52 Practice Makes Perfect VII
More practice!
Exercise 52.1: Two springs
Two springs with spring constants 
and 
are attached to a mass 
as shown. The springs are unstretched. You grab the mass, and displace it a distance 
to the left, and let go. The mass oscillates back and forth.
Find the period of the resulting oscillations, and the equation that describes these oscillations, i.e. find 
.
If you get stuck, you can check my drawing.
Exercise 52.2: Floor gives out
Start by watching ~10 seconds of this video of carnival ride.
You can see what’s going on: the people are inside a large cylinder. The cylinder is spun to an angular velocity 
, and then the floor is lowered. Remarkably, the people don’t fall! They remain glued to the walls. Suppose the walls have a static frictional coefficient 
with clothes, and that the radius of the cylinder is 
. What is the minimum angular velocity required for people not to slide down the wall once the floor is removed? If you get stuck, you can look at my drawing.
Exercise 52.3: Sliding Boxes
Two boxes of mass and 
are attached by a string, and are allowed to slide down a ramp as shown. The large box has a frictional coefficient , and the small box has a frictional coefficient 
that is smaller than . Find the acceleration of the blocks, and the tension of the rope. If you get stuck, check your drawing agains mine, and take it from there.