# System With Increasing Mass

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1. Mar 31, 2016

### i_hate_math

1. The problem statement, all variables and given/known data
A railroad car moves under a grain elevator at a constant speed of 4.50 m/s. Grain drops into the car at the rate of 420 kg/min. What is the magnitude of the force needed to keep the car moving at constant speed if friction is negligible?

2. Relevant equations
U=V+dV-Vrel , U is the velocity of dM, which is 0 in this case
dM/dt • Vrel = M • dV/dt where V is the velocity not volume

3. The attempt at a solution
So from the question, dM/dt is 420kg/min=70kg/s,
I played with the 1st rocket equation, was able to get (4.5+dV)*70=M*a=Force needed.
But how do I find dV with limited information on the system given?

2. Mar 31, 2016

### haruspex

No it isn't.
Since you do not define all your variables, I cannot tell whether these equations are correct.
Consider the mass added to the car in one second. What is its gain in momentum? What rate of change of momentum does that imply? What is the relationship between force and rate of change of momentum?

3. Mar 31, 2016

### i_hate_math

Okay, i see. So the force required is the new applied force applied to the car so it moves at the same constant speed. i did it again with using the chain rule:
d(MV)/dt=V • dM/dt + M • dV/dt, where M • dV/dt is the thrust of the car before mass started to vary. then the additional force required is just V • dM/dt = 4.5 • 7 = 32.5 N

4. Mar 31, 2016

### i_hate_math

Does that look alright?

5. Mar 31, 2016

### haruspex

Small arithmetic error, but otherwise fine.

6. Mar 31, 2016

### i_hate_math

aw bugger me its 31.5. thanks heaps

7. Apr 1, 2016