Alexander, who weighs 159lbs , decides to climb Mt. Krumpett, which is 5460ft high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100g bar contains 10g of fat, 40g of protein, and 50g of carbohydrates.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?
How would I even go about solving this problem? The total calories is 450 for a total bar that I calculated, is this right?
yes, 450 Food calories is correct.
I am reluctant to work this out, as the problem is ridiculous. It wants you to assume 100 percent efficiency in conversion of candy to gravational potential energy ...which is a most riciculous assumption...then assume there is no gain of energy (loss of PE) going back down the mountain. All this makes the problem border on science fiction. Also, I wonder if whomever created this problem is competent in science.
All that notwithstanding...
numbercandybars*450FoodCalories*2000calories/FoodCalorie*4.18joules/cal
is the energy from the candy bar.
The change in gravitaional potential energy going up the mountain is mass*g*change in height.
set those equal, and you can solve for the number of candy bars given the silly assumptions above.
I am getting 22.6, but it says that is the wrong answer.
450*2000*4.18=3762000
159*5460*9.8=8507772
I am setting them equal to eachother and getting 2.26, but it says the answer is wrong. Please help.
To determine how many bars Alexander should pack for his journey, we need to calculate the total energy (calories) he would need for both the uphill climb and the return trip. Then, we can divide this total energy by the number of calories provided by each bar to find the number of bars required.
First, let's calculate the total energy needed for the uphill climb. We know that Alexander's weight is 159 lbs and the mountain's height is 5460 ft. We can use the concept of potential energy to calculate the energy needed. The formula for potential energy (PE) is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
To calculate the mass (m) in kilograms, we need to convert Alexander's weight from pounds to kilograms. The conversion factor is 1 lb = 0.453592 kg. So, Alexander's mass is approximately 159 lbs * 0.453592 kg/lb = 72.121128 kg.
Next, we need to calculate the energy (PE) needed for the uphill climb. We'll assume that Alexander's starting position is at sea level, where potential energy is zero. Therefore, the energy needed for the uphill climb is equal to the potential energy gained at the mountain peak.
PE = mgh
PE = 72.121128 kg * 9.8 m/s^2 * 5460 ft
PE = 72.121128 kg * 9.8 m/s^2 * 5460 ft * 0.3048 m/ft (to convert ft to meters)
PE = 237376.64178 Joules
Now, let's calculate the energy needed for the return trip. Since the journey includes a descent from the mountain peak to sea level, the energy needed for the uphill climb is also needed for the return trip.
Total energy needed = energy needed for uphill climb + energy needed for return trip
Total energy needed = 2 * 237376.64178 Joules
Total energy needed = 474753.28356 Joules
Next, let's calculate the number of bars required. You mentioned that each bar contains 450 calories (I assume this is the total energy content). However, to accurately calculate the number of bars needed, we need to account for the different macronutrients listed on the label.
According to the label, each bar weighs 100 grams and contains 10g of fat, 40g of protein, and 50g of carbohydrates. Since 1 gram of fat or carbohydrates provides approximately 9 calories, and 1 gram of protein provides approximately 4 calories, we can use these conversion factors to calculate the total energy content of each bar.
Energy content of 10g fat = 10g * 9 calories/g = 90 calories
Energy content of 40g protein = 40g * 4 calories/g = 160 calories
Energy content of 50g carbohydrates = 50g * 9 calories/g = 450 calories
Total energy content of one bar = 90 calories + 160 calories + 450 calories = 700 calories
Finally, we can calculate the number of bars needed by dividing the total energy needed by the energy content of each bar.
Number of bars needed = Total energy needed / Energy content of one bar
Number of bars needed = 474753.28356 Joules / 700 calories (since 1 calorie ≈ 4.18 Joules, we can convert Joules to calories)
Number of bars needed ≈ 678.219 * 700 (approximating the conversion)
Number of bars needed ≈ 474753.28356 calories / 700 calories
Number of bars needed ≈ 678.219 bars
Since we cannot have a fraction of a bar, Alexander should pack at least 679 bars to provide sufficient energy for the journey, considering the margin of safety.