A 70 kg man weighs 686 N on the Earth's surface. How far above the surface of the Earth would he have to go to "lose" 14% of his body weight?
i don't even know where to start with this question... i need help!
.86 = Rearth^2/r^2
because
W = G m M/R^2
and G m M does not change
remember that they really ask for
r-Rearth
the distance above ground, not the bigger radius from earth center
could try and explain more in depth? like wat does W stand for? his weight? and i don't really get how your solving it..
F=(G*m1*m2)/r^2
F- force
G- gravitational constant
m1- mass on earth
m2- mass of object
r- radius on earth plus given distance over it
.86*686=589.96 to find final force
plug in everything..
589.96=(6.67*10^-11*70*5.98*10^24)/ (h+6,370,000)^2
Solve for h!
h=509411
=]
To solve this problem, we need to understand the relationship between weight and distance from the surface of the Earth. The weight of an object is determined by the force of gravity acting upon it.
First, let's determine the weight lost by the man. We know that he weighs 686 N on the Earth's surface, and we want to find the weight when he loses 14% of his body weight.
To find this weight, we can calculate 14% of his initial weight:
Weight lost = 14% of 686 N
Weight lost = 0.14 * 686 N
Weight lost = 95.84 N
So, the weight lost by the man is 95.84 N.
The next step is to understand that as you move away from the Earth's surface, the force of gravity decreases. This decrease is determined by the inverse square law.
The inverse square law states that the force of gravity is inversely proportional to the square of the distance between the object and the center of the Earth.
To find the distance at which the man will lose 14% of his body weight, we need to determine how far he would have to go for the force of gravity to decrease by 95.84 N.
Let's denote the initial distance from the Earth's surface as d1 and the final distance as d2. We can set up the following equation using the inverse square law:
(686 N - 95.84 N) / (686 N / d1^2) = (686 N / d2^2)
Simplifying the equation:
(590.16 N) / (686 N / d1^2) = (686 N / d2^2)
Cross-multiplying and solving for d2:
d2^2 = (686 N / d1^2) * (590.16 N)
d2^2 = (686 N * 590.16 N) / (d1^2)
d2^2 = 404,270.56 N^2 / (d1^2)
Taking the square root of both sides:
d2 = sqrt(404,270.56 N^2 / (d1^2))
Now, substitute the value of d1 (the distance from the surface of the Earth) into the equation and solve for d2:
d2 = sqrt(404,270.56 N^2 / (d1^2))
To find the distance d2, you need to know the initial distance d1. Without this information, it is not possible to calculate the distance at which the man will lose 14% of his body weight.