1. 10/31 Momentum Examples  Tomorrow: Begin Rotational Dynamics Read Ch 9 sec 1-3  Suggested problems from Ch 7 22, 35, 36, 37, 53, 55  HW: None assigned today (Happy Halloween)  Exam 3: Thursday, 11/14  Exam 4: Thursday, 12/5  Final Exam: Monday, 12/16, 8:00 am

2. Methods for Momentum  p sys,i = p sys,f  Best when things stick together   p A =  p B  Good when you know velocity before and after for one object  Components for 2-D  Can find components first since the components are conserved also. (see next example)

3. p t,i,y = ?24,000 kg m/s A car and a truck, velocities and masses shown, collide and lock bumpers. Find the final velocity (magnitude and direction) of the pair.  vfvf 37 0 v t = 5 m/s v c = 15 m/s M t = 8000 kg M c = 2000 kg x y p c,i,y = ? p sys,f,x = ? p sys,f,y = ? p t,i,x = ? p c,i,x = ? 0 24,000 kg m/s 32,000 kg m/s 30,000 kg m/s 62,000 kg m/s

4. A car and a truck, velocities and masses shown, collide and lock bumpers. Find the final velocity (magnitude and direction) of the pair.  vfvf 37 0 v t = 5 m/s v c = 15 m/s M t = 8000 kg M c = 2000 kg x y p sys,f,y = p sys,f,x = p sys,f = ? v sys,f = ?  = ? 66,500 kg m/s 6.65 m/s tan -1 24,000/62,000 = 21° 24,000 kg m/s 62,000 kg m/s

5. Momentum in 2-D A 0.5 kg ball moving at constant velocity of 8 m/s east strikes an identical object at rest. After the collision ball A is moving at 7.5 m/s at an angle of 20°. Find the velocity and angle of the blue ball. v A,i = 8 m/s 0.5 kg x y v A,f = 7.5 m/s 20°  = ? v B,f = ? AB p Sys,i,y = p Sys,f,y p Sys,i,x = p Sys,f,x Momentum is conserved in the x and y directions independently p Sys,i = p Sys,f

6. Momentum in 2-D A 0.5 kg ball moving at constant velocity of 8 m/s east strikes an identical object at rest. After the collision ball A is moving at 7.5 m/s at an angle of 20°. Find the velocity and angle of the blue ball. v A,i = 8 m/s 0.5 kg p A,i = mv = 4 kg m/s east x y v A,f = 7.5 m/s 20°  = ? v B,f = ? AB p i,y = 0 p i,x = 4 kg m/s p A,f,y = mv sin 20° p B,f,y = 1.28 kg m/s p A,f,x = mv cos  = 7.5(0.5) cos 20° p A,f,x = 3.52 kg m/s p B,f,x = 0.48 kg m/s p A,f,y = mv sin 20° = 7.5(0.5) sin 20° p A,f,y = 1.28 kg m/s

7. Momentum in 2-D A 0.5 kg ball moving at constant velocity of 8 m/s east strikes an identical object at rest. After the collision ball A is moving at 7.5 m/s at an angle of 20°. Find the velocity and angle of the blue ball. v A,i = 8 m/s 0.5 kg p A,i = mv = 4 kg m/s east x y v A,f = 7.5 m/s 20°  = ? v B,f = ? AB p B,f,y = 1.28 kg m/s p B,f,x = 0.48 kg m/s p B,f = 1.37 kg m/s (a 2 + b 2 = c 2 )  = tan -1 1.28/0.48 = 69  v B,f = 2.74 m/s (p = mv)