A rod of mass 'M' and length 'l' with end A hinged is lying on smooth horizontal table. A particle of mass 'm' with velocity 'u' strikes at right angle to the other end of the rod. Considering perfectly elastic collision find the
1. angular velocity of rod after impact
2. velocity of particle after impact
3. Impulsive reaction at end A
106as rod is hinged,
using cons. of ang. momentum,
mul = mvl + Ml2ω/3 ... (i) (v = vel. of particle after collision, ω=ang vel. of rod)
using COR eqn:
ωl-v = u .... (ii)
So u can solve for ω and v..
which solves first two parts.
To find impulsive reaction at A,
draw the FBD of the rod and of the particle during the collision (remember hinge will give both hori and vertical reaction)
1Thanks !!!
Once the ' ω' is found out Impulsive reaction at hinge can be obtained by by equating aljebric linear impulse equation in y- direction. I think there will be no reaction in x - direction
106I think there will be no reaction in x - direction
Not necessary
It depends on the values of m and M( possible other things as well)