A 6.00Kg puck on a frictionless surface is constrained to a circular orbit by a

Question

A 6.00Kg puck on a frictionless surface is constrained to a circular orbit by a 3.00 meter long string attached to a rod. Assume the string is attached to the rod by a ring that lets it revolve around the rod without friction. The string can withstand up to a 30.0N tension without breaking. a. What is the maximum tangential velocity that the puck can have without breaking the string? b. What is the maximum radial acceleration without breaking the string? c. At the "breaking" radial acceleration, once the string breaks (assume string has no mass), what is the kinetic energy of the puck? d. If the puck is modeled as a non-isolated system, what is the total energy of the released puck?

Explanation / Answer

part a:

maximum tangential velocity should be such that centripetal force is equal to tension withstood by the string

hence mass of the puck*tangential speed^2/radius of the circular motion=30

==>6*v^2/3=30

==>v=sqrt(30*3/6)=3.873 m/s

part b:

maximum radial acceleration=v^2/radius

=3.873^2/3=5 m/s^2

part c:

kinetic energy=0.5*mass*speed^2

=0.5*6*3.873^2

=45 J

part d:

total energy of the released puck = potential energy+kinetic energy

as potential energy is 0,

total energy = kinetic energy=45 J

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