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**Physics (mechanics) AP Problem---involving kinetic energy of a moving object**

The following is an AP Physics Mechanics question. I have some questions about understanding what it's asking me to do and about impulse.

PROBLEM:

An open-top railroad car (initially empty and of mass Mo) rolls with negligible friction along a straight horizontal track and passes under the spout of a sand conveyor. When the car is under the conveyor, sand is dispensed from the conveyor in a narrow stream at a steady rate (delta-M)/(delta-t)=C and falls vertically from an average height h above the floor of the railroad car. The car had initial speed Vo and sand is filling it from time t=o to t=T. Express your answers to the following in terms of the given quantities and g.

a) Determine the mass M of the car plus the sand that it catches as a function of time t for 0<t<T.

b) Determine the speed V of the car as a function of time t for 0<t<T.

c) i. Determine the initial kinetic energy Ki of the empty car.

ii. Determine the final kinetic energy Kf of the car and its load.

iii. Is kinetic energy conserved? Explain why or why not.

d) Determine expressions for the normal force exerted on the car by the tracks at the following times.

i. Before t=0

ii. For 0<t<T

iii. After t=T

MY ANSWERS

a)Mass = Mo+Ct

b) V=(MoVo)/(Mo+Ct)

c) i. Ki=(1/2)MoVo

ii. kf = (1/2)(MoVo)

iii. ??? (they shouldn't be equal, as I have it, should they???)

d) i. Mg

ii. (Mo+Ct)g

iii. (Mo+Ct)g

I know I didn't get it all right.... Alright, here are MY QUESTIONS (regarding specific letters of the answers)---(IF YOU CAN EVEN HELP ME WITH ONE OF THESE QUESTIONS I'D BE SO GRATEFUL!!!!!):

a) should the "t" in this answer be lower case or upper case? I was confused about that.

b)I set the initial and final momentums equal to solve this part (b)..... But I feel like I never took the sand into account in the initial momentum. I had: MoVo=(Mo+Ct)V (initial momentum = final momentum).

c)shouldn't c) i. and ii. NOT be the same???----because energy isn't conserved in collisions(right????)

another question: I never took the height the sand falls (h) into account anywhere, which I'm sure i should have..... in which part---and how???

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