Problems for the oral exam in physics at the Leningrad Polytechnic Institute

Kvant 1971, No. 12 p. 39-40 Tag GUIM

Rough automatic draft, low quality: expect mistakes and awkward wording. It will be replaced by a better translation. Original →

M. M. Kozlov, I. G. Kochnev

The oral exam in physics consists of answering theory and solving problems. We will not touch upon the answers received to theoretical questions. This is an important topic and certainly deserves special consideration.

The task in the entrance exam represents a specific goal - to check how deeply and informally the examinee understands the existence of physical phenomena. A simple example. If an applicant formulates Newton’s laws, but does not have the ability to use these laws when solving a problem, then his theoretical answer, of course, provides. Thus, the task plays a significant role in assessing knowledge.

The applicant must be able to analyze a problem, choose the optimal way to solve it, justify it and correctly perform the technical part of the task.

Below are a number of problems that have appeared in the last 3 years in the entrance exams of the LPI. When solving problems, special attention should be paid to some “difficult” questions and typical mistakes that are typical for applicants.

In mechanics, with the exception of purely kinematic problems, the most challenging problems for applicants are those on the work of a variable force, the friction force, and the calculation of the centripetal force. Many people do not have a clear idea that the centripetal force is either the resultant (that is, equal) of all forces acting on the body - equally

measured motion along a circle, or, in the general case of linear motion, is the projection of the resulting force onto the radius of curvature. Those who consider the centripetal force to be a force of a special nature cannot solve even the simplest problems involving linear motion, since they cannot use Newton’s II law when solving it.

When solving problems on the molecular-kinetic theory, in particular on gas laws, the most difficulties were caused by problems that required some transformations of the unified gas law, and tasks in which it was necessary to move from one unit of measurement to others (for example, from mm rm. cm to amp).

In the “Electrostatics” section, the largest number of errors were associated with the inability to perform numerical calculations. Not all applicants have sufficient skills in applying the concepts and formulas of electrostatics to solve the problem of the movement of individual contaminants (for example, electrons) in an electrostatic field. Quite difficult for applicants are tasks in which they need to find an equal electrostatic force and other forces.

An important place among the exam problems is occupied by problems on constructed electric current. The most difficult tasks for applicants are those in which it is necessary to calculate a section of a circuit with an emf source, for example, with a charging battery. They don’t always do the right thing

calculation for a circuit in which electrical energy is converted into other types of energy, in particular mechanical energy.

Difficulties that arise in such problems can be easily overcome based on the law of conservation and transformation of energy (see problem 6).

Analysis of solutions to problems in optics shows that the most difficult application of the lens formula is in the calculations of optical systems consisting of not one, but two lenses. In such problems, compliance with the rules of signs in the lens formula becomes especially important (task 7).

Let us now present several problems from the exam papers.

A small ball of mass $m$ , carrying a charge $q$ , is suspended on a thread of length $l$ . The ball moves along a circle lying in a horizontal plane, and a second, stationary ball carrying the same charge is fixed in the center of the circle. Find the angular velocity of the ball.
The air pressure inside the bottle, tightly sealed with a stopper, at a temperature of $7^\circ$ C was equal to 1 amm. To what temperature must the air in the bottle be heated in order for the cork to fly out of it, if it is known that in order to remove the cork from a cold bottle at $7^\circ$ C, it is necessary to do 1 J of work. The length of the plug is $l = 4$ amm, the section of the plug is $s = 4$ amm².
When manufacturing pressure increased by 0.5 mm, the gas density changed by 0.5 kD/m³. What was the initial density of the gas if the initial pressure was 1 amm?
A metal ball with a volume of 1 cm³ has a mass of 8 g and contains 8.6 x 10²² of free electricians. What part of these electrics must be removed from each of two such balls so that the layer of electrostatic repulsion completely compensates for the force of gravitational attraction between them ( $\gamma = 6,67·10^{-11} \cdot \text{н} \cdot \text{m}^2/\text{к}^2$ )?
The winding of the electric motor of the constructed current is made of wire with a total resistance of $R = 0,2$ ohm. When switched on with voltage $U = 120$ v, current $I = 30$ a flows through the winding of a running motor. Find the mechanical power, develop the electric motor.
Change of current in the oscillatory counterretor of the electrinite wave.

$I = 0,3 \sin 15,7 t$ .

Find the length of the electrinite wave emitted by the circuit.

The rounder consists of two identical thin biconvex lenses having a focal length of 5 cm and located at a distance of 2.5 cm from each other. Find the distance between the focus of the eyepiece and the lens close to it.
Find the force acting at the point of attachment of the movable block to the ceiling if a load of mass 60 kg suspended from the block shown at figure is supported by the weight of a person who pulls a vertical downward rope.
How much work must be done to place three identical, located at infinity in the rest frame, exact charges of magnitude $q = 5 \cdot 10^{-8}$ k at the vertices of an equilateral triangle on a side of 5 cm ( $\varepsilon = 1$ )?
The potential difference at the battery terminals is 8.5 V, while a current of 3 A flows through the battery. If you change the direction of the current to the opposite and the magnitude of the current is reduced by 1 A, then the absolute value of the potential difference will increase by 2.5 V. Find Ed. With. and the internal resistance of the battery.
Two electric heaters, labeled 600 W, 220 W and 400 W, 220 W, are connected in series and connected to a 220 W network. How much electrical power is consumed by each heater?
At a distance of 15 cm from the center of the silvered Christmas tree ball there is a Christmas tree tree 1 cm long. The diameter of the ball is 8 cm, and the tree is located perpendicular to the symmetry axis of the ball passing through the middle of the tree. Find at what distance from the center of the ball the image of the tree is located and determine the size of the image.