A 494 kg uniform solid sphere has a radius of 0.390 m. Find the magnitude of the gravitational force exerted by the sphere on a 49.1 g particle located
(a) 1.45 m from the center of the sphere
1 ? N
(b) at the surface of the sphere
2 ? N
(c) 0.200 m from the center of the sphere
3 ? N
To find the gravitational force exerted by the sphere on the particle, we can use the equation for gravitational force:
F = G * (m1 * m2 / r^2)
where F is the gravitational force, G is the gravitational constant (6.67430 × 10^-11 N(m/kg)^2), m1 is the mass of the sphere, m2 is the mass of the particle, and r is the distance between the centers of the sphere and the particle.
(a)
First, we need to find the mass of the particle. Given that the mass of the particle is 49.1 g, we convert it to kg:
m2 = 49.1 g = 0.0491 kg
Now, we can calculate the gravitational force:
F = G * (m1 * m2 / r^2)
F = (6.67430 × 10^-11 N(m/kg)^2) * ((494 kg) * (0.0491 kg) / (1.45 m)^2)
Solving this equation will give you the magnitude of the gravitational force exerted by the sphere on the particle when it is 1.45 m from the center of the sphere.
(b)
When the particle is at the surface of the sphere, the distance between the centers of the sphere and the particle is equal to the radius of the sphere.
r = 0.390 m
Using the same formula as above:
F = G * (m1 * m2 / r^2)
F = (6.67430 × 10^-11 N(m/kg)^2) * ((494 kg) * (0.0491 kg) / (0.390 m)^2)
Solving this equation will give you the magnitude of the gravitational force exerted by the sphere on the particle at the surface of the sphere.
(c)
When the particle is 0.200 m from the center of the sphere, we can use the same formula again:
F = G * (m1 * m2 / r^2)
F = (6.67430 × 10^-11 N(m/kg)^2) * ((494 kg) * (0.0491 kg) / (0.200 m)^2)
Solving this equation will give you the magnitude of the gravitational force exerted by the sphere on the particle when it is 0.200 m from the center of the sphere.