Physics 261: Problem Set #6

1. (K+K 3.12) Here you can use the rocket equation or the delta t method (I prefer the latter!). Remember that F in the rocket equation is the EXTERNAL force. What is it here? This problem is analogous to the rocket in free space, with a similar type answer. Note that you can immediately determine the mass as a function of time. Don't plug in numbers until the very end; define variables for each of the given quantities, like the relative velocity.
2. (K+K 3.17) You need to know the initial and final velocity of the water, just before and just after hitting the can. The initial velocity is determined by the height, given v0 (it's easiest to use the energy method here!). The final velocity is your assumption; what final velocity will give the most momentum transfer? (Note: The answer clue has at least one typo. If I assume that the weight W = 8N [not kg] (as might happen if one mistyped 98 as 08), I get about 17m.)
3. (K+K 3.18) Use the delta t method to find a differential equation for the velocity (check: it turns out to be independent of M.) Note that dM/dt is not a constant here! Find when dv/dt goes to zero to find the terminal velocity. (This is much easier than solving the equation completely.)
4. (K+K 4.1) How is the force at the top of the loop related to the block's velocity at that point (remember polar coordinates!)? If you know the velocity you need there, energy arguments should tell you the initial height needed. Apply Newton's law for the radial component at that point in the loop. According to the conditions of the problem, how are the normal force and mg related?
5. (K+K 4.3) Remember that you can apply momentum conservation as well as energy conservation, IF APPROPRIATE. In what part can you use momentum conservation (hint: you must assume no external forces act).
6. (K+K 3.20) Another rocket equation or delta t problem (but be careful of the signs if you use the former.) You can check the terminal velocity once again without solving the equation.