Answer:
a) m*g*hi = m*g*hf
h
= h
b) ratio = 1.22
c) the potential energy is converted to both rotational kinetic energy and translational kinetic energy
Step-by-step explanation:
For a frictionless system : initial energy = final energy
i.e. Ei = Ef
a) Prove
Total Initial energy for First cylinder ( Ei ) = m*g*hi
The final energy of the first cylinder ( Ef ) = m*g*hf
and this energies are purely potential energies
According to conservation of energy :
m*g*hi = m*g*hf
hi = hf ( and this holds for both cylinders because they where both kept at the same height initially )
i.e. initial height = final height ( hence it is proved that both cylinders will reach their initial heights )
b) Determine the ratio of the time taken by both cylinders
lets assume height of incline ( h ) = Lsin
where L = distance covered by cylinder
Final velocity of first cylinder ( V1 ) =
Final velocity of second cylinder ( V2 ) =
( following the application of the law of conservation of energy )
Given that ; Time taken = displacement / velocity
hence the ratio = ( h / v1 ) / ( h / v2 )
where h = Lsin
the ratio = 1.22
c) The time for the rolling motion is greater than the time for the sliding motion because the potential energy is converted to both rotational kinetic energy and translational kinetic energy