Three balls A, B and C are kept in a straight line. The separation between A and C is 1 m, and B is placed at the midpoint between them. The masses of A, B, C are 100 g, 200 g and 300 g respectively. Find the net gravitational force on (a) A, (b) B, and (c) C.
To find the net gravitational force on each ball, we need to calculate the force exerted by each ball individually and then add them up.
The gravitational force between two objects can be calculated using 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 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the objects, and r is the separation between the objects.
(a) Net gravitational force on ball A:
To calculate the gravitational force on ball A, we need to consider the masses of balls B and C and their distances from A.
The gravitational force on ball A due to ball B is:
F1 = (G * m1 * m2) / r^2
Where m1 is the mass of A (100 g), m2 is the mass of B (200 g), and r is the separation between A and B (0.5 m since B is placed at the midpoint between A and C).
The gravitational force on ball A due to ball C is:
F2 = (G * m1 * m3) / r^2
Where m3 is the mass of C (300 g), and r is the separation between A and C (1 m).
The net gravitational force on A is the sum of F1 and F2:
Net gravitational force on A = F1 + F2
(b) Net gravitational force on ball B:
To calculate the gravitational force on ball B, we need to consider the masses of balls A and C and their distances from B.
The gravitational force on ball B due to ball A is:
F3 = (G * m2 * m1) / r^2
Where m2 is the mass of B (200 g), m1 is the mass of A (100 g), and r is the separation between B and A (0.5 m since B is placed at the midpoint between A and C).
The gravitational force on ball B due to ball C is:
F4 = (G * m2 * m3) / r^2
Where m3 is the mass of C (300 g), and r is the separation between B and C (0.5 m since B is placed at the midpoint between A and C).
The net gravitational force on B is the sum of F3 and F4:
Net gravitational force on B = F3 + F4
(c) Net gravitational force on ball C:
To calculate the gravitational force on ball C, we need to consider the masses of balls A and B and their distances from C.
The gravitational force on ball C due to ball A is:
F5 = (G * m3 * m1) / r^2
Where m3 is the mass of C (300 g), m1 is the mass of A (100 g), and r is the separation between C and A (1 m).
The gravitational force on ball C due to ball B is:
F6 = (G * m3 * m2) / r^2
Where m3 is the mass of C (300 g), m2 is the mass of B (200 g), and r is the separation between C and B (0.5 m since B is placed at the midpoint between A and C).
The net gravitational force on C is the sum of F5 and F6:
Net gravitational force on C = F5 + F6
By plugging in the given values for the masses and using the gravitational constant, you can calculate the net gravitational force on each ball.