Three masses are located as follows: a 3.5-kg mass is at the origin, a 4.2-kg mass at (0.0 m, 7.0 m) , and a 6.5-kg mass at (24.0 m, 0.0 m) . What is the gravitational energy of the system of masses?
G = 6.67 x 10^-11 N·m²/kg².

Question

Quizplus · Accepted Answer

The gravitational energy of the system of masses is given by:$$U = -\frac{Gm_1m_2}{r_{12}} - \frac{Gm_1m_3}{r_{13}} - \frac{Gm_2m_3}{r_{23}}$$where:* G is the gravitational constant (6.67 x 10^-11 N·m^2/kg^2)* m_1, m_2, and m_3 are the masses of the three objects (3.5 kg, 4.2 kg, and 6.5 kg)* r_12 is the distance between the first and second objects (7.0 m)* r_13 is the distance between the first and third objects (24.0 m)* r_23 is the distance between the second and third objects (24.0 m)Plugging in the values, we get:$$U = -\frac{(6.67 x 10^{-11} N·m^2/kg^2)(3.5 kg)(4.2 kg)}{7.0 m} - \frac{(6.67 x 10^{-11} N·m^2/kg^2)(3.5 kg)(6.5 kg)}{24.0 m} - \frac{(6.67 x 10^{-11} N·m^2/kg^2)(4.2 kg)(6.5 kg)}{24.0 m}$$$$U = -2.8 × 10^{-10} J$$Therefore, the correct answer is A.

Three Masses Are Located as Follows: a 3