## Exercises and problems in Physics |

## New experimental problem:

**m. 207. **Investigate how the volume of an inflated, initially
approximately spherical balloon changes as the balloon is gradually
pulled under water using a thread.

## New exercises:

**FGy. 3254. **There is half a metre of oil with a density of
800 kg/m^{3} atop half a metre of
water in a barrel. A prism with a length of 1 m and a
cross-section of 1 dm^{2} floats in
this liquid. The bottom 10 cm of this prism is made of aluminium
with a density of 2700 kg/m^{3}, the
rest is made of pinewood with a density of 500 kg/m^{3}. The prism is slowly and cautiously lifted out
from the liquid. How much work do we do and how much work does the
upthrust do? (The prism remains vertical all the time.)

**FGy. 3255. **There is 10 g of oxygen in a cylinder closed
by a piston. This gas goes through the equilibrium states described by
the formula

while its volume increases from the initial 10 litres to 25 litres. What are the lowest and highest pressures and temperatures of the gas during this process?

**FGy. 3256. **There is one point-like body with a charge of
6^{.}10^{-8} C and a mass of
2 g at rest in each vertex of an equilateral triangle with
50 cm sides. What are the electric field strength and the
potential at the centre of the triangle? What is the initial
acceleration of the bodies when their fastenings are simultaneously
released, and what final speed do they reach? (All other forces should
be neglected.)

**FGy. 3257. **A prism of mass *M*=3 kg forming a
slope of inclination can slide
without friction on a horizontal table. A rectangular body of mass
*m*=1 kg is placed onto this slope, where it can slide down
without friction, while the prism moves with some acceleration. At
what angle is the acceleration of
the prism maximum?

## New problems:

**FF. 3258. **A flea goes up a flight of stairs jumping from
edge to edge on the stairs. When can he get up with less work: when he
takes the stairs one by one or two by two? In which case does he
arrive upstairs sooner?

**FF. 3259. **A ship can increase its speed using a built-in
pump that sucks in a mass *m *of water per unit time through an
opening in the ship's bottom, and ejaculating it backwards at speed
*c *with respect to the ship. What is the maximum speed that the
ship can reach if the drag is proportional to the square of its speed:
*F*_{k}=*B*^{.}*v*^{2}?

**FF. 3260. **A metal sphere can be charged to charge
*Q*_{1} using a belt generator. When
it touches another, uncharged metal sphere, charge *Q*_{2} is passed over. Continuing this procedure -
i.e. touching the first sphere to the belt generator and then to the
second sphere -, what is the maximum charge that can accumulate on
the second sphere?

**FF. 3261. **A point-like body with a mass of 0.1 kg
starts with zero initial speed from point *A *of a hyperbolic
slope of equation *y*=1/*x*, as shown in the figure. What is
the pressing force in point *B *if friction is negligible?

**FF. 3262. **There is helium gas in a horizontal cylinder with
heat insulating walls, closed by a piston. The piston of mass *m
*can move without friction in the cylinder. The atmospheric
pressure is *p*_{a}; the temperature
of the helium is initially *T*_{0},
its volume is *V*_{0}. Releasing the
fastening of the piston, the atmospheric pressure suddenly compresses
the gas, heating it up to temperature *T*. What is the maximum
speed of the piston during this process? (Data: *m*=100 kg,
*p*_{a}=10^{5} Pa, *V*_{0}=1 m^{3},
*T*_{0}=300 K,
*T*=600 K.)

## New advanced problem:

**FN. 3263. **There is a coil of 3600 turns in the central part
of the iron core shown in the figure. The cross-section of the coil is
20 cm^{2} here and
5 cm^{2} elsewhere. The relative
permeability of iron is 4600. What pd. do the voltmeters read, while
the current flowing in the coil increases uniformly from zero to
10 A in 0.1 s? (The internal resistance of the battery is
negligible. *U*_{0}=18 V,
*R*_{1}=3 , *R*_{2}=2 .)