Gravity: How Does It Affect Elf Rope Tension?

How does gravity affect the tension in a rope when an elf hangs from it?

When an elf named Sneezy hangs from a rope at the North Pole, he produces a tension of 445 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?

Answer:

The tension Sneezy the elf will produce in the rope at the equator will slightly decrease due to the decrease in gravitational pull. The exact value can be computed by calculating elf's mass based on the tension at North Pole (using T=mg), and then using this to find the tension at the equator.

Gravity plays a significant role in determining the tension in a rope when an object is hanging from it. In this case, when Sneezy the elf hangs from a rope at the North Pole, the tension in the rope is 445 N. However, when the same elf hangs from a similar rope at the earth's equator, the tension in the rope will slightly decrease.

The decrease in tension is due to the difference in gravitational pull between the North Pole and the equator. Since gravity is less at the Earth's equator compared to the North Pole, the tension in the rope will also decrease when Sneezy hangs from it at the equator.

To calculate the tension at the equator, we can first determine Sneezy's mass using the tension at the North Pole and the formula T=mg. Once we have the mass, we can then find the tension at the equator using the formula T=mg with the gravity at the equator.

Without the exact value for the difference in gravity between the North Pole and the equator, we cannot calculate the exact tension at the equator. However, by considering the approximate values of gravity at both locations (9.8 m/s² at the North Pole and 9.78 m/s² at the equator), we can estimate the change in tension.

By rearranging the formula T=mg, we can find the mass of Sneezy at the North Pole. Using this mass, we can then calculate the tension at the equator by considering the difference in gravity between the two locations.

Understanding how gravity affects the tension in a rope when an object is hanging from it is crucial in various scenarios where such calculations are necessary for safety or engineering purposes.