Burning Calories Weight loss is a major industry in the United States. Many peop

Question

Burning Calories

Weight loss is a major industry in the United States. Many people are constantly counting calories. We need to be careful, since the usage of calorie in food is often misused. Calories reported on food labels are actually kilocalories (kcal). One kilocalorie equals 1000 calories, or is the amount of energy required to raise the temperature of one liter of water by 1°C. If you diet consists of 2000 kcal per day, your body will convert 350,000 J/hr into heat or work.

An energy balance shows that there are only two ways to lose weight (not counting water loss). First, you can reduce the calorie intake. Second, you can increase your caloric expenditure. Analyze the following situations, assuming that fat contains approximately 7700 kcal/kg.

If a normal diet containing 2400 kcal/day is reduced to 500 kcal/day, how many days does it take to lose 1 lbm of fat?

How many miles would you have to run to lose 1 lbm of fat if running at a moderate pace of 12 km/hr expends 400 kJ/km?

If two joggers each run 10 km/day, with one running at a pace of 5 kg/hr and the other running at a pace of 10 km/hr, which will lose more weight?

Explanation / Answer

Part -1

1 Kg of fat = 7700 Kcal of energy (As given in problem)

Hence, 1 lbm of fat = 0.45 x 7700 = 3465 Kcal (since 1 lb = 0.45 kg)

Now the reduction in energy in diet per day = ( 2400 - 500) = 1900 Kcal

No of days required to loss 1 lbm fat = 3465/1900 = 1.82 days

Nearly 2 days.

Part - 2

400 KJ/Km = 153.857 Kcal/mile (Since 1 KJ = 0.24 Kcal, 1 Km = 0.6213 mile)

and 12 km/hr = 7.46 mile / hr

1 lbm of Fat = 3465 Kcal

153.857 Kcal of fat loss by running 7.46 mile

1 Kcal of fat loss by running 7.46 / 153.857 mile

Hence , 3465 Kcal of fat loss by running = ( 7.46 x 3465) / 153.857 = 168 mile

Part - 3

Distance is 10 km

1st jogger covered the distance in = 10/5 = 2 hr

2nd jogger covered the distance in = 10/10 = 1 hr

Since the 2nd jogger is running at a faster speed, his oxygen intake will be greater and so his heart pump rate .As a result he will lose more weight.

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