ABSTRACT
In order to solve this problem it is necessary to divide the velocities into components, one along the line of impact and one perpendicular to the line of impact as illustrated in Fig. D5.2.
In the direction along the line of impact the collision is a central impact and can be dealt with by resolving along the line of impact. In the conservation of momentum (equation D4.1):
mA . v + m . v = mA . v’A + m . v’B (D4.1)
the velocity components terms in Fig. D5.2 are substituted to give:
mA . vA.cosqA + mB . vB .cosqB = mA . v’A.cosq’A + mB . v’B .cosq’B (D5.1)
Similarly, using the coefficient of restitution (equation D4.3) and substituting the velocity components of Fig. D5.2 gives:
e = (D5.2)
In the direction perpendicular to the line of impact, the velocity is not affected as the interaction between the two objects in this direction is considered frictionless so there is no interacting force to slow the velocities in this direction. In other words, their momentum in this direction is conserved so the following can be written:
vA.sinqA = v’A.sinq’A (D5.3)
vB.sinqB = vA.sinqA (D5.4)
Equations D5.1-D5.4 enable four unknowns to be calculated provided the other seven variables (of the 11 which make up these problems) are known. An example is given in Fig. D5.3.
