Exercises and problems in Physics September 1998

New experimental problem:

m. 199. A small water droplet in cooking oil has an approximately spherical shape, and is sinking with constant velocity. Determine the relationship between the velocity of descent and the size of the droplet.

New exercises:

FGy. 3171. Press release: ,,In July 1997 the Ethiopian runner Haile Gebrselassie broke the world record of the 10 000 m flat race in Oslo with a result of 26:31.32 minutes. This meant an improvement of Morocco's runner, Salah Hissou, by 6.76 seconds.'' Assuming that the two athletes compete against each other running at constant velocities and set their own records,

a) what is the distance between them 1 minute after the start?

b) what is the distance between them when the Ethiopian athlete reaches the finishing line?

FGy. 3172. We put a closed glass-case with air and a small bird inside on a scale. It is obvious that the scale indicates the weight of the bird too, when it is sitting on the bottom of the case. What is the combined weight if the bird is hovering in the mid-air inside the case? What is the weight if we use a cage instead of the closed glass-case?

FGy. 3173. How many people can float in the sea with a cork life-belt of 10 kg if an average person's weighs is taken to be 60 kg and 95% of his body-volume is under water? The average density of the human body is 1.06 g/cm³, the density of sea-water is 1030 kg/m³, and that of cork is 240 kg/m³.

FGy. 3174. At the beginning of an experiment we have He gas in a 40-litre bottle under 6 MPa pressure at 18 degrees centigrade. At the end of the experiment the pressure in the bottle is decreased by 30%, and the temperature is 20 degrees centigrade. How much He gas was used up? What is the price of the spent gas if the price of a newly filled bottle is 20000 Ft and the net filling mass is 1.3 kg?

FGy. 3175. We have a room-bike equipped for measuring work too. The diameter of the bike's wheel is 60 cm. There are two break-shoes fitted to the rim of this wheel and the friction force is 5 N per break-shoe. A test person uniformly pedals the wheel for 10 minutes at 48 revolutions per minute. During this time, the test person uses up 2.2 litres of excess oxygen. The utilization of 1 litre of excess oxygen decreases the chemical energy of the body by 20 kJ. What is the efficiency of the work done by the human organism?

FGy. 3176. The sun shines here and there even in a dense forest. When the humidity is high enough, one can observe shiny beams of vapour that don't appear to be parallel. Are they in fact parallel?

New problems:

FF. 3177. A plastic sucking disk weighing 3.5 g is fired from a toy-gun hitting the lower end of a vertically positioned 50 cm long wooden slat. The weighing 230 g. The upper end of the hanging slat is fixed with a horizontal axle. After the collision at the lower end the slat deflects from the vertical position by 15 degrees. What was the velocity of the banging "bullet"? FF. 3178. A 20 cm long ruler weighing 0.05 kg rests on a frictionless table. At a given instance a horizontal force of 0.01  N acts perpendicularly to the axis at one end of the ruler. What is the acceleration at the opposite end of the ruler at this moment?

FF. 3179. A thin, homogeneous stick of mass m and length L may rotate in the vertical plane around a horizontal axle pivoted at one end of the stick. A small ball of mass m and charge Q is attached to the opposite end of this stick. The whole system is positioned in a homogeneous electric field of magnitude E=mg/Q. The electric field is parallel with the stick held horizontally at the beginning.

a) What is the acceleration of the small ball at the instance of releasing the stick?

b) What is the velocity and the acceleration of the end of the stick when it swings through the vertical position? Determine the direction of the acceleration at this time.

FF. 3180. A parallel-plate capacitor of 2 nF capacitance is charged to 100 V and then disconnected from the charging source. The space between the plates is filled with mica of relative dielectric constant \(\displaystyle epsilon" ALIGN=ABSCENTE\)_r=5.

a) What is the quantity of work needed for extracting the mica from the plates?

b) What will be the voltage after removing the mica?

FF. 3181. The vertical bar and it's supporting base illustrated has a combined mass of M. At the lower end of the bar there is a spring of equilibrium length l₀=16 cm attached to the base plate. The small bead of mass m=0,1 kg can slide down on the bar without friction. When the bead is carefully placed onto the spring, the spring is compressed by x₀=2 cm.

a) What is the spring constant?

b) At what height h should the bead be released, so that the spring should compress to x₁=8  cm?

c) Let us assume that in question b) during impact the bead gets glued to the free end of the spring. What is the minimal mass M needed to prevent the support from jumping up?

FF. 3182. A given substance containing radioactive isotope \(\displaystyle ^{131}_{53}I" ALIGN=ABSCENTE\) of mass 8^.10^-11 g is used for an examination of the thyroid gland. 50% of the isotope infiltrates and remains in the thyroid gland, the rest is evacuated within 24 hours. The half-life of the isotope is 8 days.

a) What is the activity of the substance before the utilization?

b) What is the activity of the iodine in the thyroid after 4 days?

c) what length of time will be required for the activity in the thyroid to drop below 1% of the initial activity of the iodine accumulated in the thyroid gland?

d) Estimate in mSv units the maximal full-body exposure (absorbed dose equivalent) from the radioactive iodine in the thyroid of a patient of 60 kg. Neglect the gamma radiation of the \(\displaystyle ^{131}_{53}I" ALIGN=ABSCENTE\), and assume one beta particle of average energy 0.1 pJ for each decay. (The quality factor for beta radiation is 1.0)

New advanced problem:

FN. 3183. Boron ions of mass number A=10 collide with particles of an unspecified element in an accelerator. The velocities of the unknown ions and the boron have the same magnitude but opposite directions. It has been observed that the maximal scattering angle of the boron ions is 30 degrees. (The motion of the particles is nonrelativistic.) What is this unknown element in the experiment?