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P O N D E R A B L E S Here, I provide some questions for you to ponder. Regard these as tutorial questions if you are a university student, or as brain fodder if you are reading this book simply to scratch an intellectual itch. Some questions are easy, others are hard. Some are short, others long. In some cases I will provide a hint or partial answer to the question posed; in other cases you are completely on your own. ≤ The hockey stop. Check out the YouTube video at www.youtube.com/watch? v=br8dfnnWL5k&feature=related, which shows how hockey players can stop quickly. They lean backwards and slide with their skate blades perpendicular to their direction of motion. Recall from chapter 2 that moving an ice skate in this direction is very di≈cult; blades are designed so that they won’t move perpendicular to their length. Note the large amount of ice chips sprayed out in front of the rapidly decelerating player. (From the video, it is clear why the ice is resurfaced between periods of a hockey game.) Some professional hockey players make use of this spray to put the opponent’s goalie at a disadvantage during a game. Assume that movement over the ice during a hockey stop can be modeled as sliding friction with a large coe≈cient of friction. From the video, estimate the angle at which the hockey player is leaning back (to prevent himself going head over heals) and from this angle, determine the friction coe≈cient. If the player’s initial speed was 10 ms–1 , how long will it take him to stop? ≤ Skate design. Check out the design of a speed-skater’s boot online. Because speed skating events (on both long and short tracks) proceed in the counterclockwise direction, skaters going around the bends must pass the right skate over the left, but never the left skate over the right. How does this influence the boot design? Contrast speed skaters’ footwear with ice hockey or figure skating skates: in both these sports the left skate may cross over the right skate as much as the other way round. ≤ Drafting. We looked at speed-skating statistics from Vancouver’s 2010 Winter Olympic Games in the figure on page 42. These statistics (medal winners’ 146 PONDERABLES times and the distances covered in each long-track event) are readily available online. How did I estimate athletes’ relative power output from such data? The energy expended by each athlete in skating a distance x is approximately E = Qmv2 + mbv2 x. The first term on the right side is the skater’s kinetic energy; the second term is the work he or she expends in overcoming aerodynamic drag. The drag factor for a single skater is about b = 0.001 m–1 ; you will find that it is 1 ⁄6 less for a team pursuit skater over the course of a race. Show from this (assuming that each skater does his fair share of time leading the team) that, when drafting, a team skater expends only 3 ⁄4 of the average power of a skater who is on his own. ≤ Curling. Derive a natural (realistic and plausible) theory of curling. Award yourself a master’s degree in physics. ≤ An altitude problem. The analysis of technical note 10 led to an equation that describes how race times vary with altitude. There are a number of simplifications that I made for this analysis but did not state explicitly. (For example, I tacitly assumed that an athlete’s speed doesn’t vary much during a race, so that it makes sense to express speed as distance divided by race duration.) Describe some of the other assumptions. Given the simplifications, why is the result believable? Much of applied physics involves making simplifying assumptions that get to the core of a problem without cutting out the essentials—of knowing when and how to simplify. Derive the result, equation (N10.4), from the earlier equations. ≤ Biathlon blues. As we saw in chapter 1, the Winter Olympics sport of biathlon is a combination of cross-country skiing and rifle shooting. The athletes swarm around a course on skis, and then remove their skis and run to a rifle range, where they shoot at a target, before repeating the process. If their shooting score is low, they must do extra laps. The winner is the first skier across the finish line. Given the...

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