Answer :
Final answer:
Calculating the moment of inertia for a playground toy with two children on it involves treating the children and seats as point masses and using the formula I = m * r². The total moment of inertia is the sum of individual moments of inertia for both child-seat combinations. The calculated total moment of inertia does not match the answer options given, suggesting a potential mistake in the question or answer choices.
Explanation:
The question is asking for the moment of inertia of a playground toy when two children are sitting on its opposite seats. To calculate this, we will treat the children and the seats as point masses located at the end of the rods with a length of 1.5 m. The moment of inertia for a point mass is given by the equation I = m * r², where m is the mass and r is the distance from the rotation axis.
First, we calculate the moment of inertia for each child and their corresponding seat:
Now we add them together to find the total moment of inertia:
I_total = I1 + I2
Substituting the values and calculating:
I1 = (16 kg + 5.7 kg)(1.5 m)² = (21.7 kg)(2.25 m²) = 48.825 kg·m²
I2 = (24 kg + 5.7 kg)(1.5 m)² = (29.7 kg)(2.25 m²) = 66.825 kg·m²
I_total = 48.825 kg·m² + 66.825 kg·m² = 115.65 kg·m²
However, none of the answer options match this result. It is crucial to double-check calculations and ensure that the given answer options are considered. In this case, it might be a mistake or a typo. Please verify the information and try to recalculate if necessary.
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