Question

1. Collision. Two identical billiard balls collide head-on to each other as shown. The incident velocities vi and v2 (before collision) are 3 m/s and 7 m/s (pay attention to their directions). a). What is the value of the velocity of the center-of-mass of the system? b). In the center of mass reference frame, the velocities of two objects are denoted as v' and v2'. Please find the values of v' and v2 e). In the center of mass reference frame, the exit velocities (after collision) of two objects are denoted as u and u2. A very useful conelusion is that the ratio uf and uzf are equal. The ratio could be denoted as c. Usually, c is in the range of-1 scs 0. In two extreme cases, c could be -1 or 0. Please show the names of these two extreme cases. d). We consider c1 case. Please list the conserved quantities in the collision. e). Ifc 1, what will be the values of exit velocities u' and u2'? f). Since we have known the values of the exit velocities in the center-of-mass reference frame, can we find the values of the exit velocities in the ground reference frame? The velocities could be denoted as u and u 12 1' v2 calculation above is based on the condition m m2, and two concrete velocities 3 m/s and 7 m/s. How about keeping the condition m m2, but changing the incident velocities to other numbers? Can you make a guess?

Answer 1

Vcm = 3m-7m/m + m = -2m/s -ve means towards ldt v_1 vector = v_1 vector - v_cm vector = 3L vector - (-2i^) = 51^m/s i. 5 m/s towards right v_2^1 = v_2 vector - Vcm vector = -7i^- (-2i^) = -5i^m/s i.e 5 m/s towards left after collision the velocities of two balls inter changed v_1^1 = -5i^m/s v_2^' = ki^m/s v_1'/v_1' = v_2'/v_2' = -1 (= c) c = -1 is for perfectly elastic collision c = 0 is for perfectly inelastic collision For c = -1 collision is perfectly elastic therefore kinectic energy and linear momentum both are conserved v_1 vector = v_1 vector + v^vector cm = -5i^- 2i^= -7i^m/s i.e 7m/s towards left v_2 vector = 2i^vector_2 + u vector_cm = 5i^- 2i^= 3i^m/s i.e 3m/s towards night \r\n In collision of same mass bodies the velocities interchanged i.e v_1 vector = v_2 vector v_2 vector = v_1