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Exercises and problems in Physics
January 2001

Please read The Conditions of the Problem Solving Competition.

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 aircraft-carrier is 600 m in the 0 oC Arctic Ocean. How long will this same ship be in the 20 oC Mediterranean Sea? How many times its original value will the immersed volume of the ship change to? (5 points)

P. 3396. A point-like 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: vA=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: t1=0.5 s, t2=1.5 s and t3=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 (cp/cV==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 d1 and d2 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 Earth--Sun--Mars 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 e-mail to: solutions@komal.elte.hu.

Deadline: 11 February 2001

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