Gravitational Attraction at Equator

[Felin]

The weight of a person at the equator, as determined by a spring balance, is 725N.

By how much does this differ from the true force of gravitational attraction at the same point? Assume that the Earth is spherically symmetric.

This question is on a section that we havn't even done yet so I am completely lost as to what to do to figure this one out.

 

[Dorothy Weglend]

There is an additonal force at the equator that isn't present at the poles. Once you realize what that is, you can calculate its magnitude.

Dorothy

 

[kyle8921]

I would like to clarify that the weight measured by a spring balance is not the same as the force of gravitational attraction. Weight is a measure of the force of gravity acting on an object, but it also takes into account other factors such as the mass of the object and its location on Earth's surface. On the other hand, the force of gravitational attraction is solely determined by the mass of the Earth and the distance between an object and its center.

In this case, the weight of a person at the equator would be slightly less than the true force of gravitational attraction at the same point. This is because the Earth is not a perfect sphere, it bulges slightly at the equator due to its rotation. This bulging results in a slightly longer distance between the center of the Earth and an object at the equator, causing a slightly weaker force of gravitational attraction compared to an object at the poles.

To calculate the difference between the weight measured by the spring balance and the true force of gravitational attraction at the equator, we would need to know the mass of the Earth and the exact location of the person on the equator. However, assuming that the Earth is spherically symmetric, we can estimate the difference to be around 0.5%. This means that the true force of gravitational attraction at the equator would be approximately 722N, while the weight measured by the spring balance is 725N.

It's important to note that this difference is very small and would not have a significant impact on everyday activities. However, it highlights the importance of understanding the difference between weight and gravitational attraction in scientific measurements.