A weightlifter has a basal metabolic rate of 92.4 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 143 kg barbell 2.40 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?
(a) To calculate the time it takes to work off a 450 Calorie bagel if the weightlifter stays in bed all day, we can use the conversion factor of 1 Calorie = 4.186 J.
First, convert the calories into joules:
450 Cal * 4.186 J/Cal = 1887 J
Next, we need to convert the joules into watts. Since the weightlifter's basal metabolic rate is given in watts, we can divide the energy in joules by the basal metabolic rate to find the time:
1887 J / 92.4 W = 20.45 seconds
To convert this time into hours, divide by the number of seconds in an hour:
20.45 seconds / 3600 s/h = 0.00569 hours
Therefore, it would take approximately 0.00569 hours (or about 20.45 seconds) for the weightlifter to work off a 450 Calorie bagel if he stays in bed all day.
(b) When the weightlifter is working out, his metabolic rate increases by about 650 W. To determine how long it would take him to work off the bagel while working out, we can use the same approach as in part (a), but with the increased metabolic rate of 650 W instead of the basal metabolic rate.
1887 J / 650 W = 2.90 seconds
Dividing by the number of seconds in an hour:
2.90 seconds / 3600 s/h = 0.000805 hours
Therefore, it would take approximately 0.000805 hours (or about 2.9 seconds) for the weightlifter to work off the bagel while working out.
(c) The amount of mechanical work necessary to lift a 143 kg barbell a distance of 2.40 m can be found using the formula:
Work = force * distance
The force required to lift the barbell can be calculated using the gravitational force formula:
Force = mass * acceleration due to gravity
Plugging in the given values:
Force = 143 kg * 9.8 m/s^2 = 1401.4 N
Now we can calculate the work:
Work = 1401.4 N * 2.40 m = 3363.36 J
Therefore, the amount of mechanical work necessary to lift the 143 kg barbell 2.40 m is approximately 3363.36 J.
(d) To calculate how many times per minute the weightlifter must repeat the process of dropping and lifting the barbell to do an amount of mechanical work equivalent to his metabolic rate increase of 650 W, we need to convert the work done per second from watts to joules.
Since 1 watt = 1 joule/second, we can convert 650 W to joules per second by multiplying by 1 J/s per 1 W:
650 W * 1 J/s per 1 W = 650 J/s
To convert this to Joules per minute, we multiply by the number of seconds in a minute:
650 J/s * 60 s/min = 39,000 J/min
To find the number of times the weightlifter must repeat the process, we divide the total work done per minute by the work per repetition:
39,000 J/min / 3363.36 J/rep = 11.6 repetitions per minute
Therefore, the weightlifter must repeat the process approximately 11.6 times per minute to do an amount of mechanical work equivalent to his metabolic rate increase of 650 W during exercise.
To answer these questions, we need to use the formulas related to energy and work. Let's break it down step by step:
(a) To determine the time it takes for the weightlifter to work off a 450 Calorie bagel while staying in bed, we can convert the Calorie value to watts.
First, recall that 1 Calorie is equal to 4.184 joules. Since 1 joule per second is equivalent to 1 watt, we can convert 450 Calories to watts by multiplying it by 4.184:
450 Cal * 4.184 J/Cal = 1881.6 J/s or 1881.6 W
Next, using the weightlifter's basal metabolic rate of 92.4 W, we can find the time required by dividing the energy required (1881.6 W) by the metabolic rate (92.4 W):
Time = Energy Required / Metabolic Rate
Time = 1881.6 W / 92.4 W ≈ 20.37 seconds
(b) If the weightlifter is working out, the additional metabolic rate of 650 W needs to be considered. We can repeat the same calculation as in part (a) using a combined metabolic rate.
Combined Metabolic Rate = Basal Metabolic Rate + Additional Metabolic Rate
Combined Metabolic Rate = 92.4 W + 650 W = 742.4 W
Now, we can calculate the time required using the new combined metabolic rate:
Time = Energy Required / Combined Metabolic Rate
Time = 1881.6 W / 742.4 W ≈ 2.53 seconds
(c) To calculate the amount of mechanical work required to lift the barbell, we can use the formula:
Work = Force * Distance
The weight of the barbell can be converted to force using the formula:
Force = Mass * Gravity
Where mass = 143 kg and gravity is approximately 9.8 m/s^2.
Force = 143 kg * 9.8 m/s^2 = 1401.4 N (approximately)
Now we can calculate the work:
Work = Force * Distance
Work = 1401.4 N * 2.40 m = 3363.36 J
Therefore, the amount of mechanical work necessary to lift the 143 kg barbell 2.40 m is approximately 3363.36 Joules.
(d) To determine how many times the weightlifter must repeat the process of dropping and lifting the barbell in order to achieve a mechanical work equivalent to the metabolic rate increase of 650 W, we need to find the work done in one repetition.
Given that the weightlifter performs the exercise repeatedly, we can assume that he raises the barbell and lowers it with the same speed, performing an equal amount of work on each movement. Therefore, the work done in one repetition is twice the work calculated in part (c), which is:
2 * 3363.36 J = 6726.72 J
To find the number of repetitions per minute, we can first convert the metabolic rate increase from watts to joules/minute:
Number of Repetitions per Minute = Metabolic Rate Increase / Work per Repetition
Number of Repetitions per Minute = 650 J/s / 6726.72 J = 0.0966 repetitions per second
Finally, converting from repetitions per second to repetitions per minute:
0.0966 repetitions/s * 60 s/min = 5.796 repetitions/min (approximately)
Therefore, the weightlifter must repeat the process approximately 5.796 times per minute to achieve an amount of mechanical work equivalent to his metabolic rate increase during exercise.