Question : A bob of mass m is suspended by a light string of length L . It is imparted a horizontal velocity vo at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, C. This is shown in figure . Obtain an expression for (i) vo; (ii) the speeds at points B and C; (iii) the ratio of the kinetic energies (KB/KC) at B and C. Comment on the nature of the trajectory of the bob after it reaches the point C.
Answer :
(i) There are two external forces on the bob : gravity and the tension (T ) in the string. The latter does no work since the displacement of the bob is always normal to the string. The potential energy of the bob is thus associated with the gravitational force only.
The total mechanical energy E of the system is conserved. We take the potential energy of the system to be zero at the lowest point A. Thus, at A :
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Answer :
(i) There are two external forces on the bob : gravity and the tension (T ) in the string. The latter does no work since the displacement of the bob is always normal to the string. The potential energy of the bob is thus associated with the gravitational force only.
The total mechanical energy E of the system is conserved. We take the potential energy of the system to be zero at the lowest point A. Thus, at A :
Click here at the bottom text for better view.
Related posts :
Work
work done by variable force
Work Energy Theorem
Potential energy
Law of conservation of energy
Friction introduction
Rolling Friction
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