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Workers want to suspend a 40kg sign from a ceiling with cables, but the cables they have available are only able to support a maximum 10 N of force before snapping. If they are planning on suspending the cables at a 45° angle, what is the least number of cables that would be sufficient to support the sign without snapping the cables?
- a)40 cables
- b)80 cables
- c)20 cables
- d)60 cables
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Workers want to suspend a 40kg sign from a ceiling with cables, but th...
Since we are given the mass, tension needed, and angles of suspension, and our variable is the number of wires. The vertical component would be Tsin45 x = 400, where x is the number of cables.
Since our maximum tension is 10 N, we can set T to 10 and solve: 10 √(2)/2 x = 400.
Rearranging the equation will give us x = 40√(2). Though you cannot use a calculator, you can automatically eliminate 20 and 40 as answers, because √(2) is greater than 1.
We also know that 40x2=80, and √(2) is less than 2, so we can eliminate 80 as a choice, since 60 is a smaller number while still being able to support the sign.
Since 60 = 1.5 x 40, and √(2) is less than 1.5, we can conclude that 60 cables would be sufficient to support the sign though technically only ~57 cables would be needed.
Most Upvoted Answer
Workers want to suspend a 40kg sign from a ceiling with cables, but th...
Calculating the Tension in the Cables:
To calculate the tension in the cables when the sign is suspended at a 45° angle, we first need to break down the forces acting on the sign. The weight of the sign is 40kg, which can be converted to Newtons by multiplying by the acceleration due to gravity (9.8 m/s^2).
Therefore, weight of the sign = 40 kg * 9.8 m/s^2 = 392 N.
Resolving the Forces:
When the sign is suspended at a 45° angle, the tension in the cables can be resolved into horizontal and vertical components. The vertical component of the tension will support the weight of the sign, while the horizontal component will balance out the tension in the other cables.
Using trigonometry, we can calculate the vertical component of the tension:
Tension (vertical) = Tension * cos(45°) = 10 N * cos(45°) = 7.07 N.
Determining the Number of Cables:
Since each cable can only support a maximum tension of 10 N, and the vertical component of the tension in each cable is 7.07 N, we need to calculate how many cables are required to support the weight of the sign.
Total vertical tension needed to support the sign = 392 N.
Number of cables required = Total vertical tension / Tension per cable = 392 N / 7.07 N ≈ 55.4.
Therefore, the minimum number of cables required to support the sign without snapping is 56 cables, which is closest to option 'D' - 60 cables.
To calculate the tension in the cables when the sign is suspended at a 45° angle, we first need to break down the forces acting on the sign. The weight of the sign is 40kg, which can be converted to Newtons by multiplying by the acceleration due to gravity (9.8 m/s^2).
Therefore, weight of the sign = 40 kg * 9.8 m/s^2 = 392 N.
Resolving the Forces:
When the sign is suspended at a 45° angle, the tension in the cables can be resolved into horizontal and vertical components. The vertical component of the tension will support the weight of the sign, while the horizontal component will balance out the tension in the other cables.
Using trigonometry, we can calculate the vertical component of the tension:
Tension (vertical) = Tension * cos(45°) = 10 N * cos(45°) = 7.07 N.
Determining the Number of Cables:
Since each cable can only support a maximum tension of 10 N, and the vertical component of the tension in each cable is 7.07 N, we need to calculate how many cables are required to support the weight of the sign.
Total vertical tension needed to support the sign = 392 N.
Number of cables required = Total vertical tension / Tension per cable = 392 N / 7.07 N ≈ 55.4.
Therefore, the minimum number of cables required to support the sign without snapping is 56 cables, which is closest to option 'D' - 60 cables.
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Workers want to suspend a 40kg sign from a ceiling with cables, but the cables they have available are only able to support a maximum 10 N of force before snapping. If they are planning on suspending the cables at a 45° angle, what is the least number of cables that would be sufficient to support the sign without snapping the cables?a)40 cablesb)80 cablesc)20 cablesd)60 cablesCorrect answer is option 'D'. 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 Workers want to suspend a 40kg sign from a ceiling with cables, but the cables they have available are only able to support a maximum 10 N of force before snapping. If they are planning on suspending the cables at a 45° angle, what is the least number of cables that would be sufficient to support the sign without snapping the cables?a)40 cablesb)80 cablesc)20 cablesd)60 cablesCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for MCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Workers want to suspend a 40kg sign from a ceiling with cables, but the cables they have available are only able to support a maximum 10 N of force before snapping. If they are planning on suspending the cables at a 45° angle, what is the least number of cables that would be sufficient to support the sign without snapping the cables?a)40 cablesb)80 cablesc)20 cablesd)60 cablesCorrect answer is option 'D'. Can you explain this answer?.
Workers want to suspend a 40kg sign from a ceiling with cables, but the cables they have available are only able to support a maximum 10 N of force before snapping. If they are planning on suspending the cables at a 45° angle, what is the least number of cables that would be sufficient to support the sign without snapping the cables?a)40 cablesb)80 cablesc)20 cablesd)60 cablesCorrect answer is option 'D'. 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 Workers want to suspend a 40kg sign from a ceiling with cables, but the cables they have available are only able to support a maximum 10 N of force before snapping. If they are planning on suspending the cables at a 45° angle, what is the least number of cables that would be sufficient to support the sign without snapping the cables?a)40 cablesb)80 cablesc)20 cablesd)60 cablesCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for MCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Workers want to suspend a 40kg sign from a ceiling with cables, but the cables they have available are only able to support a maximum 10 N of force before snapping. If they are planning on suspending the cables at a 45° angle, what is the least number of cables that would be sufficient to support the sign without snapping the cables?a)40 cablesb)80 cablesc)20 cablesd)60 cablesCorrect answer is option 'D'. Can you explain this answer?.
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