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?

Question

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?

turingtest · Answer

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.

wondermath · Answer

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