how far from the center of the earth would a person with a weight of 469N on earth have to be to have a weight off 55.4N?
weight decreases as the square of distance, so since the weight ratio is
55.4/469 = 0.1181
the distance ratio will have to be
1/√.1181 = 2.909
so, what's 2.909 times the earth's radius?
To determine the distance from the center of the Earth where a person would have a weight of 55.4N, we need to understand the concept of gravity and how it changes with distance.
First, let's understand that weight is the force exerted on an object due to gravity. On Earth, the weight of an object is directly proportional to the mass of the object and the acceleration due to gravity. The formula we can use to calculate weight is:
Weight = mass * acceleration due to gravity
On Earth, the acceleration due to gravity is approximately 9.8 m/s². So, for the person with a weight of 469N on Earth, we can rewrite the equation as:
469N = mass * 9.8 m/s²
To calculate the mass, we divide both sides of the equation by 9.8:
mass = 469N / 9.8 m/s²
mass ≈ 47.86 kg
Now, let's consider the person's weight at a different distance from the center of the Earth, where they have a weight of 55.4N. We know that weight is directly proportional to the mass and acceleration due to gravity. However, the acceleration due to gravity changes with distance from the center of the Earth.
To determine the distance at which the person has a weight of 55.4N, we need to use the concept of the inverse square law. According to this law, the strength of gravity decreases with the square of the distance. Mathematically, it can be expressed as:
g₁ / g₂ = (r₂ / r₁)²
Where:
g₁ and g₂ are the acceleration due to gravity at distances r₁ and r₂ respectively.
We can rearrange the equation to solve for the distance r₂ as:
r₂ = √((g₁ / g₂) * r₁²)
At the surface of the Earth (r₁), the acceleration due to gravity is 9.8 m/s² (g₁), and the weight is 469N (which we calculated as the person's weight on Earth). To find the distance (r₂) where the weight is 55.4N (g₂), we can plug these values into the formula:
r₂ = √((9.8 m/s² / 55.4N) * (radius of the Earth)²)
The radius of the Earth is approximately 6,371 km or 6,371,000 meters. Plugging in the values:
r₂ = √((9.8 m/s² / 55.4N) * (6,371,000 m)²)
r₂ ≈ 516,687 meters or 516.7 km
Therefore, a person with a weight of 469N on Earth would need to be approximately 516.7 km from the center of the Earth to have a weight of 55.4N.