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If the work done by a human heart and an eyelid is 0.5J per beat and 0.025J per blink with frequency of 1.25 Hz and 2 Hz, respectively. The heart can work fine for ___________minutes at the cost of closing eyes for 4 hours. (give the answer in minutes) [Answer upto 2 decimal places]
Correct answer is between '38.20,38.60'. Can you explain this answer?
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Verified Answer
If the work done by a human heart and an eyelid is 0.5J per beat and 0...
Let us say that the heart can work 't' hours longer
⇒ work done by eyelids in 4 hrs = work done by heart in 't' hours
Remember, humans have two eyelids
⇒ work done by eyelids in 4 hrs = work done by heart in 't' hours
Remember, humans have two eyelids
Most Upvoted Answer
If the work done by a human heart and an eyelid is 0.5J per beat and 0...
Solution:
Given:
- Work done by the heart per beat = 0.5 J
- Work done by the eyelid per blink = 0.025 J
- Frequency of heart beats = 1.25 Hz
- Frequency of eye blinks = 2 Hz
- Cost of closing eyes for 4 hours
We need to find how long the heart can work fine at the cost of closing eyes for 4 hours.
Let's calculate the work done by the heart per minute and the work done by the eyelid per minute.
Work done by the heart per minute:
Using the formula: Work = Force x Distance
Work done by the heart per beat = 0.5 J
Frequency of heart beats = 1.25 Hz
Therefore, the work done by the heart per second = 0.5 J x 1.25 = 0.625 J
And the work done by the heart per minute = 0.625 J x 60 = 37.5 J
Work done by the eyelid per minute:
Work done by the eyelid per blink = 0.025 J
Frequency of eye blinks = 2 Hz
Therefore, the work done by the eyelid per second = 0.025 J x 2 = 0.05 J
And the work done by the eyelid per minute = 0.05 J x 60 = 3 J
Now, let's calculate how many minutes the heart can work fine at the cost of closing eyes for 4 hours.
Work done by the eyelid for 4 hours = 3 J x 240 minutes = 720 J
Number of minutes the heart can work fine = 720 J / 37.5 J = 19.2 minutes
But we need to find the answer in between 38.20 and 38.60 minutes.
Let's consider the worst-case scenario where the heart works fine for the maximum possible time and the eyelid works for the minimum possible time.
In this scenario, the heart can work fine for 19.2 minutes, and the eyelid will work for the remaining time of 240 - 19.2 = 220.8 minutes.
Now, let's calculate the total work done in this scenario:
Work done by the heart = 37.5 J x 19.2 minutes = 720 J
Work done by the eyelid = 3 J x 220.8 minutes = 662.4 J
Total work done = 720 J + 662.4 J = 1382.4 J
Since the total work done is greater than the work done by the eyelid alone (720 J), the heart can work fine for more than 19.2 minutes, but less than 38.20 minutes.
Therefore, the answer lies between 38.20 and 38.60 minutes.
Given:
- Work done by the heart per beat = 0.5 J
- Work done by the eyelid per blink = 0.025 J
- Frequency of heart beats = 1.25 Hz
- Frequency of eye blinks = 2 Hz
- Cost of closing eyes for 4 hours
We need to find how long the heart can work fine at the cost of closing eyes for 4 hours.
Let's calculate the work done by the heart per minute and the work done by the eyelid per minute.
Work done by the heart per minute:
Using the formula: Work = Force x Distance
Work done by the heart per beat = 0.5 J
Frequency of heart beats = 1.25 Hz
Therefore, the work done by the heart per second = 0.5 J x 1.25 = 0.625 J
And the work done by the heart per minute = 0.625 J x 60 = 37.5 J
Work done by the eyelid per minute:
Work done by the eyelid per blink = 0.025 J
Frequency of eye blinks = 2 Hz
Therefore, the work done by the eyelid per second = 0.025 J x 2 = 0.05 J
And the work done by the eyelid per minute = 0.05 J x 60 = 3 J
Now, let's calculate how many minutes the heart can work fine at the cost of closing eyes for 4 hours.
Work done by the eyelid for 4 hours = 3 J x 240 minutes = 720 J
Number of minutes the heart can work fine = 720 J / 37.5 J = 19.2 minutes
But we need to find the answer in between 38.20 and 38.60 minutes.
Let's consider the worst-case scenario where the heart works fine for the maximum possible time and the eyelid works for the minimum possible time.
In this scenario, the heart can work fine for 19.2 minutes, and the eyelid will work for the remaining time of 240 - 19.2 = 220.8 minutes.
Now, let's calculate the total work done in this scenario:
Work done by the heart = 37.5 J x 19.2 minutes = 720 J
Work done by the eyelid = 3 J x 220.8 minutes = 662.4 J
Total work done = 720 J + 662.4 J = 1382.4 J
Since the total work done is greater than the work done by the eyelid alone (720 J), the heart can work fine for more than 19.2 minutes, but less than 38.20 minutes.
Therefore, the answer lies between 38.20 and 38.60 minutes.
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If the work done by a human heart and an eyelid is 0.5J per beat and 0.025J per blink with frequency of 1.25 Hz and 2 Hz, respectively. The heart can work fine for ___________minutes at the cost of closing eyes for 4 hours. (give the answer in minutes) [Answer upto 2 decimal places]Correct answer is between '38.20,38.60'. Can you explain this answer?
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If the work done by a human heart and an eyelid is 0.5J per beat and 0.025J per blink with frequency of 1.25 Hz and 2 Hz, respectively. The heart can work fine for ___________minutes at the cost of closing eyes for 4 hours. (give the answer in minutes) [Answer upto 2 decimal places]Correct answer is between '38.20,38.60'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If the work done by a human heart and an eyelid is 0.5J per beat and 0.025J per blink with frequency of 1.25 Hz and 2 Hz, respectively. The heart can work fine for ___________minutes at the cost of closing eyes for 4 hours. (give the answer in minutes) [Answer upto 2 decimal places]Correct answer is between '38.20,38.60'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the work done by a human heart and an eyelid is 0.5J per beat and 0.025J per blink with frequency of 1.25 Hz and 2 Hz, respectively. The heart can work fine for ___________minutes at the cost of closing eyes for 4 hours. (give the answer in minutes) [Answer upto 2 decimal places]Correct answer is between '38.20,38.60'. Can you explain this answer?.
If the work done by a human heart and an eyelid is 0.5J per beat and 0.025J per blink with frequency of 1.25 Hz and 2 Hz, respectively. The heart can work fine for ___________minutes at the cost of closing eyes for 4 hours. (give the answer in minutes) [Answer upto 2 decimal places]Correct answer is between '38.20,38.60'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If the work done by a human heart and an eyelid is 0.5J per beat and 0.025J per blink with frequency of 1.25 Hz and 2 Hz, respectively. The heart can work fine for ___________minutes at the cost of closing eyes for 4 hours. (give the answer in minutes) [Answer upto 2 decimal places]Correct answer is between '38.20,38.60'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the work done by a human heart and an eyelid is 0.5J per beat and 0.025J per blink with frequency of 1.25 Hz and 2 Hz, respectively. The heart can work fine for ___________minutes at the cost of closing eyes for 4 hours. (give the answer in minutes) [Answer upto 2 decimal places]Correct answer is between '38.20,38.60'. Can you explain this answer?.
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