when an object is 100m above the surface of earth. The earth's attraction for it is 10N. In order then the earth's attraction on the same object is only 5N. how far should be taken to object be away from surface of earth.
F1 =G•m•M/R1²
F2= G•m•M/R2²
F1=10 N, F2 = 5 N
F1=2F2
G•m•M/R1² =2 G•m•M/R2²
1/R1²=2/R2²
R2=√2•R1
Earth’s radius is R = 6.378•10^6 m.
h1=100 m, h2=?
R1=R+h1
R2=R+h2
R+h2=√2• (R+h1),
h2 =[√2• (R+h1)] – R.
To calculate the distance the object should be from the surface of the Earth in order for the Earth's attraction to be 5N, we can use the concept of gravitational force.
We know that gravitational force is inversely proportional to the square of the distance between the centers of two objects, and proportional to the product of their masses.
Let's assume the mass of the object remains constant.
We have the following information:
Initial distance (d1) = 100m
Initial force (F1) = 10N
Final force (F2) = 5N
Using the equation for gravitational force:
F = (G * m1 * m2) / d^2
where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between their centers.
Since the mass of the Earth remains constant, we can express the force as:
F = (G * m1 * m_earth) / d^2
Now we can set up a ratio using the relationship between the initial force (F1) and the final force (F2):
F1/F2 = (G * m1 * m_earth) / d1^2 / (G * m1 * m_earth) / d2^2
10/5 = (G * m_earth) / 100^2 / (G * m_earth) / d2^2
2 = (1/10000) / (1/d2^2)
2 = d2^2 / 10000
d2^2 = 2 * 10000
d2 = sqrt(2 * 10000)
d2 ≈ 141.4 m
Therefore, the object should be approximately 141.4 meters away from the surface of the Earth in order for the Earth's attraction on the same object to be 5N.
To find the distance at which the Earth's attraction on the object is only 5N, we need to use the inverse square law of gravity. According to this law, the force of gravity between two objects decreases with the square of the distance between them.
Let's say the initial distance between the object and the surface of the Earth is d1 = 100m, and the initial gravitational force is F1 = 10N.
From the inverse square law, we can write:
F2 / F1 = (d1 / d2)^2
Where F2 is the desired gravitational force (5N) and d2 is the distance at which it occurs.
Substituting the given values, we have:
5N / 10N = (100m / d2)^2
Simplifying the equation, we get:
0.5 = (100m / d2)^2
Taking the square root of both sides:
sqrt(0.5) = 100m / d2
Now, rearranging the equation:
d2 = 100m / sqrt(0.5)
Calculating the expression on the right side:
d2 ≈ 141.4m
Therefore, the object should be around 141.4m away from the surface of the Earth in order for the Earth's gravitational attraction to be 5N.