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?

I am not going to do this for you. If you really do not know how to go about it here is a recipe:

1. convert 450 food calories which is 450,000 physics calories to joules.
http://www.rapidtables.com/convert/energy/Calorie_to_Joule.htm

Joules/second sleeping = 64.6
64.6 Joules/second * t = Joules per bagel from above
t is in seconds so divide it by 3600 to get hours (a answer)

2. Joules/ second while working out is
64.6 + 650
so get number of seconds for the Joules from 1. above. again divide by 3600 for hours

3. m g h = 126 * 9.8 * 2.1 (C answer)

m g h /t in seconds = 650 Joules/s or watts
t is the time to lift it in seconds

t/60 = time to lift in minutes
so 60/t = answer in lifts/ minute

Thank you i tried doing it a million different ways but kept making a mistake somewhere i really appreciate it this truly helped me understand.

To solve these problems, we need to use the following formula:

Work = Power * Time

First, let's convert the units:

1 Calorie (Cal) = 4.18 Joules (J)

(a) To work off a 450 Calorie bagel while staying in bed, we need to find the time it takes using the weightlifter's basal metabolic rate:
Work = Power * Time
450 Cal * 4.18 J/Cal = 1878 J
64.6 W * Time = 1878 J
Time = 1878 J / 64.6 W

(b) To work off the same bagel while working out, we need to find the time it takes using the increased metabolic rate:
Work = Power * Time
450 Cal * 4.18 J/Cal = 1878 J
(64.6 + 650) W * Time = 1878 J
Time = 1878 J / (64.6 + 650) W

(c) The work required to lift a barbell can be calculated using the formula:
Work = Force * Distance
Work = 126 kg * 9.8 m/s^2 * 2.10 m

(d) To find the number of lifts per minute, we need to convert the increase in metabolic rate to joules:
Power = 650 W = 650 J/s

Then, we need to calculate the work done per lift:
Work per lift = Force * Distance
Work per lift = 126 kg * 9.8 m/s^2 * 2.10 m

Finally, we can determine the number of lifts per minute:
Number of lifts per minute = Power / Work per lift

Let's calculate these values step-by-step:

(a) Time = 1878 J / 64.6 W

(b) Time = 1878 J / (64.6 + 650) W

(c) Work = 126 kg * 9.8 m/s^2 * 2.10 m

(d) Number of lifts per minute = Power / Work per lift

To answer these questions, we will need to use the concepts of metabolic rate, energy expenditure, and work.

(a) To calculate the time it takes for the weightlifter to work off the 450 Calorie bagel while staying in bed, we need to convert the Calorie unit to Joules. Each Calorie is equivalent to 4.184 Joules. So, the bagel contains 450 * 4.184 = 1884 Joules.

The weightlifter's basal metabolic rate is given as 64.6 W, which means he burns 64.6 Joules per second. We can find the time it takes to burn off the bagel by dividing the energy content of the bagel by the metabolic rate: 1884 / 64.6 ≈ 29.14 seconds.

To convert this time to hours, divide it by 3600 (the number of seconds in an hour): 29.14 / 3600 ≈ 0.0081 hours.

Therefore, it takes the weightlifter approximately 0.0081 hours (or about 30 seconds) to work off the 450 Calorie bagel while staying in bed.

(b) When the weightlifter is working out, his metabolic rate increases by 650 W. To calculate the time it takes to work off the bagel while working out, we use the new metabolic rate (64.6 W + 650 W = 714.6 W).

Following the same process as in part (a), we can find the time it takes to burn off the bagel with the increased metabolic rate: 1884 / 714.6 ≈ 2.63 seconds.

Converting this time to hours: 2.63 / 3600 ≈ 0.0007 hours.

Therefore, it takes the weightlifter approximately 0.0007 hours (or about 3 seconds) to work off the bagel while working out.

(c) To calculate the amount of mechanical work necessary to lift the 126 kg barbell over a 2.10 m height, we use the equation: work = force * distance.

The force required to lift the barbell is equal to its weight, which can be calculated using the formula: weight = mass * acceleration due to gravity.

The acceleration due to gravity is approximately 9.8 m/s^2. So, the weight of the barbell is: weight = 126 kg * 9.8 m/s^2 = 1234.8 N.

Now, we can calculate the work: work = force * distance = 1234.8 N * 2.10 m ≈ 2592.48 Joules.

Therefore, the amount of mechanical work necessary to lift the 126 kg barbell 2.10 m is approximately 2592.48 Joules.

(d) To find out how many times per minute the weightlifter must lift and drop the barbell to do an amount of mechanical work equivalent to his metabolic rate increase of 650 W, we need to calculate the work done per repetition.

Given that the metabolic rate increase is 650 W and the time for each repetition is 1 minute (60 seconds), the work done per repetition is: work per repetition = metabolic rate increase * time per repetition = 650 W * 60 s = 39,000 Joules.

Now, we can calculate the number of repetitions needed to do the same amount of work as the metabolic rate increase: repetitions = total work / work per repetition = 2592.48 Joules / 39,000 Joules ≈ 0.0664 repetitions (since one repetition is not possible).

Therefore, the weightlifter needs to repeat the process approximately 0.0664 times per minute to do an amount of mechanical work equivalent to his metabolic rate increase of 650 W during exercise.