A 80 kg man weighs 784 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?
Let Re be the earth's radius and h be the required altitude. Since g is inversely proportional to radius squared,
[Re/(Re + h)]^2 = 0.85
Look up Re and solve for h
To find out how far above the surface of the Earth the man would have to go to "lose" 15% of his body weight, you need to understand the concept of gravitational force and use the formula provided.
We know that the weight of an object is given by the equation:
Weight = mass × gravitational acceleration
In this case, the weight of the man on the surface of the Earth is 784 N, and his mass is 80 kg. The gravitational acceleration on Earth is approximately 9.8 m/s^2.
Weight = 784 N
Mass = 80 kg
Gravitational acceleration = 9.8 m/s^2
We want to find the height where the weight is reduced by 15%. Let's call this height 'h'.
Now, the weight at a certain height can be calculated using the equation:
Weight at height = mass × gravitational acceleration × (1 - (height/R)^2)
Where R is the radius of the Earth and height is the distance above the surface of the Earth.
In this case, we want to find the height where the weight is 15% less than the weight on the Earth's surface.
Weight at height = 0.85 × Weight on Earth's surface
Substituting the known values into the equation, we get:
0.85 × 784 N = 80 kg × 9.8 m/s^2 × (1 - (h/R)^2)
Now, we can solve for h by rearranging the equation:
(1 - (h/R)^2) = (0.85 × 784 N) / (80 kg × 9.8 m/s^2)
Simplify the equation:
(1 - (h/R)^2) = 0.107
Now, set up the equation to solve for (h/R)^2:
(h/R)^2 = 1 - 0.107
Calculate (h/R)^2:
(h/R)^2 = 0.893
Finally, take the square root of both sides to find h/R:
h/R = √(0.893)
Solving for h/R, we get:
h/R = 0.945
To find the distance above the surface of the Earth, we need to multiply h/R by the radius of the Earth. The average radius of the Earth is approximately 6,371 kilometers (6,371,000 meters):
h = 0.945 × 6,371,000 m
Thus, the man would have to go approximately 6,019,295 meters (6,019 kilometers) above the surface of the Earth to "lose" 15% of his body weight.