The loading dock has a platform truck where shipments are placed while waiting for pickup. There is a chain attached to the floor and the truck to prevent it from rolling away uncontrolled, but still allows free movement around the loading dock area. The chain is in a pile on the floor when the truck is next to the door. As the truck rolls away from the door, it pulls some chain out of the pile. Your job as the intern is to develop the equations needed to size this chain. To do this, we need to know the impulse of the system at any distance from the door.

(a) Develop the equation of motion for this system. Note, this is a system that is gaining mass as it moves away from the door.
(b) Develop the equation to find the acceleration of this system.
(c) Solve for the velocity of the system.

GIVEN:

M = mass of the truck and whatever cargo is on it
rho = density of the chain (mass per length)
L = initial length of chain attached to the truck and included in the initial system
x = distance truck travels (length of chain added to the system as it moves)
System is initially at rest.