Conservation of energy on the merry-go-round?

Question

A child runs tangentially to a merry-go-round's rim.  The kinetic energy of the system then goes down, even if the child was running faster than the rim.  So even if the rim picks up speed, the system's KE goes down.  That's why you have to use conservation of angular momentum instead of conservation of energy to solve for, say, the final angular velocity.

But where did the "lost" energy go?  Of course, it ends up as stored elastic energy in the bending of the axis of the merry-go-round.  It's the energy required to divert the child's inertia into circular motion.  Now, obviously this potential energy can be found by taking the difference of initial KE and final KE.  But is there no other way of evaluating the energy of centripetal motion?  Seems like there should be a simple formula for the energy resulting from circular motion.

Or is it like the car collision problem, or the ballistic pendulum problem, where there's no formula for the energy "lost" but it can always be calculated?

Thanks in advance.

Rona Lachat · Accepted Answer

Last sentence your answer.You are asking for a specific formula for a general statement. Take into account the object on the merry-go-round is constantly changing direction and needs energy to do this.

Let&#39;slearntothink · Answer

In many problems, where only conservative forces do not act, energy is not conserved. But linear momentum and angular momentum is conserved as the  system as a whole is isolated. Using this lost energy can be found out. simplest problem of this kind is when an object colliding with another gets stuck to it. In fact there is no perfectly elastic collision. because some dissipation of energy has to take place. Only difference is that in so called elastic collisions the dissipated energy is very very small. In actual collisions there has to be some vibrations, which are never friction-free harmonic vibrations.

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Conservation of energy on the merry-go-round?

2 Answers