Question

An object is constrained by a cord to move in a circular path of radius 0.5m on a horizontal frictionless surface. The cord will break if its tension exceeds 16N. The maximum kinetic energy the object can have is

Answer 1

Given:

An object is constrained by a cord to move in a circular path of radius 0.5m on a horizontal frictionless surface. The cord will break if its tension exceeds 16N.

To find:

Max kinetic energy of object ?

Calculation:

Let velocity of the object be v :

So, max tension should be 16 N equal to its centrifugal force at critical conditions.

$\sf \therefore \: f_{c} = 16$

$\sf \implies \: \dfrac{m {v}^{2} }{r} = 16$

$\sf \implies \: m {v}^{2} = 16 \times r$

$\sf \implies \: \dfrac{1}{2} m {v}^{2} = 8 \times r$

$\sf \implies \ KE_{max} = 8 \times r$

$\sf \implies \ KE_{max} = 8 \times 0.5$

$\sf \implies \ KE_{max} = 4 \: joule$

So, max kinetic energy is 4 Joule