A man has a mass of 80kg on the Earth's surface.


Part A
How far above the surface of the Earth would he have to go to "lose" 13% of his body weight?

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To solve this problem, we need to understand the concept of weight and gravitational force. Weight is the force experienced by an object due to the gravitational pull of the Earth.

Part A:
To find how far above the surface of the Earth the man would have to go to "lose" 13% of his body weight, we need to first calculate this weight loss.

Step 1: Calculate the weight of the man on the Earth's surface.
The weight of an object is calculated using the formula W = m * g, where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s²).

Weight on Earth = mass * acceleration due to gravity
Weight on Earth = 80 kg * 9.8 m/s² = 784 N

Step 2: Calculate the weight loss.
To determine the weight loss, we need to find 13% of the original weight. (13% can be written as 0.13)

Weight loss = 0.13 * Weight on Earth
Weight loss = 0.13 * 784 N = 101.92 N

Step 3: Find how far above the Earth's surface the man would have to go to lose this weight.
Inversely proportional to the square of the distance, the gravitational force becomes weaker as you move away from the Earth's surface. Therefore, the man needs to move farther from the Earth's surface to lose a certain amount of weight.

The formula we can use is GMm/r², where G is the universal gravitational constant, M is the mass of the Earth, m is the mass of the object, and r is the distance from the center of the Earth.

The acceleration due to gravity on the surface of the Earth (g) can be expressed as g = GM/r².

So, we can rearrange the formula to find the distance (r) required to lose 13% of the weight:

r = √(GM / ((Weight on Earth - Weight loss) / Weight on Earth))

Step 4: Calculate the distance.
We can use the following values:
- Mass of the Earth (M) = 5.972 x 10^24 kg
- Universal gravitational constant (G) = 6.67430 x 10^-11 N(m/kg)²
- Weight on Earth = 784 N
- Weight loss = 101.92 N

Plugging in these values into the formula, we can find the distance above the Earth's surface.

r = √((6.67430 x 10^-11 N(m/kg)² * (5.972 x 10^24 kg)) / ((784 N - 101.92 N) / 784 N))

Using a calculator, the result would be approximately 6,635,752 meters.

Therefore, the man would have to go approximately 6,635,752 meters above the surface of the Earth to "lose" 13% of his body weight.

weight= forcegravity=GMeM/r^2

So I see this relationship:

.87=(radiusearth/(radiusEarth+height))^2

solve for height