**P. 4950.** A car of mass 1200 kg started from rest and speeded up at an acceleration of 2 m/s\(\displaystyle {}^2\) along a straight horizontal path of length 200 m. Its wheels did not slide.

\(\displaystyle a)\) What was the total frictional force exerted between the ground and the wheels?

\(\displaystyle b)\) What is the final kinetic energy of the car? (The mass of the wheels can be neglected.)

\(\displaystyle c)\) How much work was done by the static frictional force?

(4 points)

**P. 4953.** Some argon gas is put into a Torricelli-tube of length \(\displaystyle L=1\) m and of cross section \(\displaystyle A=2\) cm\(\displaystyle {}^2\), therefore the height of the mercury in the tube is only \(\displaystyle h_1=0.4\) m. The ambient air pressure is \(\displaystyle p_0=10^5\) Pa, and the initial temperature is 20 \(\displaystyle {}^\circ\)C.

\(\displaystyle a)\) What is the mass of the argon gas above the mercury?

\(\displaystyle b)\) The temperature of the gas is slowly increased. What is the temperature of the gas when the height of the mercury in the tube is \(\displaystyle h_2=0.36\) m?

\(\displaystyle c)\) How much work was done by the extending gas during the process?

(5 points)

**P. 4954.** One end of a metre stick, which has fairly big mass, can be rotated freely about a horizontal axle. Put 11 five-forint coins onto the initially horizontal stick at a distance of 10 cm from each other.

\(\displaystyle a)\) What happens to the coins right after the moment when the stick was released?

\(\displaystyle b)\) Which coins do not move with respect to the stick at the moment when the stick encloses an angle of 10\(\displaystyle {}^\circ\) with its original position? The coefficient of static friction between the stick and the coins is 0.5.

(5 points)

**P. 4955.** Two small balls of mass \(\displaystyle m\) and of charge \(\displaystyle Q\) are moving on the horizontal ground, and at a certain instant they are at a distance of \(\displaystyle d\). At this instant their speeds are \(\displaystyle v_0\), and the direction of their velocity vectors makes an angle of \(\displaystyle \alpha\) with the direction of the line connecting the two balls, as shown in the *figure.*

\(\displaystyle a)\) What is the least distance between the balls?

\(\displaystyle b)\) What are their speeds at this moment?

(5 points)