A thin spherical shell has a radius of 2.4 m and a mass of 410 kg, and its center is located at the origin of a coordinate system. Another spherical shell with a radius of 1 m and mass 135 kg is inside the larger shell with its center at 0.6 m on the x axis. What is the gravitational force of attraction between the two shells?
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To find the gravitational force of attraction between the two shells, 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 6.67 x 10^-11 N m^2 / kg^2), m1 and m2 are the masses of the shells, and r is the distance between the centers of the shells.
Let's calculate step by step:
Step 1: Calculate the distance between the centers of the shells:
The center of the smaller shell is located at 0.6 m on the x-axis, and the center of the larger shell is at the origin (0,0). The distance between these two centers can be found using the Pythagorean theorem:
d = sqrt((0.6)^2 + (0)^2) = sqrt(0.36) = 0.6 m
Step 2: Now we can calculate the gravitational force:
F = G * (m1 * m2) / r^2
= (6.67 x 10^-11 N m^2 / kg^2) * (135 kg * 410 kg) / (0.6 m)^2
Substituting the values:
F = (6.67 x 10^-11) * (135 * 410) / (0.6)^2
= (6.67 x 10^-11) * (55250) / (0.36)
= (6.67 x 10^-11) * (1.534 x 10^7)
= 1.004138 x 10^-3 N
Therefore, the gravitational force of attraction between the two shells is approximately 1.004138 x 10^-3 N.
Each shell can be treated as a point-source mass with all of its mass at the center of the spherical shell.
The two centers are 0.6 m apart.
F = G*410*135/(0.6)^2
You don't need to use the radii of the shells. Look up the universal gravity constant G and do the numbers.