How far would you have to drill into the Earth, to reach a point where your weight is reduced by 8.0 ? Approximate the Earth as a uniform sphere.
Nevermind, it's just 8% of earth's radius.
To determine how far you would have to drill into the Earth to reach a point where your weight is reduced by 8.0, we need to calculate the distance from the Earth's surface to this point.
Here's the step-by-step explanation on how to do this:
1. First, we need to understand the concept of weight reduction. Weight is directly proportional to the mass of an object, and weight reduction occurs when the gravitational force acting on an object decreases. We know that the gravitational force is inversely proportional to the square of the distance between two objects.
2. Newton's law of universal gravitation can be expressed as: F = (G * m1 * m2) / r^2, where F is the gravitational force between two objects, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
3. For our case, we will assume that the mass of the Earth does not change as we drill into it, and we want to find the distance (r) at which the gravitational force on us is reduced by 8.0.
4. Let's consider two points: the Earth's surface and the point at which we want to find the reduced weight. The mass of Earth at the surface is consistent throughout, so we can cancel it out in our equation.
5. The equation can now be written as: F(earth's surface) / F(drilled point) = (r(Drilled))^2 / (r(Earth's Surface))^2 = 1 - 8.0 /100, where r(Drilled) is the distance from the drilled point to the Earth's center, and r(Earth's Surface) is the radius of the Earth.
6. Simplifying further, we have: (r(Drilled))^2 / (r(Earth's Surface))^2 = 0.92.
7. Taking the square root of both sides of the equation, we get: r(Drilled) / r(Earth's Surface) = √0.92.
8. Rearranging the formula, we find: r(Drilled) = r(Earth's Surface) * √0.92.
9. Finally, we need to multiply the radius of the Earth (approximately 6,371 kilometers or 3,959 miles) by the square root of 0.92 to calculate the distance from the Earth's surface to the point where the weight is reduced by 8.0.
10. Plugging in the values and calculating will give you the final answer.
Keep in mind that this calculation assumes that the Earth is a uniform sphere. The answer will be an approximation, as the Earth's density and composition do vary. Moreover, factors such as Earth's rotation, tectonic activity, and other geophysical phenomena might affect the result.