Cart A is $0\mathrm{.}500$ kg while Cart B is $0\mathrm{.}250$ kg$.$ The carts are on an inclined track $(10\mathrm{.}0$ degrees with the horizontal$)$ Cart A has a friction pad attached, with a uk$=0\mathrm{.}400,$ while cart b is frictionless. Attached to cart A$,$ as shown, is a string that goes over a frictionless pulley which eventually connects to block c $(1\mathrm{.}50$kg$)$ The system is set in motion by giving it a push down the hill.

Cart A is $0\mathrm{.}500$ kg while Cart B is $0\mathrm{.}250$ kg $.$ The carts are "velcro$-$ed$"$ together. The carts are on a inclined track $(10\mathrm{.}0^($@$)$ with the horizontal$)$ Cart A has a friction pad attached, with a mu$\_($k$)=0\mathrm{.}400,$ while Cart B is frictionless. Attached to Cart A$,$ as shown, is a string that goes over a frictionless pulley which eventually connects to block C $(1\mathrm{.}50$ kg $).$

The system is set in motion by giving it a push down the hill.

The system is set in motion by giving it a push down the hill.

Draw a force diagram

a$.$ While the system is moving downhill $($after the hand is gone$),$ what is the acceleration of the system and the tension in the rope attached to Cart A $?$

b$.$ Given enough time, the system eventually changes direction and heads uphill. During this time, what is the acceleration of the system, the force on Cart B from Cart A$,$ and the tension in the rope attached to Cart A $?$