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A block of mass m slides down a frictionless ramp to a loop-the-loop with radius R. The mass starts from initial height such that it makes it entirely around the loop without losing contact with the track. At the top of the loop (point A), the mass has speed v. What is the magnitude of the acceleration of the mass when it is at point A

Respuesta :

Answer:

[tex] \frac{v^{2} }{R}[/tex]

Explanation:

[tex]R[/tex] = radius of the loop

[tex]m[/tex] = mass of the block

[tex]v[/tex] = speed of the block at top of the loop at point A

[tex]a[/tex] = magnitude of acceleration of block at A

At point A, the block moves in a circle and hence experience centripetal force. Due to this centripetal force, the centripetal acceleration of the block can be given as

[tex]a = \frac{v^{2} }{R}[/tex]