A Free Response Practice Question Involving Newtonian Mechanics and Electromagnetism for AP Physics B

I give below a free response practice question involving fundamental principles in Newtonian mechanics and electromagnetism. Even though this question is meant for AP Physics B aspirants, I would advise AP Physics C aspirants also to try it. Here is the question:

A cart carries a block of mass m₁ which is connected to a soft iron cylinder of mass m₂ using an inxtensible string of negligible mass passing over a light frictionless pulley as shown in the adjoining figure. The soft iron cylinder is suspended vertically with its lower end inside a current carrying coil fixed to the cart. The cylinder and the coil are coaxial and their vertical sides touch each other without any friction between them. The current carrying coil exerts a magnetic force of constant magnitude f₂ on the soft iron cylinder and the entire system consisting of the cart of mass M (with the current carrying coil), and the connected masses m₁ and m₂ are moving with a constant acceleration ‘a’ in the positive x-direction under the action of a constant force F (fig.) in the same direction. There is no friction between the cart and the block m₁ and the block and the cylinder are at rest relative to the cart during the accelerated motion of the cart. Assume that g = 10 ms^–2.

Now answer the following:

(a) Write an expression for the acceleration ‘a’ of the cart in terms of the net force on the cart and the masses involved

(b) If m₁ = 11 kg, m₂ = 1 kg and a = g/10 calculate the magnitude of the magnetic force f₂ on the cylinder.

(c) If the current in the coil were in the opposite direction, will the direction of the magnetic force change? Justify your answer.

(d) If a cylindrical permanent magnet were used instead of the soft iron cylinder will your answer for part (c) be different? Justify your answer.

Try to answer this question which carries 15 points. You may take 15 minutes for answering this. I’ll be back soon with a model answer for you.