Lab 7. Challenge.

Challenge 1:   Position where 99% of the terminal velocity is attained (bonus 15%).

Assume a magnet is dropped with zero initial velocity into a copper tube. Its velocity will increase and will approach its terminal value . Find the distance traveled by the magnet when its speed equals to 99% of its terminal value, i.e. find the distance traveled when the speed is . The answer is expected in terms of  and gravitational acceleration . Use measured values of  for black magnet in ¾” and 1” L type tubes to evaluate such distances. You were instructed to place upper pickup coil 10-11cm from the end of the tube. Was that sufficient to ensure that the speed of the (black) magnet attained 99% of its terminal value by the time it passes upper pickup coil?

 

 

Challenge 2:   Model 4 – thick wall tube (bonus 10-15%).

Both our theoretical models for the terminal speed of the magnet in the conducting tube assumed the tube’s wall thickness is negligibly small compared to the radius of the tube. For the tubes in our experiments this assumption is justified. But for tubes with thick walls even our sophisticated Model 2 is not accurate. Find expression for the terminal speed of the magnet in the tube with inner radius  and outer radius  (with wall thickness  not negligibly small compared to ).

Hint: do not start from scratch. You may use a point dipole approximation (treat magnet as a point dipole, based on Model 1 - 10% bonus) or consider magnet’s dimensions (based on Model 2 – 15% bonus). Treat a thick wall tube as a coaxial combination of many thin wall tubes (use Model 3, generalize (M. 23) for many coaxial tubes) and integrate over tube’s radius .