## Exercises and problems in Physics |

## New experimental problem:

**m. 204.** Observe the motion of balls started from the
side of a bath wiped dry and bunged. Due to the slope of the bottom of
the bath, the balls moving to and fro drift towards the bung. How does
the average drift velocity in the direction of the slope of the bath
depend on the height *h *of the starting point? Make experiments
using balls of different material and size (e.g. steel ball, glass
ball, table-tennis ball, etc.), and using different starting points
with the same height *h *as well. (6 points)

## New exercises:

**FGy. 3224.** 5 cm^{3}
of water is mixed with 5 cm^{3} of
heavy water in one vessel, and 5 g of water is mixed with
5 g of heavy water in another one. Which mixture is of higher
density? (3 points)

**FGy. 3225. **A bus driver is separated from the passengers by a
Plexiglas pane mounted behind him. A car moving at a speed of
110 km/h starts to overtake the bus travelling at a speed of
80 km/h. In what direction and at what speed does the reflection
of the lights of the car made by the Plexiglas pane move, as seen by a
passenger on the bus? (3 points)

**FGy. 3226. **An inert gas with a volume of 2 dm^{3} and a pressure of 10^{5} Pa expands to a volume of
6 dm^{3} in such a way that the
process can be represented on a (*p,V*) diagram by a straight
line. At the end of the process, the increase of the internal energy
of the gas is twice the work done by the gas.

- a) Determine the pressure of the gas in the final state.

b) How much heat does the gas take up during the expansion? (4 points)

**FGy. 3227. **An astronaut throws a stone on the Moon at
an angle of 60^{o} with the horizontal
and at an initial speed of 20 m/s. What are the tangential and
the normal components of the acceleration of the stone 3 seconds after
the throwing? What is the radius of curvature of the trajectory in
this point? (5 points)

## New problems:

**FF. 3228. **A small body of mass *m *can be fastened
to any point of a homogeneous rod of length *l *and mass *M
*suspended at one end. Where should the small body be fixed so that
the period of the rod is minimum? What is this minimum period?
(E.g. let *m*=6*M*.)

**FF. 3229. **A body starting from the top of a slope of
inclination and height *h
*slides down the slope and rebounds from a wall perpendicular to
the slope. It loses some mechanical energy both while sliding and
while rebounding. What distance does it cover in how much time before
it finally stops? The coefficient of dynamic friction is , the collision number (the ratio of the
speeds after to before rebounding) is *k*. Numerical data: =30^{o},
*h*=1 m, =, *k*=.

**FF. 3230. **The top plate of a charged plane capacitor is
fixed, while the bottom one is kept in equilibrium by the
gravitational and electrostatic forces. What is the type of the
equilibrium when *a*) the charge, *b*) the pd. of the
capacitor is constant?

**FF. 3231. **A metal ring with a mass of 1 gram and a
charge of 2^{.}10^{-8} C
rotates at high velocity about its symmetry axis perpendicular to its
plane. Calculate its magnetic dipole momentum if its momentum is
0.1 kg m^{2} s^{-1}.

## New advanced problem:

**FN. 3232. **On a slope of inclination , the coefficient of friction grows proportionally to
the distance from the top of the slope: =^{.}*x*. Describe the motion of a tyre of
mass *m *and radius *r *starting from the top of the
slope. In how much time will the tyre start rolling without friction?