Q37 of 48 Page 46

The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.13. If the length of the pendulum is 1m, calculate

(a) the height to which bob A will rise after collision.


(b) the speed with which bob B starts moving. Neglect the size of the bobs and assume the collision to be elastic.



Let be the mass of the bob and be the initial height of the bob.


Potential energy of a particle raised to the height h is =


And kinetic energy of the particle with velocity v is given as


=


Just before collision, bob A reaches ground and its potential energy gets converted to kinetic energy,


∴ conserving energy we get,



-----(1)


(a) Using the result that when two bodies of same mass collide, their velocities are mutually interchanged,


Bob A must come to rest and bob B must gain the velocity in equation (1).


a) ∴ from above we conclude the bob A will not rise to any height since its velocity will become zero after collision.


b) ∵ the velocities are interchanged,


∴ velocity of bob B =


More from this chapter

All 48 →
35

A ball of mass m, moving with a speed 2v0, collides inelastically (e > 0) with an identical ball at rest. Show that

(a) For head-on collision, both the balls move forward.


(b) For a general collision, the angle between the two velocities of scattered balls is less than 90°.


 36

Consider a one-dimensional motion of a particle with total energy E. There are four regions A, B, C and D in which the relation between potential energy V, kinetic energy (K) and total energy E is as given below:

Region A: V > E


Region B: V < E


Region C: K > E


Region D: V > K


State with reason in each case whether a particle can be found in the given region or not.


 38

A raindrop of mass 1.00 g falling from a height of 1 km hits the ground with a speed of 50 m s–1. Calculate

(a) the loss of P.E. of the drop.


(b) the gain in K.E. of the drop.


(c) Is the gain in K.E. equal to loss of P.E.? If not why.


Take g = 10 m s-2


 39

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.