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3 kg of wet clothes are hung on the middle of a clothesline with posts 6ft apart. The clothesline sags down by 3 feet. What is the total tension upon the clothesline?
- a)15√(2) N
- b)60√(2) N
- c)30√(2) N
- d)15√(2)/2 N
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
3 kg of wet clothes are hung on the middle of a clothesline with posts...
- If the clothes are hung in the middle of the line, this means we can treat the horizontal portion of a triangle as 3ft, and with the line sagging down 3ft, we can treat this as a 45-45-90 triangle, since the vertical and horizontal sides are equal.
- If the weight of the clothes pulls the line into the equivalent of a 45-45-90 triangle triangle, we can treat the force vectors accordingly.
- Because there are two anchor points for the clothesline, we can assume the horizontal components cancel each other out. The vertical component, 30N (F=ma, using 10m/s2 for the gravitational constant) should then equal Tcos45 + Tcos45, or 2Tcos45 since we have a 45-45-90 triangle. (sin45 could also be used, remember that cos45 = sin45)
- Solve for T:
2∗T∗cos 45 = 30
T∗cos 45 = 15
T∗(1/√(2) T = 15
T = 15√(2)
Most Upvoted Answer
3 kg of wet clothes are hung on the middle of a clothesline with posts...
Given data:
- Weight of wet clothes: 3 kg
- Distance between posts: 6 ft
- Sag in the clothesline: 3 ft
Calculating the tension:
- The weight of the clothes creates a vertical force downward.
- The tension in the clothesline creates a force upward.
- The sag in the clothesline creates a horizontal force component.
Vertical forces:
- The weight of the clothes creates a force of 3 kg * 9.8 m/s^2 = 29.4 N downward.
- The tension in the clothesline must balance this force, so the tension is also 29.4 N upward.
Horizontal forces:
- The sag in the clothesline creates a horizontal force component that must also be balanced by the tension in the clothesline.
- The sag is 3 ft, so the horizontal force component is 3 ft * 9.8 m/s^2 = 29.4 N.
- The total horizontal force is 2 * 29.4 N = 58.8 N.
Calculating the total tension:
- The total tension in the clothesline is found by combining the vertical and horizontal components.
- Using Pythagoras' theorem, T^2 = 29.4^2 + 58.8^2 = 3061.2.
- T = sqrt(3061.2) = 55.31 N.
- The total tension upon the clothesline is 55.31 N, which is approximately 15√2 N.
Therefore, the correct answer is option A) 15√2 N.
- Weight of wet clothes: 3 kg
- Distance between posts: 6 ft
- Sag in the clothesline: 3 ft
Calculating the tension:
- The weight of the clothes creates a vertical force downward.
- The tension in the clothesline creates a force upward.
- The sag in the clothesline creates a horizontal force component.
Vertical forces:
- The weight of the clothes creates a force of 3 kg * 9.8 m/s^2 = 29.4 N downward.
- The tension in the clothesline must balance this force, so the tension is also 29.4 N upward.
Horizontal forces:
- The sag in the clothesline creates a horizontal force component that must also be balanced by the tension in the clothesline.
- The sag is 3 ft, so the horizontal force component is 3 ft * 9.8 m/s^2 = 29.4 N.
- The total horizontal force is 2 * 29.4 N = 58.8 N.
Calculating the total tension:
- The total tension in the clothesline is found by combining the vertical and horizontal components.
- Using Pythagoras' theorem, T^2 = 29.4^2 + 58.8^2 = 3061.2.
- T = sqrt(3061.2) = 55.31 N.
- The total tension upon the clothesline is 55.31 N, which is approximately 15√2 N.
Therefore, the correct answer is option A) 15√2 N.
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3 kg of wet clothes are hung on the middle of a clothesline with posts 6ft apart. The clothesline sags down by 3 feet. What is the total tension upon the clothesline?a)15√(2) Nb)60√(2) Nc)30√(2) Nd)15√(2)/2 NCorrect answer is option 'A'. Can you explain this answer? for MCAT 2025 is part of MCAT preparation. The Question and answers have been prepared according to the MCAT exam syllabus. Information about 3 kg of wet clothes are hung on the middle of a clothesline with posts 6ft apart. The clothesline sags down by 3 feet. What is the total tension upon the clothesline?a)15√(2) Nb)60√(2) Nc)30√(2) Nd)15√(2)/2 NCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for MCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 kg of wet clothes are hung on the middle of a clothesline with posts 6ft apart. The clothesline sags down by 3 feet. What is the total tension upon the clothesline?a)15√(2) Nb)60√(2) Nc)30√(2) Nd)15√(2)/2 NCorrect answer is option 'A'. Can you explain this answer?.
3 kg of wet clothes are hung on the middle of a clothesline with posts 6ft apart. The clothesline sags down by 3 feet. What is the total tension upon the clothesline?a)15√(2) Nb)60√(2) Nc)30√(2) Nd)15√(2)/2 NCorrect answer is option 'A'. Can you explain this answer? for MCAT 2025 is part of MCAT preparation. The Question and answers have been prepared according to the MCAT exam syllabus. Information about 3 kg of wet clothes are hung on the middle of a clothesline with posts 6ft apart. The clothesline sags down by 3 feet. What is the total tension upon the clothesline?a)15√(2) Nb)60√(2) Nc)30√(2) Nd)15√(2)/2 NCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for MCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 kg of wet clothes are hung on the middle of a clothesline with posts 6ft apart. The clothesline sags down by 3 feet. What is the total tension upon the clothesline?a)15√(2) Nb)60√(2) Nc)30√(2) Nd)15√(2)/2 NCorrect answer is option 'A'. Can you explain this answer?.
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