How Do Carts Behave and Springs Compress in an Elastic Collision?

AI Thread Summary
In an elastic collision involving two carts, the first cart (0.60 kg) moves at 5.0 m/s west and collides with a second cart (0.80 kg) moving at 2.0 m/s east, with a spring involved (k=1200 N/m). The calculations for the velocities after the collision yield a velocity of -3 m/s for the first cart (east) and 4 m/s for the second cart (west). There is confusion regarding the maximum compression of the spring, with a reminder that the potential energy in the spring is given by U = 0.5 * k * X^2. The discussion highlights the need to revisit the calculations for part (a) to ensure accuracy before proceeding to part (b). Clarification on the spring compression is essential for a complete understanding of the collision dynamics.
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In an elastic head-on collision, a 0.60 kg cart moving at 5.0 m/s (W) collides with a 0.80 kg cart moving at 2.0m/s (E). the collision is cushioned by a spring (k=1200 N/m)

a find the velocity of each cart after the collision

b find the maximum compression of the spring

ATTEMPT:

cart 1:
v1=( m1-m2/m1+m2)(v1)
v1= (0.6-0.8/0.6+0.8)(7)
v1= -1

then i did -1 + -1 = -3 m/s (E)

cart 2:

v2= (2m1/m1+m2) (v1)
v2= 6
6 + -2= 4 m/s (W)

i'm totally lost for part b
 
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It may help to recall the potential energy stored in a compressed spring is equal to

U = 0.5 * K * X^2
 
you might want to check (a) again
i am getting different answers
 

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