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A string tied on a roof can bear a max tension of 50 kg wt. The min acceleration that can be acquired by a man of 98 Kg to descend will be?
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A string tied on a roof can bear a max tension of 50 kg wt. The min ac...
Let T be the Tension in the string.
let the acceleration of the descending man be a. It is the weight of the person which gives acceleration to the person. But tension opposes the weight.
m g - T = m a
T = m (g - a)
a = g - T/m
given the maximum tension T, so we get the minimum acceleration. So the person must descend with more acceleration than this.
a = g - 50 * g / 98 = 4.8 m/sec^2 if g = 9.8 m/s^2
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A string tied on a roof can bear a max tension of 50 kg wt. The min ac...
The Problem:
A string tied on a roof can bear a maximum tension of 50 kg wt. We need to calculate the minimum acceleration that can be acquired by a man weighing 98 kg to descend.
Understanding the Problem:
To solve this problem, we need to consider the tension force in the string and the weight of the man. The tension force in the string should not exceed the maximum tension it can bear. The force of gravity acting on the man will accelerate him downwards. We need to find the minimum acceleration required for the man to descend safely.
Solution:
Step 1: Calculate the weight of the man.
Given that the weight of the man is 98 kg, we can calculate his weight using the equation:
Weight = mass × acceleration due to gravity
Weight = 98 kg × 9.8 m/s² = 960.4 N
Step 2: Calculate the maximum tension in the string.
Given that the maximum tension the string can bear is 50 kg wt, we need to convert it to Newtons using the conversion factor:
1 kg wt = 9.8 N
Maximum tension = 50 kg wt × 9.8 N/kg wt = 490 N
Step 3: Calculate the minimum acceleration.
To calculate the minimum acceleration, we need to consider the tension force in the string and the weight of the man. The net force acting on the man should be equal to his weight, as he needs to descend with a constant velocity (zero net force).
Using Newton's second law of motion:
Net force = mass × acceleration
960.4 N - Tension force = 98 kg × acceleration
Since the tension force should not exceed the maximum tension the string can bear (490 N), we can write the equation as:
960.4 N - 490 N = 98 kg × acceleration
Simplifying the equation:
470.4 N = 98 kg × acceleration
Dividing both sides by the mass of the man:
acceleration = 470.4 N / 98 kg ≈ 4.8 m/s²
Therefore, the minimum acceleration that can be acquired by a man weighing 98 kg to descend safely is approximately 4.8 m/s².
Conclusion:
The minimum acceleration required for the man to descend safely is approximately 4.8 m/s². This calculation is based on considering the weight of the man and the maximum tension the string can bear. It ensures that the tension force in the string does not exceed its maximum capacity, allowing the man to descend without any risk.
A string tied on a roof can bear a maximum tension of 50 kg wt. We need to calculate the minimum acceleration that can be acquired by a man weighing 98 kg to descend.
Understanding the Problem:
To solve this problem, we need to consider the tension force in the string and the weight of the man. The tension force in the string should not exceed the maximum tension it can bear. The force of gravity acting on the man will accelerate him downwards. We need to find the minimum acceleration required for the man to descend safely.
Solution:
Step 1: Calculate the weight of the man.
Given that the weight of the man is 98 kg, we can calculate his weight using the equation:
Weight = mass × acceleration due to gravity
Weight = 98 kg × 9.8 m/s² = 960.4 N
Step 2: Calculate the maximum tension in the string.
Given that the maximum tension the string can bear is 50 kg wt, we need to convert it to Newtons using the conversion factor:
1 kg wt = 9.8 N
Maximum tension = 50 kg wt × 9.8 N/kg wt = 490 N
Step 3: Calculate the minimum acceleration.
To calculate the minimum acceleration, we need to consider the tension force in the string and the weight of the man. The net force acting on the man should be equal to his weight, as he needs to descend with a constant velocity (zero net force).
Using Newton's second law of motion:
Net force = mass × acceleration
960.4 N - Tension force = 98 kg × acceleration
Since the tension force should not exceed the maximum tension the string can bear (490 N), we can write the equation as:
960.4 N - 490 N = 98 kg × acceleration
Simplifying the equation:
470.4 N = 98 kg × acceleration
Dividing both sides by the mass of the man:
acceleration = 470.4 N / 98 kg ≈ 4.8 m/s²
Therefore, the minimum acceleration that can be acquired by a man weighing 98 kg to descend safely is approximately 4.8 m/s².
Conclusion:
The minimum acceleration required for the man to descend safely is approximately 4.8 m/s². This calculation is based on considering the weight of the man and the maximum tension the string can bear. It ensures that the tension force in the string does not exceed its maximum capacity, allowing the man to descend without any risk.
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A string tied on a roof can bear a max tension of 50 kg wt. The min acceleration that can be acquired by a man of 98 Kg to descend will be? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A string tied on a roof can bear a max tension of 50 kg wt. The min acceleration that can be acquired by a man of 98 Kg to descend will be? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A string tied on a roof can bear a max tension of 50 kg wt. The min acceleration that can be acquired by a man of 98 Kg to descend will be?.
A string tied on a roof can bear a max tension of 50 kg wt. The min acceleration that can be acquired by a man of 98 Kg to descend will be? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A string tied on a roof can bear a max tension of 50 kg wt. The min acceleration that can be acquired by a man of 98 Kg to descend will be? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A string tied on a roof can bear a max tension of 50 kg wt. The min acceleration that can be acquired by a man of 98 Kg to descend will be?.
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