An engineer is designing a curved off-ramp for a freeway. Since the off-ramp is curved, she wants to bank it to make it less likely that motorists going too fast will wipe out. If the radius of the curve is r , how great should the banking angle, θ, be so that for a car going at a speed v , no static friction force whatsoever is required to allow the car to make the curve? State your answer in terms of v , r , and g , and show that the mass of the car is irrelevant.
The figure shows an old-fashioned device called a flyball governor, used for keeping an engine running at the correct speed. The whole thing rotates about the vertical shaft, and the mass M is free to slide up and down. This mass would have a connection (not shown) to a valve that controlled the engine. If, for instance, the engine ran too fast, the mass would rise, causing the engine to slow back down. (a) Show that in the special case of a =0, the angle θ is given by
The figure shows two blocks of masses m 1 and m 2 sliding in circles on a frictionless table. Find the tension in the strings( L1 and L2) if the period of rotation (time required for one complete rotation) is P .