**P. 4361.** A car travelled at a speed of , when a pedestrian stepped down from the sidewalk. The driver braked suddenly and the accident was avoided. The braking-distance was 6.25 m.

*a*) The car in the next lane could only stop in a distance of 9 m. What was the speed of this car if the accelerations of the two cars were the same.

*b*) What were the braking times of the two cars? *c*) What is the ratio of their initial kinetic energies if their mass is the same?

(4 points)

**P. 4364.** The *figure* shows two rods, a copper one and an aluminum one, which comes out of a wall. At a temperature of 20 ^{o}C the length of the copper rod is 2 m, and the length of the aluminum one is 1 m. The gap between them is 1.3 mm.

*a*) At what temperature will the gap disappear?

*b*) What is the size of the gap at a temperature of 0 ^{o}C?

(4 points)

**P. 4365.** In a container there is a sample of air at a pressure of 5^{.}10^{5} Pa, and at a temperature of 350 K. The air is compressed at constant pressure to 4/5 of its original volume, while a 1000 J work is done.

*a*) What will the temperature of the air be?

*b*) What is the change in the internal energy of the sample of air?

*c*) What is the density of the compressed air?

(4 points)

**P. 4366.** The area of the bottom of a cylinder-shaped vessel is 78,5 cm^{2}. The height of the water coloumn in it at a temperature of 18 ^{o}C is 15 cm. Then the temperature of both the vessel and the water is increased to 48 ^{o}C.

*a*) Will the hydrostatic pressure exerted to the bottom of the vessel increase or decrease? What percent is the change?

*b*) Will the gravitational potential energy of the water, with respect to the bottom of the vessel, increase or decrease? What percent is the change? (Neglect the evaporation of water!)

(5 points)

**P. 4367.** An easily moveable, airproof piston of negligible mass closes a cylinder shaped container, made from some good heat-conducting material. The area of the base of the cylinder is 1,0 dm^{2}. In the cylinder, below the piston, there is 2 ml water at room temperure, and a very little air. The cylinder is immersed into some liquid, the temperature of which is 100 ^{o}C, and is kept in it for a long time. What happens? At what height will the piston be at rest?

(5 points)