## Wondermath 4 years ago A cart with mass 0.340 kg moving on a frictionless linear air track at 1.2 m/s strikes a second cart of unknown mass at rest. The collision between the two carts is elastic. After the collision, the first cart continues in its original direction at 0.66 m/s. a) What is the mass of the second cart? b) What is the velocity of the second cart after impact?

1. TuringTest

Momentum:$P_{1i}+P_{2i}=P_{1f}+P_{2f}$$m_1v_{1i}=m_1v_{1f}+m_2v_2$And for elastic collisions we have conservation of kinetic energy$K_{1i}+K_{2i}=K_{1f}+K_{2f}$$\frac12m_1v_{1i}^2=\frac12m_1v_{1f}^2+\frac12m_2v_{2f}^2$So we have a system of equations:$m_1v_{1i}=m_1v_{1f}+m_2v_2$$m_1v_{1i}^2=m_1v_{1f}^2+m_2v_{2f}^2$Two equations+two unknowns=solvable problem.

2. Wondermath

how come we don't use the two equations for elastic collisions|dw:1327884980480:dw| and the other one?

3. TuringTest

Maybe you can, that equation doesn't ring a bell for me offhand. I was just doing it the way it occurred to me.

4. Wondermath

oh ok thx