**P. 4536.** The theoretical limit of the efficiency of wind turbines is the so called *Betz-limit* is 59.3%. There are other losses, but the most modern wind turbines efficiency is approximately 84% of the Betz-limit.

*a*) How many megajoule kinetic energy is carried during 1 second by an air flow of speed of 27 km/h to that wind turbine which is at a height of 100 m, and which has 44 m-long blades?

*b*) What is the maximum output power of the turbine at this wind speed?

(4 points)

**P. 4538.** A frictionless slope, having a cross section of a quadrant of radius *R*=20 cm, is attached to a moveable cart as shown in the *figure.* The horizontal surface of the cart is rough, the coefficient of friction is =0.8. A point-like object falls freely from a height, measured from the plateau of the cart, of *h*=2*R* onto the top of the slope, and arrives tangentially. It slides along the path and just stops at the end of the cart. How long is the cart?

(5 points)

**P. 4539.** The base of a solid 4*r*-high right cylinder is a circle of radius *r*. One side of the surface of a tale made of hard but flexible material is slippery, whilst on the other side the frictional coefficient is . The two parts are separated by a straight line. The cylinder is placed to the slippery side of the table (with its circular base on the tabletop), and is given a push perpendicularly to the separation line. Will the cylinder fall when it reaches the separation line or not, and if yes how, if *a*) =0.2; *b*) =0.7; *c*) =1.4? (The rotational inertia of a cylinder of mass *m*, radius of *r* and height of 4*r* about a horizontal axis through its centre of mass is .)

(6 points)