**P. 4095.** The traffic in some part of a three-lane motorway is restricted to only one lane. In this part the cars move uniformly at a speed of 54 km/h and 11-m long gaps are formed between them.

*a*) What is the speed of the cars before the one-lane part, if the gap between them is 2 m?

*b*) What will the length of the gaps between the cars be after the one-lane part if the cars speed up to a velocity of 126 km/h?

Let us consider the length of each car 4 m.

(4 points)

**P. 4099.** A sample of water of mass *m*_{1} and of temperature *t*_{1} is in a thermos flask, and warmer water of mass *m*_{2} and of temperature *t*_{2} is poured to it. After the themal equilibrium is reached the temperature is measured. Next time, because we are curious, we swop the two samples of water, so the colder water of mass *m*_{1} and of temperature *t*_{1} is poured into the thermos in which there is the other sample of water of mass *m*_{2} and of temperature *t*_{2}. Surprisingly it is found that the equilibrium temperature in the second case is different from the one measured in the first time.

*a*) How can you explain this difference?

*b*) The difference between the two equilibrium temperatures is 1.9 ^{o}C. What can you deduce from this?

*Data:* *m*_{1}=300 g, *t*_{1}=20 ^{o}C, *m*_{2}=600 g, *t*_{2}=80 ^{o}C.

(4 points)

**P. 4100.** A wall divides the cylindrical, thermally insulated container of volume 20 litres into two parts as shown in the *figure.* There is vacuum in the left part which is closed by a thermally insulated fixed piston, and in the other part there is Nitrogen gas at a pressure of *p*=5^{.}10^{5} and at a temperature of 300 K. (The external pressure is 10^{5} Pa.) The door on the wall opens because of the excess pressure, and the gas expands immediately. Then the fixing of the piston is ceased, and the gas is pushed back into its original place.

*a*) How much work was performed during the compression of the gas?

*b*) What are the temperature and the pressure of the gas at the end of the process?

(5 points)

**P. 4103.** The mass of a two-engine plane is *m*. Because of some breakdown there is a considerable difference between the thrusts of the engines, which is . Despite of the breakdown the pilot managed to drive the plane horizontally along a straight line.

*a*) What is the force exerted on the vertical surface of the tail if the distance between the tail and the centre of mass is one and a half times the distance between the two engines?

*b*) Why and by what angle did the pilot have to lean the plane?

The plane is symmetrical, and it can be assumed that after the breakdown air resistance is exerted at the plane of symmetry.

(5 points)