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- Homework Statement
- 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 2.0 m/s [E]. The collision is cushioned by a spring (k = 1200 N/m).

1 Determine the velocity of each cart after the collision.

2 Determine the maximum compression of the spring.

- Relevant Equations
- n/a

The way I learned to solve this was to switch to a frame of reference where one object is stationary.

given: m1 =0.6kg v1 = 5.0m/s [W], m2 = 0.8kg v2 = 2.0 m/s [E]

Setting v2 to rest by adding 2.0 m/s W to each object

New velocities are v1 = 7.0 m/s [E] and v2 = 0.0m/s

Then using the equations for v1

v1f = V1 (m1 - m2) / (m2 + m1)

= (7.0)(0.6-0.8) / (0.8-0.6)

= -7 m/s

and for v2f

v2f = 2m1(v1) / (m2+m1)

= 2 (0.6) (7.0) / (0.8 + 0.6)

= 6 m/s

Switching back to Earth's frame of reference

v1f = 1.8 m/s

v2f = 4.0 m/s

I get these answers, yet i see other answers online using conservation of energy and they get different answers from me. Am I doing this properly?

given: m1 =0.6kg v1 = 5.0m/s [W], m2 = 0.8kg v2 = 2.0 m/s [E]

Setting v2 to rest by adding 2.0 m/s W to each object

New velocities are v1 = 7.0 m/s [E] and v2 = 0.0m/s

Then using the equations for v1

v1f = V1 (m1 - m2) / (m2 + m1)

= (7.0)(0.6-0.8) / (0.8-0.6)

= -7 m/s

and for v2f

v2f = 2m1(v1) / (m2+m1)

= 2 (0.6) (7.0) / (0.8 + 0.6)

= 6 m/s

Switching back to Earth's frame of reference

v1f = 1.8 m/s

v2f = 4.0 m/s

I get these answers, yet i see other answers online using conservation of energy and they get different answers from me. Am I doing this properly?