(a) Determine the center-of-mass velocity of the two carts in Figure 6.8 

(a) before and after the collision, and verify that it is equal to the velocity of the carts at the point where the two \(v_{x}(t)\) curves intersect. 

(b) Is the velocity of the carts at the point where the two \(v_{x}(t)\) curves intersect always equal to the center-of-mass velocity? 

(c) Determine the velocities of the two carts in the zeromomentum reference frame, before and after the collision, and show that in this reference frame the momentum of the system is always zero.

Transcribed Image Text:

Figure 6.8 Velocity-versus-time graphs for two carts colliding on a low-friction track as seen (a) from the Earth reference frame and (b) from a reference frame moving along the track at VEM = -0.20 m/s relative to Earth. The inertias are 0.36 kg for cart 1 and 0.12 kg for cart 2. (a) Earth reference frame (b) Reference frame M (VEM = -0.20 m/s) UME VM2 UME UM2 UMI E cart 2 cart 1 E cart 2 cart 1 E cart 2 cart 1 E cart 2 cart 1 VEX (m/s) 1.2 0.8 cart 2 0.4 0 AVEL cart 1 -0.4 0 20 40 VMx (m/s) 1.2 0.8 cart 2 0.4 AVMIX AUM2x cart 1 0 t (ms) -0.4 60 60 80 100 120 0 20 20 40 g- 60 80 100 t (ms). 120