Given your recent involvement in international espionage, you're hardly surprised when James Bond appears at your doorstep one evening. You offer him a drink, but in keeping with the politically correct nature of this problem set, you point out to him that he is going to have to do without the usual vodka martini. Nonetheless, he asks that you serve his fruit smoothie "shaken, not stirred". You're only too happy to oblige.
1. You begin to assemble the drink by mixing together strawberries and bananas in a blender. You place those fruits in the blender's plastic container and turn on the motor. A sharp blade attached to the motor spins rapidly in the middle of the plastic container and slices the fruit into tiny pieces. The container is nearly frictionless, so what holds the fruit in place as the blender's spinning blade slices through it?
2. Having chopped up the fruit, it's time to add orange juice and ice. To impress Mr. Bond, you decide to drop the ice into the drink from several feet above it. You release several pieces of ice simultaneously and they fall dramatically into the liquid. Supposing that air resistance has no significant effect on their motion, which pieces of ice fall fastest: large, small, or neither? Justify your answer.
3. It's time for the shake. You put the top on the container and begin to shake it vigorously up and down. As you shake the container, you can feel yourself pushing upward on it as you move it upward and pushing downward on it as you move it downward. At what times are you doing (positive) work on the container: moving it upward, moving it downward, or both? Explain why that is the case.
4. As you reverse directions and begin moving the container downward, the drink inside it often rises upward and hits the top of the container. During those moments, is there a force pushing the drink upward—toward the top of the container? If so, what is that force? If not, what is causing the drink to rise, even though the container is descending?
You've made plans to go mountain biking on Observatory Hill and are about to ride up its side for the first time. For simplicity, we'll assume that the uphill path is straight and has a uniform slope the entire way. You are balancing precariously on your bicycle at the bottom of that path, waiting for this problem to begin.
5. While you are not moving anywhere yet, you are getting tired. Balancing the bicycle without moving is exhausting. As you balance there on the motionless bicycle, are you doing (positive) work, zero work, or negative work on the bicycle? Explain your answer.
6. It's time to start climbing the hill. You push down extra hard on the pedals and you and the bicycle begin to accelerate up the hill. In what direction does the net force on you and the bicycle point during the time when you are accelerating uphill?
7. After a few seconds, you are traveling at a good pace and decide to stop accelerating. You then continue uphill at a constant velocity. While you are going uphill at a constant velocity, what is the net force on you and the bicycle? (Remember that your answer may involve an amount and a direction.)
8. Your friend is also riding a bicycle up Observatory Hill. While you head straight uphill to the top, your friend weaves back and forth on the road. As a result, your friend travels exactly twice as far as you do in the process of climbing the hill. The two of you started and finished at the same place and you both weigh the same amount. Neglecting friction and air resistance, compare the amounts of work the two of you did while climbing the hill: are they the same? Are they different? If different, by what fraction do they differ?