1.6 Theory Questions
1. (1 pt) If a quantity called A is conserved, what is its derivative dA/dt?
2. (1 pt) You are in a stationary sailboat in a still body of water on a windless day. On the boat, you find a large, powerful fan. What is the most effective way to orient the sail and fan to propel the boat forward? Is is even possible use the fan to move the boat?
3. (1 pt) The moon has no atmosphere, so objects are free to move above the surface without any effects from nonconservative forces. An astronaut finds an ideal trampoline that dissipates no energy and fixes it to the ground to perform an experiment. First, she drops a marble onto the trampoline and measures the maximum height reached after one bounce. Then, she repeats the experiment using a bowling ball dropped from the same height. Does one object bounce higher than the other? Explain.
4. (1 pt) A rocket generates thrust by ejecting particles from its exhaust. During lift-off, the exhaust pushes directly against the surface of the earth. If the rocket is floating in the vacuum of space, far away from any surfaces, can the same engine be used for propulsion?
5. (1 pt) Use the definitions of momentum p? = m?v? and kinetic energy K = 1/2m|v|² to express the kinetic energy in terms of momentum.
6. (1 pts) This problem is a precursor to the analysis of your experiment. As described in the Section 1.3, real collisions are always subject to some energy dissipation. The approximate conservation of mechanical energy can be expressed as E_f = R · E_i where R is the fraction of energy remaining after the collision. Sketch a plot of E_f vs. E_i for R = 1 and R = 0.5 (on the same plot). If energy is entirely conserved, what is the value of R?
7. (1 pt) In most real collisions, colliding objects are free to rotate about their centers of mass. Imagine a collision between two diatomic molecules as depicted below. Initially, the red molecule is stationary and the blue molecule moves with linear momentum p? with no rotational motion. After the collision, both molecules translate in the same direction, but now they also rotate. What caused the molecules to rotate? Is energy still conserved?
