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metalrose
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A momentum question - having conceptual difficulties - please help..!
A freight car of mass M contains a mass of sand m'. At t = 0 a
constant horizontal force F is applied in the direction of rolling and at
the same time a port in the bottom is opened to let the sand flow out at
constant rate dm/dt. Find the speed of the freight car when all the sand
is gone. Assume the freight car is at rest at t = o.
F = d(P)/dt
I applied the above equation to the system of "freight car".
Which is,
F = d(P)/dt, where P is the momentum of the freight car at any instant of time.
Now P = mv, where m and v are the total mass and velocity of the freight car at any instant. Now, d(P)/dt should be
v(dm/dt) + m(dv/dt) ..... (right?)
But I looked up the solution, and over there it is instead given,
d(P)/dt = d(mv)/dt = m(t) x (dv/dt)
where m(t) is the mass of the freight car at time 't'.
So essentially, in the solution, m has been taken out of differentiation. My question is, why is it so?
What is wrong with my differential equation, d(P)/dt = d(mv)/dt = v(dm/dt) + m(dv/dt) ?
Please help...
Thanks
Homework Statement
A freight car of mass M contains a mass of sand m'. At t = 0 a
constant horizontal force F is applied in the direction of rolling and at
the same time a port in the bottom is opened to let the sand flow out at
constant rate dm/dt. Find the speed of the freight car when all the sand
is gone. Assume the freight car is at rest at t = o.
Homework Equations
F = d(P)/dt
The Attempt at a Solution
I applied the above equation to the system of "freight car".
Which is,
F = d(P)/dt, where P is the momentum of the freight car at any instant of time.
Now P = mv, where m and v are the total mass and velocity of the freight car at any instant. Now, d(P)/dt should be
v(dm/dt) + m(dv/dt) ..... (right?)
But I looked up the solution, and over there it is instead given,
d(P)/dt = d(mv)/dt = m(t) x (dv/dt)
where m(t) is the mass of the freight car at time 't'.
So essentially, in the solution, m has been taken out of differentiation. My question is, why is it so?
What is wrong with my differential equation, d(P)/dt = d(mv)/dt = v(dm/dt) + m(dv/dt) ?
Please help...
Thanks