A weightlifter has a basal metabolic rate
of 80.0 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 120-kg barbell 2.00 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?
(e) Could he actually do repetitions at the rate found
in part (d) at the given metabolic level? Explain.
To answer these questions, we need to make use of some given information and formulas related to metabolic rate, work, and energy.
(a) To calculate the time it takes for the weightlifter to work off a 450-Calorie bagel while staying in bed all day, we need to convert the Calorie unit to Joules.
1 Calorie = 4.186 J
So, 450 Calories = 450 * 4.186 J
Next, we need to use the formula for work to calculate the time required.
Work = Power * Time
Power = Metabolic rate = 80.0 W
Time = unknown
Rearranging the formula, we have:
Time = Work / Power
Time = (450 * 4.186 J) / 80.0 W
(b) When the weightlifter is working out, his metabolic rate increases by about 650 W. We will use the same formula as in part (a) to calculate the time required while he is working out.
Power = Metabolic rate with workout = 80.0 W + 650 W
Time = Work / Power
Time = (450 * 4.186 J) / (80.0 W + 650 W)
(c) To calculate the amount of mechanical work necessary to lift the 120-kg barbell 2.00 m, we can use the formula:
Work = Force * Distance
Force = Weight = mass * gravity
Weight = 120 kg * 9.8 m/s^2
Distance = 2.00 m
Work = (120 kg * 9.8 m/s^2) * 2.00 m
(d) To calculate how many times the weightlifter must repeat lifting the barbell per minute to do an amount of mechanical work equivalent to his metabolic rate increase of 650 W during exercise, we first need to convert the metabolic rate from Watts to Joules per minute.
1 W = 1 J/s
So, 650 W = 650 J/s
Next, we can use the formula for work:
Work = Power * Time
Power for lifting the barbell = Work done lifting the barbell / Time lifting the barbell
(e) To determine if the weightlifter could actually do repetitions at the rate found in part (d) at the given metabolic level, we need to compare the power required for repetitions to the metabolic rate increase of 650 W during exercise.
If the power required for repetitions is greater than 650 W, it means he cannot sustain that rate with his current metabolic level.