If two is company and three is a crowd, what is 4 and 5?
2 answers:
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Answer:
The height is
A circular hoop of different diameter cannot be released from a height 30cm and match the sphere speed because from the conservation relation the speed of the hoop is independent of the radius (Hence also the diameter )
Explanation:
From the question we are told that
The height is
The angle of the slope is
According to the law of conservation of energy
The potential energy of the sphere at the top of the slope = Rotational kinetic energy + the linear kinetic energy
Where I is the moment of inertia which is mathematically represented as this for a sphere
The angular velocity is mathematically represented as
So the equation for conservation of energy becomes
Considering a circular hoop
The moment of inertial is different for circle and it is mathematically represented as
Substituting this into the conservation equation above
Where is the height where the circular hoop would be released to equal the speed of the sphere at the bottom
Recall that
Substituting values