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Exercises and problems in Physics
September 1997

New experimental problem:

m. 190. How many cubic centimetres of gas are released during the dissolution of a single sparkling tablet?

New exercises:

FGy. 3079. In order to crack nuts bare-fisted, one usually takes two nuts into one's hand at the same time. Why is it easier to crack a nut with this method?

FGy. 3080. In the house of a person who is weak of hearing, a light bulb is also lit when somebody rings the door-bell. The ring can be operated both from the garden gate and from the door of the house. Draw such a circuit.

FGy. 3081. The speed of a 100-metre-wide river is 2 m/s everywhere. A boat that can travel at a constant speed of 1 m/s in standing water sets off from one bank. How far is the nearest point that the boat can reach on the opposite bank?

FGy. 3082. In the figure ammeter I reads a current of 10 mA, while the voltmeter reads a p.d. of 3 V. What does ammeter II read? The ammeters are identical, the internal resistance of the battery is negligible.

FF. 3083. The height of the cabin of a spacecraft is 3 metres. The air in the cabin is in normal state. What is difference between the pressure at the floor and at the ceiling of the cabin
a) before taking off, in the vertical position of the cabin?
b) after taking off, when the spacecraft rises with an acceleration of 40 m/s2?
c) when the spacecraft orbits the Earth?

New problems:

FF. 3084. An insect sets off upwards from the shaft of the minute hand of a church-clock exactly at 12 o'clock. Moving uniformly along the hand, it reaches the end of the hand in a quarter of an hour. When was it at the highest position?

FF. 3085. A prism of height h, width h/2 and mass M and with a homogeneous mass distribution is placed onto a horizontal plane. One end of a thread running in a pulley is fastened to the bottom of the prism, a body of mass m is hung from the other end and the system is left alone. Friction is negligible everywhere. At what ratio m/M is the prism tilted?

FF. 3086. A small body of mass m and speed v0 slides up onto a slope of mass M standing on a horizontal surface. Friction is negligible everywhere, the bottom of the slope is tangent to the horizontal plane. What is the maximum height the small body can reach on the slope?

FF. 3087. Large rain drops grow by capturing small rain drops that collide with them during their fall. Give an estimate of the increase of mass in 10 seconds of a drop with a diameter of 3 mm, the speed of which grows uniformly from 5 m/s to 7 m/s. The drop in question hits droplets with a diameter of floating in the air. The spatial distribution of the droplets is uniform, there are 200 of them in average in a cubic centimetre.

New advanced problem:

FN. 3088. A certain helicopter can hover when the mechanical power output of its engine is P. A second helicopter is an exact copy of the first one, but reduced to 1/2 (its linear dimensions are half as large). What mechanical power output is needed to make this second helicopter hover?

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