Current in relation to magnetic fields and velocity

[Nuru]

Magnetic Field on an incline

This is what looks to be a fairly simple magnetic field problem, but I don't have much experience in relating velocities to electrical currents, so I'm a bit stuck. The problem as described is

The two conducting rails in the drawing are tilted upwards so they make an angle of 30.0° with respect to the ground. The vertical magnetic field has a magnitude of 0.047 T. The 0.19 kg aluminum rod (length = 1.6 m) slides without friction down the rails at a constant velocity. How much current flows through the bar?

So my variables to my knowledge are
I = unknown
m = 0.19 kg
B = 0.047 T
a = 9.8 m/s (gravity)
L = 1.6 m

The formula I know for this sort of thing is simply $$F = ILB\sin{\theta}$$. My first approach was to use the relation $$F\,=\,MA$$ and substitute that in so I had: $$MA\,=\,ILB\sin{\theta}$$

This turns into $$I\,=\, \frac{MA}{LB\sin{\theta}}$$

So $$I\,=\,\frac{(.19 kg)(9.8 m/s)}{(1.6 m)(0.047 T)\sin{30}}$$

then $$I\,=\,49.5212766$$

However, that obviously isn't right. Did I miss an important detail? I found another problem which was identical except that it had a frictional coefficient they applied in the numerator and they had a $$\theta$$ of 90. Unless I misunderstood something it seems like this should be solvable the same way. Any help would be appreciated.

 

[Nuru]

I think the problem is that I'm using the gravity component in the y-axis instead of for the plane, but I'm not sure how to do that correctly.

 

[ogb p]

I would first check the units of the final answer to see if they make sense in the context of current (amps). It seems like you have correctly applied the formula for the force on a current-carrying wire in a magnetic field, but there may be a mistake in the units or in the conversion of angles. I would also double check the given values and make sure they are accurate.

Additionally, since the problem involves a sliding motion, there may be other forces at play that could affect the current flowing through the bar. Friction, for example, could play a role in slowing down the bar and reducing the current. It may be helpful to draw a free body diagram and consider all the forces acting on the bar.

Furthermore, it may be useful to consider the direction of the current in relation to the direction of the magnetic field. Depending on the orientation, the current may either be in the same direction or opposite direction as the force, which would affect the final calculation.

Overall, it is important to carefully analyze all the given information and consider any potential factors that may affect the final answer. As a scientist, it is important to approach problems with a critical and analytical mindset to ensure accurate and reliable results.