A square of edge length 19.0 cm is formed by four spheres of masses m1 = 6.00 g, m2 = 3.50 g, m3 = 1.00 g, and m4 = 6.00 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.20 g?
_N i + _N j
You have to put the gravitational equation in vector form and add.
To calculate the net gravitational force in vector form, we need to combine the individual gravitational forces exerted by each sphere onto the central sphere.
The equation for gravitational force between two objects is given by:
F = G * (m1 * m2) / r^2
Where:
- F is the magnitude of the gravitational force
- G is the gravitational constant (approximately 6.674 x 10^-11 N*m^2/kg^2)
- m1 and m2 are the masses of the objects
- r is the distance between the centers of the objects
Given that our desired answer is in unit-vector notation, we need to calculate the x-component and y-component of the net gravitational force independently.
Now, let's calculate the net gravitational force in the x-direction:
For m1 and m5, the gravitational force will act in the negative x-direction.
For m2, the gravitational force will act in the positive x-direction.
For m3 and m4, there won't be any force in the x-direction because they are directly above and below m5.
So, the x-component of the net gravitational force can be calculated as follows:
Fnet_x = (-F1_x) + F2_x
Where Fnet_x is the x-component of the net gravitational force, F1_x is the x-component of the gravitational force between m1 and m5, and F2_x is the x-component of the gravitational force between m2 and m5.
Similarly, let's calculate the net gravitational force in the y-direction:
For m1 and m5, there won't be any force in the y-direction because they are directly to the left and right of m5.
For m2, the gravitational force will act in the negative y-direction.
For m3 and m4, the gravitational force will act in the positive y-direction.
So, the y-component of the net gravitational force can be calculated as:
Fnet_y = (-F2_y) + F3_y + F4_y
Where Fnet_y is the y-component of the net gravitational force, F2_y is the y-component of the gravitational force between m2 and m5, F3_y is the y-component of the gravitational force between m3 and m5, and F4_y is the y-component of the gravitational force between m4 and m5.
By plugging in the appropriate values for masses and distances into the gravitational force equation and performing the necessary calculations, you can determine the x- and y-components of the net gravitational force.