You have a summer job at a company developing systems to safely lower heavy load

Question

You have a summer job at a company developing systems to safely lower heavy loads down ramps. Their system uses a conducting bar sliding on two parallel conducting rails separated by 2.0 m that run down a ramp. The test ramp is inclined at an angle of 36.9 degrees. The bar is perpendicular to the rails and is in contact with them. A 100 kg test load rests on top of the conducting bar. The mass of the bar is small enough to be ignored. The bar slides down the rails through a uniform magnetic field of 5.0 T which points parallel to the ramp (up the ramp). Your group finds that without the magnetic field turned on, the force of kinetic friction between the bar and the rails is only half of that needed for the load to slide at a constant speed as desired. The coefficient of kinetic friction is 0.375. Your task is to determine if the magnetic "brake" can make up the difference. You wonder if this is even possible. If so, what current would need to pass through the conducting bar and in what direction?

Explanation / Answer

F = I L X B (I L cross B) force on current carrying in magnetic field If I is directed to the left (looking up the ramp) then I L X B will be directed perpendicular to the ramp and increase the effective weight of the object on the ramp (and a corresponding increase in N the normal force) Ff = u M g cos 36.9 the frictional force which must be doubled So if the normal force is doubled the frictional force will be doubled I L B = M g cos 36.9 gives the magnetic force equal to the gravitational normal force I = M g cos 36.9 / (L B) = 100 * 9.8 * cos 36.9 / 20 = 39.2 amps

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