a particle is made to move along a vertical circular path with radius r find the height reached by the bloock over the wedge if there is no friction
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The particle has a velocity v before moving along a vertical circular path of radius r.
Let the center of the circular path be C. Let the vertical radius through C be CB. Let A be the point on the circle at which the particle stops finally. The particle loses speed when it moves up, as gravity decelerates it.
Initial total energy of the particle = K E = 1/2 * m * v²
final total energy of the particle = P E = m g h, where h = r (1 - Cos θ)
θ is the angle between CB and CA.
we apply the conservation of energy principle.
m g h = 1/2 * m * v²
=> h = r (1 - cos θ) = v² /(2 g)
Let the center of the circular path be C. Let the vertical radius through C be CB. Let A be the point on the circle at which the particle stops finally. The particle loses speed when it moves up, as gravity decelerates it.
Initial total energy of the particle = K E = 1/2 * m * v²
final total energy of the particle = P E = m g h, where h = r (1 - Cos θ)
θ is the angle between CB and CA.
we apply the conservation of energy principle.
m g h = 1/2 * m * v²
=> h = r (1 - cos θ) = v² /(2 g)
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