**P. 3974.** A body of mass *m*_{1}=2 kg slides down from the top of an inclined plane (the angle of inclination is =20^{o}.) A cart of mass *m*_{2}=1 kg is attached to this body with a thread of length =1.6 m as shown in the figure. The thread initially is straight. Along the first part of the slope, the length of which is /2, friction is negligible, along the second part, the length of which is /2, the coefficient of friction is =0.6. How far will the two objects be when the cart reaches the pulley?

(4 points)

**P. 3976.** A disc of radius *R* is moved with a constant *u* velocity on an air-cushioned table. Another small disc collides with it elastically with a speed of *v*_{0}=0.3 m/s, the velocities of the discs are parallel. The distance *d* shown in the figure is equal to *R*/2, friction between the discs is negligible.

*a*) For which *u* will the small disc move perpendicularly to its original motion after the collision?

*b*) What will be the speed of the small disc in this case?

(5 points)

**P. 3978.** A rod of mass *m* and length =1 m slides down on a slope such that one of its end slides along the slope and the other slides along the horizontal without friction. Initially the rod touches the incline, the figure shows a snapshot of the motion later.

*a*) Find the speed of the endpoints *A* and *B* when the rod reaches the horizontal position.

*b*) What are these speeds when the rod encloses an angle of 30^{o} with the horizontal.

(5 points)

**P. 3981.** A generator of constant voltage but of variable frequency is connected to a series *RLC *circuit. Gradually changing the frequency the current reaches a maximum, when the voltage across the inductor is *U*_{1}. If the frequency is further increased the current decreases, but the voltage across the inductor still increases. Later the voltage across the coil reaches its maximum of *U*_{2} and then it decreases.

Determine the quotient of in terms of *R*, *L* and *C*.

(5 points)