The center of a 4.0 kg sphere and a 7.5 kg sphere are separated by a distance of 1.5 m where is the center of mass of the two sphere system
To determine the center of mass of the two-sphere system, you need to use the concept of weighted averages. The center of mass can be thought of as the point where the entire mass of the system is concentrated.
In this case, you have two spheres with masses of 4.0 kg and 7.5 kg, respectively, separated by a distance of 1.5 m. To find the center of mass, follow these steps:
1. Identify the individual centers of mass of each sphere. The center of mass of a sphere is located at its geometric center, which is the same as its actual center if the sphere has a uniform density.
2. Weight each center of mass based on the mass of its respective sphere. The weight ratio can be determined by dividing each mass by the total mass of the system. In this case, the total mass is 4.0 kg + 7.5 kg = 11.5 kg.
Mass ratio of the 4.0 kg sphere: 4.0 kg / 11.5 kg = 0.348.
Mass ratio of the 7.5 kg sphere: 7.5 kg / 11.5 kg = 0.652.
3. Multiply each mass ratio by the distance between the center of mass and the center of each sphere (1.5 m) to obtain the weighted distances.
Weighted distance of the 4.0 kg sphere: 0.348 * 1.5 m = 0.522 m.
Weighted distance of the 7.5 kg sphere: 0.652 * 1.5 m = 0.978 m.
4. Add up the weighted distances to find the total distance from the center of mass of the system.
Total distance from the center of mass: 0.522 m + 0.978 m = 1.500 m.
Based on this calculation, the center of mass of the system is located at a distance of 1.500 m from the center of the 4.0 kg sphere and 0.000 m from the center of the 7.5 kg sphere.