A 85 kg man weighs 833 N on the Earth's surface. How far above the surface of the Earth would he have to go to "lose" 18% of his body weight?
gravitational force (weight) is inversely proportional to the square of the distance between the masses
Earth radius ... 6.38E6 m
[6.38E6 / (6.38E6 + h)^2 = 1 - .18 ... 6.38E6 = (h + 6.38E6) √.82
solve for h
To determine the distance above the surface of the Earth that a person would have to go to "lose" a certain percentage of their body weight, we can use the concept of gravitational force.
The weight of an object on the Earth's surface can be calculated using the equation:
Weight = mass x gravitational acceleration
The gravitational acceleration on the Earth's surface is approximately 9.8 m/s^2.
Given that the man weighs 833 N, we can rearrange the equation to solve for his mass:
Weight = mass x gravitational acceleration
833 N = mass x 9.8 m/s^2
Dividing both sides of the equation by 9.8 m/s^2, we find:
mass = 833 N / 9.8 m/s^2
mass ≈ 85 kg
Now, we need to find the weight of the man after losing 18% of his body weight:
Weight after losing 18% = 0.82 x Weight
Calculating:
Weight after losing 18% = 0.82 x 833 N
Weight after losing 18% ≈ 682.06 N
Now, we need to find the gravitational force acting on the man after losing 18% of his body weight. We can set up an equation:
Weight after losing 18% = mass x gravitational acceleration
Substituting the values:
682.06 N = mass x 9.8 m/s^2
Solving for mass:
mass = 682.06 N / 9.8 m/s^2
mass ≈ 69.6 kg
Now, let's find the distance above the Earth's surface that the man needs to go to lose 18% of his body weight. We can use the formula for gravitational force:
Gravitational force = G x mass1 x mass2 / (distance)^2
Where G is the gravitational constant (~6.67430 x 10^-11 N m^2/kg^2), mass1 is the mass of the Earth, mass2 is the mass of the man, and distance is the distance above the Earth's surface.
Solving for the distance:
distance = √(G x mass1 x mass2 / Gravitational force)
Since we're calculating the change in distance, we need to consider the difference in mass:
distance = √(G x mass1 x (mass1 - mass2) / Gravitational force)
Substituting the values:
distance = √(6.67430 x 10^-11 N m^2/kg^2 x 5.972 x 10^24 kg x (5.972 x 10^24 kg - 69.6 kg) / 682.06 N)
Calculating this equation will give us the distance above the Earth's surface that the man needs to go to lose 18% of his body weight.