A solid uniform sphere has a mass of 7.0 104 kg and a radius of 1.2 m.
(a) What is the magnitude of the gravitational force due to the sphere on a particle of mass m = 0.7 kg located at a distance of 2.1 m from the center of the sphere?
N
(b) What if it is 1.0 m from the center of the sphere?
N
Okay so far i have F=Gm1m2/r^2
G=6.67 x10^-11
m1=.7
m2=7.0x10^4
what do i use for r?
a. f=(G*m1*m2)/r^2
=(6.67x10^-11*.7*70000)/2.1^2)
=7.4*10^-7 N
b. f=(G*m1*m2)/r^2
=(6.67*10^-11*.7*70000)/1^2
=3.29*10^-6
To calculate the magnitude of the gravitational force due to a solid uniform sphere on a particle at a given distance, you can use the equation for Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where:
F is the gravitational force
G is the gravitational constant (approximately 6.67 x 10^-11 N * m^2 / kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, the mass of the sphere (m1) is given as 7.0 x 10^4 kg, and the mass of the particle (m2) is given as 0.7 kg. The distance from the center of the sphere to the particle (r) is given as 2.1 m.
(a) To find the magnitude of the gravitational force when the particle is at a distance of 2.1 m from the center of the sphere:
F = G * (m1 * m2) / r^2
F = (6.67 x 10^-11 N * m^2 / kg^2) * (7.0 x 10^4 kg * 0.7 kg) / (2.1 m)^2
Calculating this expression will yield the magnitude of the gravitational force in Newtons.
(b) To find the magnitude of the gravitational force when the particle is at a distance of 1.0 m from the center of the sphere:
F = G * (m1 * m2) / r^2
F = (6.67 x 10^-11 N * m^2 / kg^2) * (7.0 x 10^4 kg * 0.7 kg) / (1.0 m)^2
Calculating this expression will yield the magnitude of the gravitational force in Newtons.