The gravitational force on the object at a height of 3200 km from the Earth's surface is approximately 42 N, not 28 N as stated in the answer.
To calculate the gravitational force on an object at a certain height above the Earth's surface, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the two objects (in this case, the mass of the object and the mass of the Earth)
r is the distance between the centers of the two objects (in this case, the distance from the center of the Earth to the object's height)
Given:
Weight of the body on the surface of the Earth, W = 63 N
Radius of the Earth, R = 6400 km = 6400000 m
Height above the Earth's surface, h = 3200 km = 3200000 m
The weight of the body on the surface of the Earth is equal to the gravitational force between the body and the Earth:
W = F = (G * m1 * m2) / R^2
To find the gravitational force at the height of 3200 km, we need to calculate the new distance between the center of the Earth and the object:
r = R + h
Substituting the values into the equation:
63 N = (G * m1 * m2) / (6400000 m)^2
Now we can solve for the mass of the object, m1:
m1 = (63 N * (6400000 m)^2) / G
Next, we can calculate the new gravitational force at the height of 3200 km, F_h:
F_h = (G * m1 * m2) / (R + h)^2
Substituting the values into the equation:
F_h = (G * m1 * m2) / (6400000 m + 3200000 m)^2
Finally, we can calculate the gravitational force at the given height:
F_h = (G * m1 * m2) / (9600000 m)^2
Substituting the values:
F_h = (6.674 × 10^-11 N m^2 / kg^2) * ((63 N * (6400000 m)^2) / G) / (9600000 m)^2
Simplifying the equation, the mass of the Earth (m2) cancels out:
F_h = (63 N * (6400000 m)^2) / (9600000 m)^2
F_h = (63 N * 6400000 m^2) / 9600000 m^2
F_h = 42 N
Therefore, the gravitational force on the object at a height of 3200 km from the Earth's surface is approximately 42 N, not 28 N as stated in the answer.