The government claims that you save gasoline by driving slower. If you are planning a trip across the US, is there really a substantial saving of gasoline if you travel 35 mph instead of 70 mph? Explain your answer to this question. Your explanation should include: (a) a brief statement of each of Newton’s three laws and how each is relevant to this question;
(b) a clear explanation of the most relevant forces for this question;
(c) a clear explanation of how the forces relate to gasoline consumption;
(d) a quantitative estimate of the relative gasoline consumption (for 35 mph vs. 70 mph).

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Part f - example: finding two forces (part i) two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. the block in (figure 1) has a mass m=10kg and is being pulled by a force f on a table with coefficient of static friction îľs=0.3. four forces act on it: the applied force f (directed î¸=30â above the horizontal). the force of gravity fg=mg (directly down, where g=9.8m/s2). the normal force n (directly up). the force of static friction fs (directly left, opposing any potential motion). if we want to find the size of the force necessary to just barely overcome static friction (in which case fs=îľsn), we use the condition that the sum of the forces in both directions must be 0. using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: fcosî¸â’îľsn=0 fsinî¸+nâ’mg=0 in order to find the magnitude of force f, we have to solve a system of two equations with both f and the normal force n unknown. use the methods we have learned to find an expression for f in terms of m, g, î¸, and îľs (no n).

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