Given: The universal gravitational con- stant is 6.672 × 10−11 N m2/kg2.
Objects with masses of 152 kg and 269 kg are separated by 0.45 m. A 53.5 kg mass is placed midway between them.
Find the magnitude of the net gravitational force exerted by the larger masses on the
53.5 kg mass. Answer in units of N.
To find the magnitude of the net gravitational force exerted by the larger masses on the 53.5 kg mass, we can use the formula for the gravitational force between two masses:
F = G * (m1 * m2) / r^2
where:
F is the gravitational force,
G is the universal gravitational constant (6.672 × 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.
In this case, we have two masses (152 kg and 269 kg) and a distance of 0.45 m. The third mass (53.5 kg) is placed midway between them.
1. First, let's calculate the gravitational force between the two larger masses:
F1 = G * (m1 * m2) / r^2
F1 = (6.672 × 10^−11 N m^2/kg^2) * (152 kg * 269 kg) / (0.45 m)^2
2. Now, calculate the gravitational force between each of the larger masses and the 53.5 kg mass:
F2 = G * (m1 * m3) / (r/2)^2
F2 = (6.672 × 10^−11 N m^2/kg^2) * (152 kg * 53.5 kg) / (0.45 m/2)^2
F3 = G * (m2 * m3) / (r/2)^2
F3 = (6.672 × 10^−11 N m^2/kg^2) * (269 kg * 53.5 kg) / (0.45 m/2)^2
3. Finally, add up these three forces to find the net gravitational force exerted by the larger masses on the 53.5 kg mass:
F_net = F1 + F2 + F3
Calculate these values and add them together to obtain the magnitude of the net gravitational force exerted on the 53.5 kg mass in units of N.