**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Oblique Central Impact

__ Oblique Central Impact:__ The figure shows 2 particles which impact in an oblique manner. Here spherical particles of mass

*m*

_{1}and

*m*

_{2}have initial velocities

*v*

_{1}and

*v*

_{2}in the same plane and approach each other on a collision course. The directions of the velocity vectors are measured from the direction tangent to the contacting surfaces. Thus, the initial velocity components along the

*t*and

*n*-axes are . Note that (

*v*

_{1})

*is a negative quantity for the particular coordinate system and initial velocities shown. Shades of 3 different situations are shown below.*

_{n}
For given initial conditions of *m*_{1}, *m*_{2}, (*v*_{1})* _{n}*, (

*v*

_{1})

*and (*

_{t}*v*

_{2})

*, (*

_{n}*v*

_{2})

*, there will be four unknowns, namely (*

_{t}*v*

_{1}')

*, (*

_{n}*v*

_{1}')

*, (*

_{t}*v*

_{2}')

*and (*

_{n}*v*

_{2}')

*. The four needed equations are obtained as follows:*

_{t}(1) Momentum of the system in the n-direction. This gives,

(2) and (3) The momentum for each particle is conserved in the *t*-direction since there is no impulse on either particle in the* t*-direction.Thus

(4) The coefficient of restitution, as in the case of direct central impact, is the positive ratio of the recovery impulse to the deformation impulse. Hence, like in the case of direct impact,

Once four final velocity components are found, the angles of the figure may be easily determined.

**An example:**Two ball of the same size and mass collide with the velocities of approach shown. For a coefficient restitution of 0.8, what are the final velocities after they part?

Applying the conservation of moment, along the line of impact,

Also,

Thus,

Solving, we get

(*V*_{2})* _{n}* will remain unchanged.

Thus, m/sec

m/sec