Question

Develop a hypothesis for why one of the two types of soup should indeed be rolling down faster than the other. This hypothesis should directly relate to the moment of inertia and should involve predictions about how the two types of soup behave while the cans are rolling downhill. Hint: Soup is a liquid.

Answer 1

Answer:

Assume two identical cans filled with two types of soup having same mass are rolling down on an inclined plane in same conditions. In terms of inertia different types of soup will indicate different viscosity. The higher viscosity fillings indicates more part of the soup mass is rotating together with the can’s body. This means that for the can with lower viscosity soup has a lower moment of inertia and the can with higher viscosity has higher moment of inertia while the same gravity makes them to roll.

incline angle = θ ; can's mass =  m ; Radius of the can's = R , Angular acceleration for Can 1 = α1 ; Angular acceleration for Can 2 = α2

T1 = Inertia of Can with high viscosity soup

T2 = Inertia of Can with low viscosity soup

M1 rolling moment of Can 1

M2 rolling moment of Can 2

equation is given by

T1*α1 = M1   - (a)

T2*α2 = M2 - (b)

M1 = M2 = m*g*R*sin(θ). (c)

as assumed T1 > T2

from the three equation (a), (b) & (c)

the α2 > α1

Angular acceleration of Can 2 is higher than Can 1. Already stated that Can 1 has more viscous soup as compared to Can 2.