A weightlifter has a basal metabolic rate of 64.6 W. As he is working out, his metabolic rate increases by about 650 W.
(a) How many hours does it take him to work off a 450 Calorie bagel if he stays in bed all day?
(b) How long does it take him if he's working out?
(c) Calculate the amount of mechanical work necessary to lift a 126 kg barbell 2.10 m.
(d) He drops the barbell to the floor and lifts it repeatedly. How many times per minute must he repeat this process to do an amount of mechanical work equivalent to his metabolic rate increase of 650 W during exercise?
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To answer these questions, we need to understand the formulas and conversions involved.
(a) To calculate the time to work off a 450 Calorie bagel while staying in bed, we first need to convert the Calorie value to work done in joules.
1 Calorie is equal to 4,184 joules, so 450 Calories is equal to (450 * 4,184) joules.
Next, divide the total work done by the metabolic rate to get the time taken.
Time = Work / Metabolic Rate
Substituting the values, Time = (450 * 4,184) joules / 64,600 joules per second.
To convert the result to hours, divide it by 3,600 (the number of seconds in an hour).
So, the time taken to work off the bagel while staying in bed is (450 * 4,184) / (64,600 * 3,600) hours.
(b) To calculate the time taken to work off the bagel while working out, we need to consider both the basal metabolic rate (BMR) and the increased metabolic rate during exercise.
The total metabolic rate during exercise is the sum of BMR and the increase, which is 64.6 W + 650 W.
Now we can follow the same steps as in part (a) to calculate the time taken, using the new total metabolic rate.
Time = Work / (BMR + Increase in metabolic rate)
Substituting the values, Time = (450 * 4,184) joules / (64.6 W + 650 W).
To convert the result to hours, divide it by 3,600.
So, the time taken to work off the bagel while working out is (450 * 4,184) / ((64.6 + 650) * 3,600) hours.
(c) To calculate the amount of mechanical work necessary to lift the barbell, we use the formula:
Work = Force * Distance
The force can be calculated using the weight of the barbell and acceleration due to gravity:
Force = Mass * Acceleration due to gravity
Substituting the values, Force = 126 kg * 9.8 m/s^2.
Next, calculate the work done:
Work = Force * Distance
Substituting the values, Work = (126 kg * 9.8 m/s^2) * 2.10 m.
(d) To calculate the number of repetitions required to do an amount of mechanical work equivalent to the metabolic rate increase during exercise, we need to know the definition of mechanical work during weightlifting.
Mechanical work is calculated using the following formula:
Work = Force * Distance
To lift the barbell, the force required is the weight of the barbell (mass * acceleration due to gravity).
The work done during each repetition is equal to the total work done during exercise divided by the number of repetitions:
Work per repetition = Total work / Number of repetitions
The number of repetitions per minute is then calculated by dividing the metabolic rate increase by the work per repetition and multiplying by 60 (to convert from seconds to minutes):
Repetitions per minute = (Metabolic rate increase / Work per repetition) * 60.