The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 6.58 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 4.78 m from the center of the circle.
Answers
Answer:1.37
Explanation:
Given
Length of Blade
Let blades be rotating at an angular velocity of
centripetal acceleration at any radial distance r is given by
at
at
thus
Final answer:
Centripetal acceleration depends inversely on the radius. The ratio of the centripetal accelerations at the end of the blade and at 4.78m from the center is approximately 0.73.
Explanation:
The centripetal acceleration of an object moving in a circle of radius r is given by the formula ac = v²/r, where v is the tangential velocity of the object. In this scenario, the velocity at both points on the blade is the same, as the blade is rotating as a whole.
Therefore, the centripetal acceleration on the blade at any point is inversely proportional to the radius from the center of the circle to that point.
So, the ratio of the centripetal acceleration at the end of the blade (6.58 m from the center) to the centripetal acceleration at a point located 4.78 m from the center, is the inverse ratio of their distances from the center. Therefore, the ratio is 4.78/6.58 which approximately equals 0.73.
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