A 75 kg man weighs 735 N on the Earth's surface. How far above the surface of the Earth would he have to go to "lose" 15% of his body weight?
The value of acceleration due to gravity on surface of the earth is
g=weight of the person/mass of the
person=735/75=9.8ms^-2
The man loses 15% of weight,
g'=g85/100
Required height =g'=g*R^2/(R+H)^2
Well, if he wants to lose 15% of his body weight, maybe he should consider going on a cosmic diet! But let's do some calculations instead. We know that his weight on Earth is 735 N, which is 100% of his weight. If he wants to lose 15% of his weight, he would need to go to a place where he weighs only 85% of his original weight. So, if we set up a proportion: 735 N is to 100% as X is to 85%, we can solve for X. Let's do some math... *cue circus music*
To determine how far above the surface of the Earth the man would have to go to "lose" 15% of his body weight, we need to understand the concept of weight and its relationship to gravitational force.
Weight is the force with which an object is attracted towards the center of the Earth or any other celestial body. It is calculated by multiplying the mass of the object by the acceleration due to gravity. On Earth, the acceleration due to gravity is roughly 9.8 meters per second squared (m/s^2).
Given that the weight of the man on the Earth's surface is 735 Newtons (N) and his mass is 75 kilograms (kg), we can use the formula:
Weight = Mass * Acceleration due to gravity
To calculate the acceleration due to gravity, we rearrange the formula:
Acceleration due to gravity = Weight / Mass
Substituting the given values:
Acceleration due to gravity = 735 N / 75 kg
Acceleration due to gravity ≈ 9.8 m/s^2
Now, let's calculate the weight the man would have to reach to "lose" 15% of his body weight:
Weight loss = 15% * Weight
Weight loss = 0.15 * 735 N
Weight loss ≈ 110.25 N
To find the distance the man needs to go above the Earth's surface, we can use the concept of gravitational force and potential energy. The potential energy of an object at a certain height above the Earth's surface is given by:
Potential energy = Weight * Height
We want to find the height, so rearranging the formula:
Height = Potential energy / Weight
Substituting the values:
Height ≈ 110.25 N / (75 kg * 9.8 m/s^2)
Height ≈ 0.1503 meters or 15.03 centimeters
Therefore, the man would need to go approximately 15.03 centimeters above the Earth's surface to "lose" 15% of his body weight.
m g = G M m /r^2
so m does not matter if we only want ration
G M is constant
r = earth radius (any units) but be consistent. You might use 6.38*10^6 kg
R = r + d
.85 G M/r^2 = G M/(r+d)^2
r^2 = .85 (r+d)^2
r = .922 (r+d)
r - .922 r = .922 d
d = r (1-.922)/.922 = .0846 r