at its center. It has a `rotational collision' with a cylindrical mass as shown in the figure. The disk has mass $m_d$, radius $r_d$, and it is initially rotating with angular velocity $\omega_0$. The cylinder has mass $m_c$, radius $r_c$, velocity $\vec v_c$, and lands and sticks with its center-of-mass at a point $r_1$ from the axis of rotation of the disk. The point of contact is the open circle on the disk in the figure. What is the final angular velocity of the disk and the weight? In what direction will the disk be rotating after the collision?

Some constants and conversion factors.

Earth mass	$5.98\times 10^{24}~kg$	Earth-Sun distance	$1.5\times 10^{11}~m$
Earth radius	$6.37\times 10^6~m$	atomic mass unit (u)	$1.66 \times 10^{-27}~kg$
1 day	$8.64\times 10^4 ~s$	1 year	$3.154 \times 10^7~s$
1 hour	$3600 ~s$	Acceleration of gravity	$9.8~m/s$
1 mile	$1.610\times 10^3~m$