Physics 8: Homework 2 Additional Questions


In addition to the problems from the book (7.E.1, 7.E.4, 7.P.1, 7.P.2, 7.P.3, 3.P.2, 3.P.4: also available here), here are more problems that are a required part of the assignment:

Useful conversion factors are: 1 Calorie = 4,184 J; 1 kg = 2.2 pounds; 1 liter of water has a mass of 1 kg; density of water is 1000 kg/m3.

  1. A 42 kg kid can't get enough of diving off the 10 meter platform, and keeps going back for more. The energy from each dive makes a splash and stirs up water, all of which ends up as heat that heats the water in the pool.
    1. How much gravitational potential energy is associated with each dive?
    2. Converting this to Calories (use approximate conversion and it should come out to a convenient, round number), how much would this amount of energy heat one liter of water?
    3. If a small pool (with a 10 m platform!) has a volume of 50 cubic meters (50,000 liters), how many dives would this eager kid have to do to heat the entire pool by 1°C?
  2. A pendulum is set into motion with an energy of 1 Joule. If the combination of air resistance and friction at the string contact pull out energy at a rate of 0.002 Watts, about how long will this pendulum maintain its oscillation?
  3. When you drink cold water, the water will be heated to body temperature (37°C). If the heat capacity of water is 1 calorie per gram per °C, (or 1 Calorie per kilogram per °C) how much energy (in Calories) does it take to drink (and then heat up) a liter of water with a starting temperature of 1°C?
  4. If that energy is taken from the fat stores in your body at a conversion rate of 9 Calories per gram, how much water would you have to drink to use up 1 kilogram of fat? Why is this not a popular diet trick (what mass of water would you have to drink)?
  5. Let's say you engage in strenuous exercise, delivering 200 Watts of externally available (i.e., output) power that does not go toward heat. If your body is 25% efficient (most of energy comes out as just heat),
    1. how much total power does your body produce (heat plus external)?
    2. how many seconds would it take to use up 1 Calorie (about 4000 J) of energy?
    3. how many Calories would you use if you kept up this rate for a solid 30 minutes?
  6. If you want to "burn off" an 800,000 Joule (about 200 Calorie) candy bar at 25% efficiency (output energy compared to total energy) via exercise,
    1. how many Joules of output energy must you deliver (just the external energy: leave out the heat)?
    2. how many Joules does it take to lift your body 1 story of a building (assume 4 meters per story, and use your own approximate mass)?
    3. how many stories must you climb to burn off the candy bar?
  7. The main reason you need to use more gas when you are driving at 80 mph than when you drive 55 mph is because of air resistance. How much more energy does it take (as a ratio) to drive 80 mph than 55 mph if you are going a pre-specified distance (e.g., to L.A. from S.D.)? Keep in mind that work is force times distance, and pay attention to how drag force scales with velocity. The ratio represents how much more gas the fast trip will take compared to the slow trip.
  8. Water, being much denser than air, is much harder to push through. Describe the energy requirements of a swimmer using the formula for drag force: Fdrag = 0.5cDρAv2, and assuming the coefficient of drag is cD = 1.0; A = 0.1 m2; v = 1 m/s,
    1. how much drag force does the swimmer experience (plug in values)?
    2. if a full lap is 50 meters, how much energy does one lap take?
    3. if the swimmer does this in 50 seconds (remember velocity was put at 1 m/s), how much power is being delivered?
    4. note: this doesn't include heat—see why swimming is such good exercise? But the example is a bit on the fast side, perhaps.

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