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(II) Four masses are arranged as shown in Fig. 6–28. Determine the x and y components of the gravitational force on the mass at the origin (m). Write the force in vector notation (î, ĵ) . <IMAGE>
8. Centripetal Forces & Gravitation
Gravitational Forces in 2D
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Find the magnitude & direction of the net gravitational force on the center 5-kg mass in the rectangle below.
A
8.6×10-8 N
B
4.28×10-7 N
C
-1.7×10-7 N
D
6.5×10-7 N
Verified step by step guidance1
Identify the forces acting on the 5 kg mass at the center due to each of the four masses at the corners of the rectangle. Use the gravitational force formula: F = G * (m1 * m2) / r^2, where G is the gravitational constant (6.674×10^-11 N(m/kg)^2), m1 and m2 are the masses, and r is the distance between the masses.
Calculate the gravitational force exerted by each of the 300 kg masses on the 5 kg mass. The distance from the center to each 300 kg mass is 0.4 m (half of 0.8 m). Use the formula to find the force magnitude.
Calculate the gravitational force exerted by each of the 100 kg masses on the 5 kg mass. The distance from the center to each 100 kg mass is 0.3 m (half of 0.6 m). Use the formula to find the force magnitude.
Determine the direction of each force. The forces from the 300 kg masses will be along the vertical axis, while the forces from the 100 kg masses will be along the horizontal axis. Consider the symmetry and direction of each force vector.
Sum the vector components of all forces to find the net gravitational force on the 5 kg mass. This involves adding the vertical components and the horizontal components separately to find the resultant force vector's magnitude and direction.
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