Question

Cart A has a mass of 6.50 kg and is going to the right at a speed of 2.60 m/s and Cart B has an unknown mass and is going to the left with a speed of 3.25 m/s. They collide and Cart A is seen going to the left at 4.13 m/s while Cart B is seen to now be going to the right with the speed of 1.40 m/s.

A. What is the mass of Cart B?

B. What was the change in Kinetic Energy during the collision?

The answers are 4.21 kg, and -39.5 J. I'd like to see the steps and formulas to complete the problem. Thank you!

Answer 1

(A) Initial momentum = Final momentum m_A u_A +m_B u_B = M_A V_A +m_B+v_B => 6.5(2.60)+M_B(-3.25) = 6.5(-4.13)+M_B(1.40) => 16.9-3.25 m_B = -26.85 +1.40 m_B => 4.65 m_B = 43.75 => m_B = 9.4 kg (B) Delat k. E = [(1/2m_Bv_B^2 +1/2 m_Av_A^2)-(1/2m_Bu_B^2+1/2m_Au_A^2)] = [(1/2 times 9.4 times 1.4^2 +1/2 times 6.5 times (-4.13)^2-(1/2 times 9.4 times (-3.25)^2 +1/2 times 6.5 times (2.6)^2] = [-6.97J]