Question

Cart 1 has an initial velocity and hits Cart 2 which is stationary. After a perfectly inelastic collision, the combined carts are traveling with exactly one third the initial velocity of Cart 1, and in the same direction. Which is correct about the mass of Cart 2

Answer 1

The mass of Cart 2 must be twice the mass of Cart 1

Explanation: e2020 answer

Answer 2

Let's use variables to illustrate the problem:

Let
m1=mass of cart 1
m2=mass of cart 2
v1 = velocity of cart 1 before collision
v2 = velocity of cart 2 before collision
v' = velocity of the carts after collision

Using the conservation of momentum for perfectly inelastic collisions:

m1v1 + m2v2 = (m1 + m2)v'

v2 = 0 because it is stationary
v' = 1/3*v1

m1v1 = (m1+m2)(1/3)(v1)
m1 = 1/3*m1 + 1/3*m2
1/3*m2 = m1 - 1/3*m1
1/3*m2 = 2/3*m1
m2 = 2m1

From here, we can say that the mass of cart 2 is twice that of the mass of cart 1.