Two air track carts move toward one another on an air track. Cart 1 has a mass o
ID: 2006472 • Letter: T
Question
Two air track carts move toward one another on an air track. Cart 1 has a mass of 0.47 kg and a speed of 0.9 m/s. Cart 2 has a mass of 0.65 kg.(a) What speed must cart 2 have if the total momentum of the system is to be zero?
(b) Since the momentum of the system is zero, does it follow that the kinetic energy of the system is also zero?
(c) Verify your answer to part (b) by calculating the system's kinetic energy.
Explanation / Answer
(a) mv1 + mv2 = 0 (.47)(.9) + (.65)v2 = 0 v2 = -.65 m/s * the negative sign indicates opposite direction from cart 1 (b)/(c) .5mv1^2 + .5mv2^2 = 0? .5(.47)(.9)^2 + .5(.65)(-.65)^2 = 0? .32798.... > 0 so no, kinetic energy is not zero. In general, kinetic energy cannot be zero unless the masses or velocities are zero. The velocities are squared in the KE equation, so even if it is negative, the end result is positive