Physics 131-3 Test 3

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

1. If someone told you the area of a circle was $A=\pi r$, how could you refute them immediately?

2. Consider the view from above of a rotator shown below in the figure. Using a video analysis system you will measure the ($x$,$y$) position of the dot on the rim of the rotator as a function of time. You will then convert that data into the angular position of the dot as a function of time as shown by $\theta$ in the figure. Where do you place the origin of your coordinate system? How do you convert your data to the proper angular position?

   

3. What is the parallel axis theorem? Describe each element or factor in your answer.

4. Recall the egg-drop contest. Suppose you simultaneously drop a bare egg and another egg inserted in your egg-drop device from the same height above the ground. Is the impulse $\Delta p$ for the bare egg bigger, smaller, or the same as impulse for the other egg? Explain. Why does the bare egg break and the other doesn't (usually!)?

5. At the moment after a bullet is fired from a stationary gun, the gun and the bullet have equal and opposite momenta. Which object - the bullet or the gun - has the greater kinetic energy? Explain in the space below and make careful use of any mathematics you need.

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

1.	15 pts.	The final two stages of a spacecraft are separated by detonating explosive bolts holding them together. The masses of the two stages are $m_1$ and $m_2$ and the magnitude of the impulse $\vert\Delta \vec p\vert$ on each stage is $J$. What is the expression (i.e., the equation) for the relative speed of the two stages after they separate in terms of $m_1$, $m_2$, $J$ and any other constants? If $m_1 = 1000~kg$, $m_2=2000~kg$, and $J=1000~Ns$, then with what relative speed do the stages separate after the detonation?
2.	15 pts.	A spinning gas cloud has roughly the shape of a disk with radius $R$ before it collapses to form a spherical star with a radius one-tenth the initial one. What is the ratio of the new rotational kinetic energy to the initial rotational kinetic energy? How much faster does the new star spin versus the original disk? Clearly show which conservation laws apply.
3.	20 pts.	You are an astronaut on the International Space Station (ISS) and you have to go outside to repair a broken antenna. You don your spacesuit with its jet-pack for moving around in the zero-g environment and grab a large, $10-kg$ wrench. The total weight of you and your spacesuit (with attached jet-pack) is $100~kg$. While outside on your EVA (Extra-Vehicular Activity) you decide to go on a joyride with your jet-pack, but end up running out of fuel and stuck about $30~m$ away from the ISS (oopps!). You don't want to call for help because it's too embarrassing and you only have enough air for another 30 minutes. Can you throw the wrench in any particular way so that you will drift back over to the ISS? Explain. What is the slowest speed you would have to throw it to reach the ISS before your air ran out?

Some constants.

Acceleration of gravity ($g$)	$9.8~m/s^2$	Neutron mass	$1.67\times 10^{-27}~kg$
Gravitation constant	$6.67 \times 10^{-11}~N-m^2/kg^2$	Proton mass	$1.67\times 10^{-27}~kg$
Earth's radius	$6.37\times 10^6~m$	$1 ~ u$	$1.67\times 10^{-27}~kg$

Moments of inertia for different objects.