Hur Hur

Are you sorry yet?

How would you approach this problem?

Posted by E-George on October 14, 2007

Because, frankly, I didn’t have a clue and used up more than 52% of available points digging through all the hints made available with the problem.

Here’s the problem:

Rail Gun

A Rail Gun uses electromagnetic forces to accelerate a projectile to very high velocities. The basic mechanism of acceleration is relatively simple and can be illustrated in the following example. A metal rod of mass m and electrical resistance R rests on parallel horizontal rails (that have negligible electric resistance), which are a distance L apart.

The rails are also connected to a voltage source V, so a current loop is formed.

The rod begins to move if the externally applied vertical magnetic field in which the rod is located reaches the value B. Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use g for the magnitude of the acceleration due to gravity.

Image and problem text courtesy of Mastering Physics

Here’s what it asked me to solve for:

Find μ_s, the coefficient of static friction between the rod and the rails.

The only hint I got that was remotely useful was to remember that the rod wouldn’t begin to move until the magnetic force was equal to the force of static friction. I also figured out that this was a rod with a current running through it, so the magnetic force = current x length x magnetic_field x sin(θ). θ is 90o, so sin(θ) = 1, making magnetic force = current x length x magnetic_field, or:

F_mag = V/R * B * L

What I’m having trouble remembering is how to figure the value for μ_s. F_static = μ_s * n, doesn’t it? So, I guess then the real question is what is equal to n (a.k.a. the normal force?). The answer to the problem states that n=m*g. Why, though? Why does the normal force m*g?

The answer for μ_s is this:

μ_s = V/R * B * L * (1 / m*g)

I should probably be embarrassed to ask, but I seriously don’t get how this conclusion gets made. Please. Elucidate.


Filed Under: Lookit - Comments:



  • Kaylee Tejeda said,

    n=mg comes from Physics 160. Back in the days of the inclined plane, the normal force was shown to be mg cosθ, and since the rail is laying flat, θ=0, so n=mg.

    This comes from a free body diagram. What are all the forces acting in the vertical direction? F_g acting down, equal to mg. And F_n acting up, equal to god knows what. But, noticing that the rod is not accelerating in the y-direction at all, then F_y=0, which tells you that the two forces acting in the y-direction are equal in magnitude but opposite in sign, so F_n = mg acting upwards.

    Next, realize that the rod won’t start to move until the magnetic force overcomes the static frictional force, or until F_mag = F_static. And, yes, F_static = μ_s * n.

    Does that help? See how far that gets you.

  • Kaylee Tejeda said,

    Oh, and F_y=0 since a_y=0 and F_y=ma_y.

    Also, if the item in question IS accelerating in the y-direction (think of an elevator taking off from rest), then F_n is NOT equal to mg. This is only true for things at rest or sliding along horizontal surfaces.

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