The weight of an object above the surface of the Earth varies inversely with the square of the distance from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from Earth’s center, what would it weight if it were 4,040 miles from Earth’s center?

Round to two decimals. 

The weight \( W \) of an object varies inversely with the square of the distance \( d \) from the center of the Earth. This relationship can be expressed as:

\[
W \propto \frac{1}{d^2}
\]

or in equation form:

\[
W = \frac{k}{d^2}
\]

where \( k \) is a constant.

### Step 1: Find the constant \( k \)
We know the weight \( W \) is 50 pounds when the distance \( d \) is 3,960 miles.

\[
50 = \frac{k}{3960^2}
\]

Solving for \( k \):

\[
k = 50 \times 3960^2
\]

\[
k = 50 \times 15,681,600
\]

\[
k = 784,080,000
\]

### Step 2: Calculate the weight at 4,040 miles
Now we use the constant \( k \) to find the new weight \( W \) when \( d = 4040 \) miles:

\[
W = \frac{784,080,000}{4040^2}
\]

Calculating \( 4040^2 \):

\[
4040^2 = 16,320,400
\]

Now substitute back:

\[
W = \frac{784,080,000}{16,320,400}
\]

\[
W \approx 48.04
\]

Therefore, the weight of the object at 4,040 miles from the Earth's center would be approximately **48.04 pounds**.

Would you like further details, or do you have any questions?

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### Related Questions
1. How would the weight change if the object were placed 5,000 miles from Earth’s center?
2. How does the inverse square law affect the gravitational force experienced by objects at various distances from the Earth?
3. How is the constant \( k \) affected if we change the weight at the initial distance?
4. What is the weight of the object if it’s placed at twice the original distance from the Earth’s center?
5. How can the concept of inverse square law be applied to fields other than gravity, like light intensity?

### Tip:
Remember that inverse square relationships are common in physics and describe how a quantity diminishes quickly as you move away from the source!

The weight of an object above the surface of the Earth varies inversely with the square of the distance from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from Earth’s center, what would it weight if it were 4,040 miles from Earth’s center? Round to two decimals.

Learn how to calculate the change in weight of an object based on its distance from Earth’s center using the inverse square law. This example demonstrates finding a constant for weight variation with distance squared, and determining weight changes from 3,960 to 4,040 miles. Ideal for high school students exploring gravitational concepts.

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