Question

You decide to visit Santa Claus at the north pole to put in a good word about your splendid behavior throughout the year. While there, you notice that the elf Sneezy, when hanging from a rope, produces a tension of 485 N

in the rope. If Sneezy hangs from a similar rope while delivering presents at the earth's equator, what will the tension in it be? (Recall that the earth is rotating about an axis through its north and south poles.)

Answer 1

To solve this problem, we need to consider the effect of the earth's rotation on the tension in the rope. When Sneezy is hanging from a rope at the North Pole, he is not affected by the rotation of the earth because he is located at the axis of rotation. However, when he is hanging from a rope at the equator, he is moving at a tangential velocity of approximately 1670 km/h due to the rotation of the earth.

This tangential velocity creates a centrifugal force that acts on Sneezy and reduces the tension in the rope. The magnitude of this force can be calculated using the formula:

F = m * v^2 / r

where F is the centrifugal force, m is the mass of Sneezy, v is his tangential velocity, and r is the radius of the earth.

Assuming that Sneezy has a mass of 50 kg and the radius of the earth is 6,371 km, we can calculate the centrifugal force as follows:

F = 50 kg * (1670 km/h)^2 / (6371 km)

= 344 N

Therefore, the tension in the rope when Sneezy is hanging from it at the equator will be:

T = 485 N - 344 N

= 141 N

So the tension in the rope will be reduced by 344 N due to the centrifugal force caused by the earth's rotation.

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