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?
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?
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 U0. can be considered constant what is the resistance of the multiplier Rmax , that should be connected in series to ignite the lamp.
b) Find the stable current if the resistance of the multiplier is R<Rmax .
Data: A=30 V, B=20 W, U0=100 V, R=50 .