An object is suspended by two ropes. One rope has a tension of 410 N at an angle of 60 to thehorizontal. The other rope has a tension of 210 N at an angle of 10 to the horizontal.ropes1060410 N210 NobjectThe object is in equilibrium.What is the mass of the object?A 40 kg B 42 kg C 390 kg D 410 kg
Question
An object is suspended by two ropes. One rope has a tension of 410 N at an angle of 60 to thehorizontal. The other rope has a tension of 210 N at an angle of 10 to the horizontal.ropes1060410 N210 NobjectThe object is in equilibrium.What is the mass of the object?A 40 kg B 42 kg C 390 kg D 410 kg
Solution
To solve this problem, we need to use the concept of equilibrium, which states that the sum of forces in any direction is zero when an object is in equilibrium.
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First, we need to resolve the forces into their horizontal and vertical components.
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For the first rope, the horizontal component (Fx1) is 410N * cos(60) = 205N and the vertical component (Fy1) is 410N * sin(60) = 355.5N.
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For the second rope, the horizontal component (Fx2) is 210N * cos(10) = 207.1N and the vertical component (Fy2) is 210N * sin(10) = 36.4N.
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The total vertical force is the sum of the vertical components, which is Fy1 + Fy2 = 355.5N + 36.4N = 391.9N.
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Since the object is in equilibrium, the total vertical force is also equal to the weight of the object, which is mass * gravity.
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Therefore, we can find the mass of the object by dividing the total vertical force by gravity (9.8 m/s^2).
So, the mass of the object is 391.9N / 9.8 m/s^2 = 40 kg.
Therefore, the answer is A) 40 kg.
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