Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (Fig. 6.14). One of the bobs is released after being displaced by 100 so that it collides elastically head-on with the other bob.
(a) Describe the motion of two bobs.
(b) Draw a graph showing variation in energy of either pendulum with time, for 0 ≤ t ≤ 2T, where T is the period of each pendulum.
a) At time period t=0
Bob A has maximum potential energy and bob B is at rest with zero energy.
At t=T/4
Bob A gains maximum velocity and collides with the bob B. bob A comes to rest and bob B gains the velocity of bob A because the collision is elastic and both have the same mass ∴ their velocity gets interchanged.
Now bob B has maximum kinetic energy.
At t=T/2
Bob B reaches the maximum height and its kinetic energy is converted to maximum potential energy. While bob A remains at rest.
At =3T/4
Bob B reaches to bob A with its maximum potential energy getting converted to max kinetic energy and collides with bob A. During the collision the interchanging of velocity takes place and bob A gains the velocity of bob B and bob B comes to rest.
At t=T
Bob A reaches the maximum height and its kinetic energy is converted to maximum potential energy. While bob B remains at rest.
And after t=T the whole process between 0<t<T repeats itself in the time period of T<t<2T
b) Here E is total energy of bob A and B ∴ we get straight lines, since they E is constant.
Now from the above discussion in part a) we get the following graphs,
For bob A,
For bob B,
Couldn't generate an explanation.
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