# Exercises and problems in Physics

November 2002

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

## Experimental problem |

**M. 237.** Make a 1.5 m-long line pendulum
using a table-tennis ball as the weight. How does the work done by the
aerodynamic drag (the energy lost) depend on the starting height
*h*? What is the average power of the aerodynamic force during a
half swing? (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. 3561.** According to a car safety
advertisement a 50 km/h collision into a wall has the same result
as falling off the top of a four-storey building. What storey height
did they think of? (3 points)

**P. 3562.** In a fruit farm the crates are
conveyed on steel plates dragged by tractors. The mass of a steel
plate is 20 kg and 400 kg of fruit is piled on it. The
friction coefficient between the plate and the soil is 0.6. To what
extent does the steel plate heat up on a 100 meter road if the
internal energy of the steel plate is increased by 40% of the work
done by the friction? (3 points)

**P. 3563.** There are two cars following
each other on a narrow straight road. Their speed is 72 km/h
each. The leading one begins to brake and stops with constant
deceleration while his velocity decreases 5 m/s a second. The
response time of the other driver is 1 second, and he can
decrease his velocity by 4 m/s a second. *a*) What
distance should there be at least between the two cars to avoid a
collision? *b*) If they keep the minimally safe distance,
how long will it take them to be at a 22 m distance of each other
after the fist one begins to brake? (4 points)

**P. 3564.** How many balloons of a
25 cm diameter can be inflated from a 0.1 m^{3}
volume gas cylinder filled with helium at a pressure of
1.5*x*10^{7} Pa? The gas pressure in a balloon rises
to 1.02*x*10^{5} Pa when the temperature of the gas
reaches the temperature of the environment. The gas cylinder has been
in the place where the balloons are filled for days. (4 points)

**P. 3565.** We want to cool down 15 l
of 80 ^{o}C water to 25 ^{o}C
by putting 0 ^{o}C ice into it. What minimum
volume should the vessel have to prevent the water from overflowing at
the rim? (3 points)

**P. 3566.** We want to throw a weight of
5 kg over a 1.5 m high wall, starting from ground level at a
2 m distance from the wall. *a*) what should the
direction of the 8 m/s initial velocity be to throw the weight
the furthest beyond the wall? What is this distance?
*b*) What is the lowest energy to use for throwing the
weight over the wall? What is the direction of the initial velocity in
this case? (5 points)

**P. 3567.** Determine the size of the two
hatched areas in the figure without using the integral calculus, by
some simple physical reasoning. (5 points)

**P. 3568.** We fix a line pendulum with a
pointlike weight of mass *m* to a horizontal metal ceiling. The
period of the pendulum for small amplitudes is
*T*_{1}. Then we put some electric charge on the weight
and make it swing with a small amplitude again. The period now is
*T*_{2}. What is the charge put on the weight? (The data:
*m*= 5 g, *T*_{1}=2.02 s,
*T*_{2}=2.03 s, *g*=9.81 m/s^{2}.)
(5 points)

**P. 3569.** There is a 1.12 A
electric current going through a working discharge tube filled with
hydrogen gas. How many electrons pass the cross-section of the tube in
one second if the number of electrons leaving the cathode is
3*x*10^{18} a second? (4 points)

**P. 3570.** We connect an *R*
resistance, an *L* inductor device and a *C* capacitor after
a sinusoidal generator of voltage *U* in a serial
arrangement. The inductivity is adjustable. When it is increased, the
current first increases then it begins to decrease. The highest
current reached is *I*_{0}, and then the voltage of the
coil is *U*_{0}. Increasing the inductivity further, the
voltage of the coil reaches a maximum of *U*_{max },
and then begins to decrease. Determine the
*U*_{max }/*U*_{0} ratio and calculate
its value when \(\displaystyle R=2\sqrt{2}X_C\). (5 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary