**P. 4519.** Recently, one of the greatest sensation was Felix Baumgartner's stratosphere jump. The Austrian sky-diver jumped out of the capsule, lifted by a Helium balloon, at a height of 39045 metres and opened his parachute after falling for 4 minutes and 17 seconds. According to the video which can be seen on the world wide web, in the first part of his motion his speed changed as it is shown in the table below:

*a*) Plot the speed-time and the acceleration-time graphs of the motion in the first 64 seconds.

*b*) His greatest registered speed was 1300 km/h, which is 1.2 times the actual speed of sound. Estimate when would he reach this record, if only the effect of gravity is counted.

(4 points)

**P. 4520.** The bodies arranged as shown in the *figure* are at rest; *m*_{1}=1 kg, =30^{o}. The rope attached to the body of mass *m*_{1} is horizontal.

*a*) Determine the magnitude of *m*_{2}.

*b*) Suppose that the rope which fixes the body of mass *m*_{1} brakes. What is the acceleration of the bodies when they begin to move?

(4 points)

**P. 4521.** A sample of air of volume *V*_{1}=3 dm^{3} and of pressure *p*_{1}=6^{.}10^{4} Pa is confined to a fixed vertical cylinder which is closed at its bottom by a piston of cross section *A*=1 dm^{2}, which can move frictionlessly. The piston is connected to the closed end of the cylinder with a spring, designed for both compression and tension, of length *L*_{0}=0.6 m and of spring constant *D*=1000 N/m. The system is in equilibrium in this position. The external air pressure is *p*_{0}=10^{5} Pa.

*a*) Find the mass of the piston.

*b*) The air in the piston is heated slowly. How much heat must be added to the confined air in order to reach that state when the spring does not exert any force on the piston?

(4 points)

**P. 4522.** News: Each saved cubic metre of natural gas protects the environment from the emission of 1.7 kg of carbon-dioxide gas. 97% of the natural gas is methane.

*a*) What is the temperature of the methane if 1.7 kg carbon-dioxide is emitted during the burning of 1 cubic metre of methane at normal pressure?

*b*) How many kg Oxygen is used and how much water vapour is gained?

*c*) By what amount is the calorific value of 1 cubic metre of methane smaller than its heat of combustion?

(4 points)

**P. 4523.** Five alike =0.5 metre long pendulums are made of electrically insulating threads and of small metal spheres of mass *m*=50 milligram. Each small sphere is given the same type of electrical charge of *Q*=10^{-7} coulomb, and the pendulums are hung at the same point. Reaching the equilibrium position, because the mutual repulsion the small spheres will be on the circumference of a horizontal circle.

*a*) What is the radius of this circle?

*b*) What would the number of revolution of the rotation of the pendulums be, if they were to rotate about a vertical axis going through the point at which they are hung, and the small spheres were to move along the circumference of the above described circle such that the spheres had no charge on them?

(5 points)