Alexander wants to know exactly how many bars to pack in his backpack for the journey. To provide a margin of safety, he assumes that he will need as much energy for the return trip as for the uphill climb. How many bars should Alexander pack?
Enter the exact answer to two significant figures. Do not round to an integer.
Alexander, who weighs 195 lb, decides to climb Mt. Krumpett, which is 5400 m high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100-g bar contains 10 g of fat, 40 g of protein, and 50 g of carbohydrates. One gram of fat contains 9 Calories, whereas each gram of protein and carbohydrates contains 4 Calories.
To determine how much food to bring, Alexander will need to take into account the energy required to climb the mountain. Gravitational potential energy is the energy stored in an object that is raised to a height. The gravitational potential energy is related to an object's mass m, the height h to which it is raised, and the acceleration due to gravity, g. The relationship is given by
The value of g near Earth's surface is 9.81 m/s2.
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