
Exercises and problems in Physics January 2001 
New experimental problem:
M. 221. Measure how much mechanical energy it
takes to completely open a door mounted with a damper. (6 points)
New problems:
P. 3394. Two cars start from the same place
at the same time. Their respective speeds are 60 km/h and 80 km/h. Is
it possible that they move away from each other at a speed of a)
140 km/h; b) 20 km/h; c) 100 km/h? (3 points)
P. 3395. The length of a steel
aircraftcarrier is 600 m in the 0 ^{o}C
Arctic Ocean. How long will this same ship be in the 20 ^{o}C Mediterranean Sea? How many times its original value
will the immersed volume of the ship change to? (5 points)
P. 3396. A pointlike body at the top of a
smooth slope of height h=1 m, and another one thrown obliquely from
point B start at the same time. They arrive at point C at the
same time and speed. How long is the slope? (5 points)
P. 3397. The end point A of the rigid,
L=2 m long rod shown in the figure moves along axis x all
the time, while the end point B moves along axis y. The speed of
point A is constant: v_{A}=1 m/s, and the rod is vertical at time
t=0. Determine the speed and the acceleration of point B and the
angular acceleration of the rod as a function of time. What are these values at
the following moments: t_{1}=0.5 s,
t_{2}=1.5 s and t_{3}=1.999 s? (The problem can be solved using
elementary methods.) (5 points)
P. 3398. In one case, a disc only rotates
about a vertical axis, while in another case it only travels horizontally. The
energy of the two motions is identical. The disc is placed flatly onto a level
table. In which case does it stop earlier? (Assume that the disc presses the
table uniformly.) (5 points)
P. 3399. A loop made of non stretchable
string is fastened to the frame shown in the figure and immersed into a
solution of soap, holding the frame. When the film inside the loop is pierced,
the loop stretches out into a circle. What force arises in the string if the
radius of the circle is 1 cm and the surface tension of the solution is
0.03 N/m? (4 points)
P. 3400. Some acetylene gas
(c_{p}/c_{V}==1.25) follows
the cycle ABCDA shown in the figure. Determine the proportion of the
energy given out by the gas to its surroundings during the isochore section of
the cycle to the expansion work done during the isobaric section of the
cycle. (4 points)
P. 3401. Three identical metal plates of area
T are at distances d_{1} and
d_{2} from each other. Metal plate A
is uncharged, while metal plates B and C have respective
charges +q and q. Metal plates A and C are
connected by switch K through a consumer of unknown resistance. What
energy does the consumer give out to its surroundings? (5 points)
P. 3402. Does the same force act between two
conductors with current flowing through them, and a conductor with current
flowing through it and an electron beam parallel to it if the other data are
identical? (4 points)
P. 3403. We would like to send some space
device from the Earth to Mars using the least possible amount of energy. At
what speed should the device be launched with respect to the Earth, and what
should the EarthSunMars angle be at the launching? (Ignore the modifying
effect of the gravitational attraction between the Earth and Mars on the
trajectory of the object.) (6 points)
Send your solutions to the following address:
KöMaL Szerkesztőség (KöMaL feladatok),
Budapest Pf. 47. 1255, Hungary
or by email to: solutions@komal.elte.hu.
Deadline: 11 February 2001
