Question

Find the center of mass of a cone of uniform density that has a radius R at the base, height h, and mass M. Let the origin be at the center of the base of the cone and have +z going through the cone vertex.

a) ( R/4 , R/4 , h/4 )
b) (0,0, 3h/8)
c) (0,0, h/4 )
d) ( R/2 , R/2, h/2)

Answer 1

To find the center of mass of a cone, we can consider it as two parts: the missing part and the overlapping part. The missing part can be thought of as a negative mass, while the overlapping part has positive mass. The center of mass is located at a point that is 3/4 of the height of the cone, and at a distance of R/4 from the center of the base of the cone in both the x and y directions.

Step-by-step explanation:

To find the center of mass of a cone, we can consider it as two parts: the missing part and the overlapping part. The missing part can be thought of as a negative mass, while the overlapping part has positive mass. When we combine these two parts, we can find the center of mass.

In this case, the missing part is like a cone with negative mass, while the overlapping part is like a cone with positive mass. The center of mass is located at a point that is 3/4 of the height of the cone, and at a distance of R/4 from the center of the base of the cone in both the x and y directions. Therefore, the correct answer is ( R/4 , R/4 , h/4 ).

The missing part can be thought of as a negative mass, while the overlapping part has positive mass. The center of mass is located at a point that is 3/4 of the height of the cone, and at a distance of R/4 from the center of the base of the cone in both the x and y directions.