Can a Mass Attached to a Spring Move in a Magnetic Field with Electric Current?

AI Thread Summary
A mass attached to a spring through which an electric current flows raises questions about its movement in a magnetic field. The spring acts like a solenoid, generating a magnetic field that could exert a force on the mass. The force on the mass depends on the direction of the current and the magnetic field, as described by the equation F = I l × B. Clarification is needed on whether the current was present initially or activated at the moment of observation. Understanding these dynamics is crucial for determining if the mass will move.
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Homework Statement



A mass is attached to a spring through which circulates an electric current. Will the mass move?

Homework Equations



F = I l \times B ?

The Attempt at a Solution



A spring is geometrically equivalent to a solenoid. Therefore, the current would generate a magnetic field which goes through the spring. What I'm not sure of is whether this magnetic field exerts a force on the solenoid or not.

Thank you.
 
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Consider what F = I l × B of a small section of the spring does on the current in the next loop of the coil. What is the direction of the resulting force ? (Ideal) springs are supposed to extend/contract in repsonse to forces in which direction ?

Problem formulation is somewhat vague: was the current there when we opened our eyes, or was it switched on at that moment ?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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