A heavy object is suspended from the ceiling using two ropes as shown above. The tension in each rope is 150. N, and the angle each rope makes with the vertical is θ = 35.3o. What is the mass of the object?
Question
A heavy object is suspended from the ceiling using two ropes as shown above. The tension in each rope is 150. N, and the angle each rope makes with the vertical is θ = 35.3o. What is the mass of the object?
Solution
To solve this problem, we need to use some principles of physics, specifically the concepts of forces and equilibrium. Here are the steps:
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Identify the forces acting on the object. In this case, we have the tension in the ropes (T) and the weight of the object (W), which is what we're trying to find.
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Since the object is in equilibrium (not moving), the sum of the forces in the vertical direction must be zero. This means that the vertical components of the tension in the ropes must balance the weight of the object.
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The vertical component of the tension in each rope can be found using trigonometry. It is T cos θ, where T is the tension in the rope (150 N) and θ is the angle the rope makes with the vertical (35.3 degrees). Since there are two ropes, the total vertical force is 2T cos θ.
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Set the total vertical force equal to the weight of the object. The weight of an object is its mass (m) times the acceleration due to gravity (g), which is approximately 9.8 m/s² on the surface of the Earth. So we have 2T cos θ = mg.
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Solve this equation for m, the mass of the object. This gives us m = 2T cos θ / g.
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Plug in the given values: m = 2(150 N) cos(35.3 degrees) / 9.8 m/s².
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Using a calculator, you'll find that the mass of the object is approximately 22.1 kg.
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