Question

please answer all parts to the question they all go with the diagram and numbers

a, b, c, d, e, f, g, h

2) (60 points) (I try hard to make the numbers actually make sense but couldn't do it with this one...) A rod with a length of 25.0 cm is falling in a Magnetic field with B = 0.6 T, as shown. At time to a battery with Emf = 15,000 V is added to the circuit as shown. At that time the rod is falling with a downward speed of 10 m/s (10,000 m/s). R=5oori m=2,5kg. 8 В g=9,8 m/s2 E L R. ting tvo differential You should get tw9, equations for this problem. One comes from Newton's second law for the motion of the rod in the combined magnetic field and gravity. The other comes from the "loop law", don't forget Faraday. The dependent variables are velocity and current. The independent variable is time. If you eliminate the current from the equations you will get an equation for the velocity which one can solve using techniques we have used in this class. a) Write down the equation from Newton's second law. b) Write down the equation from the "loop law". c) Write down the solution to the combined velocity equation for the velocity as a function of time. What are values of the constants in the solution? d) At what time does the rod change it's direction of motion? e) What is the current as a function of time? Does it ever change direction? f) What is the final velocity? What is its direction? g) Extra Credit: What is the time constant for the motion? h) Extra Credit: How far had the rod fallen from t=0 by the time it changed direction (to solve this you need to integrate the velocity function and find the position, don't forget the constant of integration)? i) Super Extra Credit: How much time has elapsed when the rod gets back to the starting point? (This problem requires solving a transcendental equation).

Answer 1