Three identical masses of 700 each are placed on the x axis. One mass is at = -100 , one is at the origin, and one is at = 370 . What is the magnitude of the net gravitational force on the mass at the origin due to the other two masses?
Take the gravitational constant to be = 6.67×10−11 .
75.4
To find the magnitude of the net gravitational force on the mass at the origin, we can calculate the gravitational force between the origin and the other two masses separately, and then find the vector sum of these forces.
The formula for gravitational force between two masses is given by:
F = G * (m1 * m2) / r^2
Where:
F = Gravitational force between the masses
G = Gravitational constant (6.67×10^-11 N(m/kg)^2)
m1 = Mass of one object
m2 = Mass of the other object
r = Distance between the centers of the two objects
Let's calculate the gravitational force between the mass at the origin and the mass at x = -100 first.
Mass of each object, m1 = m2 = 700 kg
Distance between the objects, r = 100 units (since they are 100 units apart on the x-axis)
Using the formula, we get:
F1 = G * (m1 * m2) / r^2
= (6.67×10^-11) * (700 * 700) / (100^2)
= 3.3385 × 10^-6 N
Now, let's calculate the gravitational force between the mass at the origin and the mass at x = 370.
Distance between the objects, r = 370 units (since they are 370 units apart on the x-axis)
Using the formula, we get:
F2 = G * (m1 * m2) / r^2
= (6.67×10^-11) * (700 * 700) / (370^2)
= 1.0447 × 10^-6 N
To find the net gravitational force on the mass at the origin, we need to sum up these two forces:
Net force = F1 + F2
= 3.3385 × 10^-6 N + 1.0447 × 10^-6 N
= 4.3832 × 10^-6 N
Therefore, the magnitude of the net gravitational force on the mass at the origin due to the other two masses is 4.3832 × 10^-6 N.