- #1
Eitan Levy
- 259
- 11
Homework Statement
A cart with no motor moves on a plane. At t=0 it has a mass equal to m0 and some velocity. Each second sand with a mass of α comes out of the cart with a velocity of 0 in relation to the plane. What is the equation of motion of the cart?
Answer: dV/dt=αv(t)/(m0-αt)
Homework Equations
F=dP/dt
The Attempt at a Solution
Basically I can't understand why the momentum of cart is conserved. I mean, if sand comes out of it with a velocity that is different than the velocity of the cart there has to be some force involved right?
What I get is dV/dt=2αv(t)/(m0-αt), because the loss of momentum of the sand translates into some force that the cart applies on it (I believe). What am I doing wrong?