- #1

Nikhil_RG

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- TL;DR Summary
- Can the equation F = m(dv/dt) + v(dm/dt) be used directly in all cases where the mass is variable.

Dear Experts.

In a problem where we need to calculate the acceleration of a satellite in a force free space which sweeps and collects interplanetary dust and a certain rate (dm/dt), I believe that the equation F = m(dv/dt) + v(dm/dt) can be used, by putting F=0 and substituting the function for (dm/dt). Can the same equation be used if the dust particles are not stationary initially?

The doubt arises from the fact that, for a cart carrying sand, moving along a smooth friction less surface, if there is a hole in it through which sand drains out at a constant rate, the velocity of the cart will remain constant. This complies very well with momentum conservation and can be easily verified. But, while trying to use the above equation for the same problem. since (dm/dt) is non zero, (dv/dt) cannot be zero.

I feel that it has to do with the relative velocity of the drained out mass with respect to the cart. But how can we mathematically derive and verify it?

In a problem where we need to calculate the acceleration of a satellite in a force free space which sweeps and collects interplanetary dust and a certain rate (dm/dt), I believe that the equation F = m(dv/dt) + v(dm/dt) can be used, by putting F=0 and substituting the function for (dm/dt). Can the same equation be used if the dust particles are not stationary initially?

The doubt arises from the fact that, for a cart carrying sand, moving along a smooth friction less surface, if there is a hole in it through which sand drains out at a constant rate, the velocity of the cart will remain constant. This complies very well with momentum conservation and can be easily verified. But, while trying to use the above equation for the same problem. since (dm/dt) is non zero, (dv/dt) cannot be zero.

I feel that it has to do with the relative velocity of the drained out mass with respect to the cart. But how can we mathematically derive and verify it?