If Anya decides to make the star twice as massive, and not change the length of any crossbar or the location of any object, what does she have to do with the mass of the smiley face to keep the mobile in perfect balance? Note that she may have to change masses of other objects to keep the entire structure balanced

mass of an object is directly proportional to the cube of its length. In this case the length is constant, the mass will also be constant for the smiley face, so that the mobile will be kept in perfect balance.

Therefore, If Anya decides to make the star twice as massive, and not change the length of any crossbar or the location of any object, she will make the mass of the smiley face twice as massive in order to keep the mobile in perfect balance.

moya1316 moya1316 · Answer 2 · 2021-10-28T11:42:13+02:00

Using the concept of center of mass, the result about the position of the equilibrium point of the system can be found:

The equilibrium point of the does not change position when the sun rises more (face) since on the Sun is the point of support.

The center of mass of a body is the point where all the external forces of the system act. If this applied force falls within the base of the mobile or is at the point of support, the system is in stable equilibrium.

The sun, as a spherical body, has the center of mass at its geometric center, which does not change as the radius increases due to the increase in mass.

In general the mobiles of the solar system, the point of support is placed on the Sun. If we increase the mass of the sun as the point of support is above it, there are no changes in the center of mass and consequently the equilibrium point is maintained.

In conclusion, the equilibrium point of the does not change position when increasing more of the sun (face) mass since on it is the point of support.

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