# Exercises and problems in Physics

November 2002

## Please read The Conditions of the Problem Solving Competition.

## Experimental problem |

**M. 238.** Fill up a vertically standing
funnel with water while closing its opening underneath. Then open the
hole, and let the water pour out. Measure the position of the water
level as a function of time. How will the sinking rate of the water
level change? (6 points)

## Theoretical problemsIt is allowed to send solutions for any number of problems, but final scores of students of grades 9-12 are computed from the 5 best score in each month. Final scores of students of grades 1-8 are computed from the 3 best scores in each month. |

**P. 3571.** There is a metal cube, which
is empty inside. The length of its edge is 5 mm, and its wall
thickness is 1 mm. The density of the metal is
8400 kg/m^{3}. What will happen to the cube if we keep it
under water and then release it? (3 points)

**P. 3572.** A certain amount of ideal
gas is going through a thermal cycle (shown in the
*figure*). What is the amount of work done by the gas in one
cycle? (3 points)

**P. 3573.** What amount of work is needed
to shut a door made of solid wood of a mass of 24 kg, so that its
edge impacts against its case with a velocity of 5 m/s? (4
points)

**P. 3574.** How much heat is to be
subtracted from 2 kg supercooled water of
-5 ^{o}C, to make ice of it of the same
temperature? (4 points)

**P. 3575.** A dog of mass *m* is
standing on a sledge of mass *M*. It is capable of jumping off
the sledge with a relative velocity of *u*, and then can run at a
velocity of *v* after the sledge and jump on it again. Neglecting
the friction of the sledge on snow-covered horizontal ground,
determine what maximum velocity the sledge and the dog can reach in
this way and how many times the dog jumps on the sledge in the
meantime? (Let *M*=30 kg, *m*=10 kg,
*u*=0.5 m/s and *v*=4 m/s.) (5 points)

**P. 3576.** We put a solid cylinder on a
fixed slope of an angle of \(\displaystyle \alpha\)=30^{o}. We pull the
cylinder using a thread coiled around it in a perpendicular direction
to the slope with a force of
*F*=*x*^{.}*mg*. The cylinder rolls down
the slope without sliding. *a*) Determine and plot the
static coefficient of friction as a function
of *x*. *b*) What is the minimum value of *x*
if the surface of the slope is very smooth? *c*) What is the
minimum value of the static coefficient of friction if the centerline
of the cylinder moves with an acceleration of 2*g*? (5
points)

**P. 3577.** What is the inductivity of a
toroid coil with a rectangular cross section? The number of turns in
the coil is *N*, and the radius of the central circle is
*R*. The lengths of the sides of the rectangle are *a* and
*b*. The sides of length *a* are parallel with the axis of
the toroid. *Data:* *N*=1000, *R*=10 cm,
*a*=6 cm, *b*=4 cm. (5 points)

**P. 3578.** The 0.1 mm diameter water
droplets of a cloud are charged up to 10 V. The smaller droplets
join into bigger droplets of a diameter of 2.7 mm. What will
their electric potential be? (4 points)

**P. 3579.** Ho much faster is a proton
than an \(\displaystyle \alpha\)-particle speeded up by the same accelerating voltage?
The initial velocities are negligible. (4 points)

**P. 3580.** In a revolving cylindrical
shape gymnasium of a space station `artificial gravitation' the same
as the terrestrial *g* is maintained. When the gymnasium is not
in use, they slow it down (out of a false understanding of economy)
with constant deceleration to maintain only half of the usual value of
gravity. How long does the deceleration take if they don't want the
carpets to slip from their places? (The static coefficient of friction
between the carpets and the floor is at least 0.1.) To what extent can
the deceleration time be reduced if we do not insist on constant
deceleration? How much time is needed to achieve complete
weightlessness this way? (6 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary