**P. 3946.** An elevator cab, whose total mass with its passengers is 600 kg, ascends uniformly. The mass of the counterweight is 300 kg. The mechanical power of the motor is 10 kW and the efficiency is 80%.

*a*) Find the speed of the lift.

*b*) Calculate the tension in the rope which pulls the lift.

(4 points)

**P. 3947.** A spiral spring of negligible mass and spring constant *D* lies un-stretched on a smooth horizontal plane. Its length is *l*_{0}, and one of its end is fixed to a vertical axle, while the to other a point-like disc of mass *m* is attached. Another disc of mass *m* collides elastically with the disc attached to the spring. The initial velocity of the moving disc is *v* and is perpendicular to the axis of the spring. Find the smallest radius of curvature of the path of the disc attached to the spring. *Data:* *D*=64 N/m, *l*_{0}=1 m, *m*=0.5 kg, *v*=8 m/s.

(5 points)

**P. 3948.** A plane flies at a height of 10 km and the state of weightlessness is created for 20 seconds. The plane ascends for 10 seconds and then descends for 10 seconds and returns to the initial height of 10 km.

*a*) Calculate the angle of elevation at the beginning of the weightlessness, if the speed at this time is 900 km/h?

*b*) To what height does the plane ascend?

*c*) What is the speed of the plane at the highest point?

(4 points)