**P. 3923.** In a thermally insulated container there was some water at a temperature of , then 1 kg ice at temperature was added. How much water was initially in the container if

*a*) there was no phase change;

*b*) the total amount of ice melted;

*c*) the total amount of water froze?

(4 points)

**P. 3929.** A disc of mass *m*=12 kg and of radius *R*=0.1 m slides down without rolling along smooth, frictionless inclined plane, which ends in a horizontal plane without break. The disc starts at a height of *h*=1.25 m (it has no initial speed and it does not rotate), and lands on the top of a cart of mass *M*=6 kg, which can move easily. The coefficient of kinetic friction between the cart and the disc is =0.4. The disc begins to roll without sliding when it is in the middle of the cart.

*a*) How long is the cart?

*b*) What is the greatest speed of the cart?

*c*) How long does it take for the disc to go through the cart?

(5 points)

**P. 3930.** The circuit of a carbon arc lamp is shown *in the figure* (to ignite the lamp the carbon electrodes are touched together, then they are slowly drawn apart.) The voltage across the gap between the carbon rods as a function of the current can be given by the following formula: , where *A* and *B* are constants.

*a*) If the voltage of the battery *U*_{0}. can be considered constant what is the resistance of the multiplier *R*_{max }, that should be connected in series to ignite the lamp.

*b*) Find the stable current if the resistance of the multiplier is *R*<*R*_{max }.

*Data:* *A*=30 V, *B*=20 W, *U*_{0}=100 V, *R*=50 .

(5 points)