Three identical masses of 500 kg each are placed on the x axis. One mass is at x_1 = -11.0 cm, one is at the origin, and one is at x_2 = 37.0 cm. What is the magnitude of the net gravitational force F_grav on the mass at the origin due to the other two masses?
Take the gravitational constant to be G = 6.67×10−11 N \m^2/kg^2.
Express your answer in newtons.
The two masses at x1 = -11 cm and at x2 = -37 cm apply forces in opposite directions to the mass at the origin.
Use Newton's universal gravity law (which you should know) to compute each of the two forces, and then SUBTRACT them.
The force due to the mass at x1 is
F1 = G (500)^2/(0.11 m)^2
To find the magnitude of the net gravitational force on the mass at the origin due to the other two masses, we can use the equation for gravitational force:
F_grav = (G * m1 * m2) / r^2
Where:
- F_grav is the gravitational force
- G is the gravitational constant (6.67×10^−11 N m^2/kg^2)
- m1 and m2 are the masses
- r is the distance between the two masses
Let's calculate the forces separately for each of the masses using this equation.
First, let's calculate the force on the mass at the origin due to the mass at x_1 = -11.0 cm.
m1 = 500 kg (mass at the origin)
m2 = 500 kg (mass at x_1 = -11.0 cm)
r = distance between the masses = x_1 - 0 = -11.0 cm = -0.11 m (converted to meters)
Now we can calculate the force:
F_grav1 = (G * m1 * m2) / r^2
= (6.67×10^−11 N m^2/kg^2) * (500 kg) * (500 kg) / (-0.11 m)^2
Next, let's calculate the force on the mass at the origin due to the mass at x_2 = 37.0 cm.
m1 = 500 kg (mass at the origin)
m2 = 500 kg (mass at x_2 = 37.0 cm)
r = distance between the masses = x_2 - 0 = 37.0 cm = 0.37 m (converted to meters)
Now we can calculate the force:
F_grav2 = (G * m1 * m2) / r^2
= (6.67×10^−11 N m^2/kg^2) * (500 kg) * (500 kg) / (0.37 m)^2
Finally, we can find the magnitude of the net gravitational force by summing up the forces:
F_grav = |F_grav1| + |F_grav2|
This will give us the magnitude of the net gravitational force on the mass at the origin due to the other two masses.