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A wagon loaded with sand leaks sand through a hole in its bottom at a constant rate lambda (mass per unit time). An external force F acts on the wagon along its direction of motion. If the instantaneous velocity of the wagon is v and the initial mass of the system is m0, which equation correctly governs the wagon's motion?
- F = m0 dv/dt + lambda v
- F = m0 dv/dt - lambda v
- F = (m0 - lambda*t) dv/dt
- F = (m0 - lambda*t) dv/dt + lambda v
Correct answer: F = (m0 - lambda*t) dv/dt
Solution
Because the sand falls out with zero velocity relative to the wagon, it produces no thrust force; the governing equation is simply F = m(t) dv/dt = (m0 - lambda*t) dv/dt.
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