Written competition (physics) commentary

◉ Question XNUMX
It is a problem of electromagnetic induction used in IH cooking heaters.That's a good question.There is a large circular coil a connected to the power supply and a small circular coil b whose center is aligned and nothing is connected.When a fluctuating current is passed through the coil a, the magnetic flux penetrating the coil b also changes with time, and as a result, an induced electromotive force is generated in the coil b, a current flows, and Joule heat is generated in the coil b.This mechanism is answered by asking five questions when a modeled variable current (Fig. 4) is passed through coil a.All the formulas needed to solve the problem are given.

Understanding how to use those formulas will be questioned.Since the positive and negative values ​​are determined by the direction of the current and the direction of the magnetic flux density, care must be taken when drawing the graph (QXNUMX and QXNUMX).Furthermore, since the letter R, which usually represents electrical resistance, is used here to represent electrical resistance per unit length, we want to make sure that we do not make a mistake (QXNUMX and QXNUMX).

In order to pass a current through the coil a, it is necessary to apply a voltage from the power supply. In QXNUMX, the voltage to be applied to the coil a is compared with and without the coil b, and is "greater than (i); Ask them to answer with three choices: (ii) smaller; (iii) same "voltage must be applied, and write the reason.This question XNUMX is a problem that makes us think "where did the Joule heat generated in the coil b come from?", And the enthusiasm of the creator can be felt.

In fact, the fluctuating current flowing through the coil a causes an induced current in the coil b, but conversely, the induced current generates an induced electromotive force in the coil a, which acts in the direction of lowering the original voltage.Therefore, in order to maintain the fluctuating current flowing through the coil a as it is even when the coil b is present, it is necessary to apply a voltage sufficient to supplement the induced electromotive force generated in the coil a by the induced current of the coil b.Actually, the product of the induced electromotive force generated in coil a and the current flowing in coil a (power added from the outside) and the power generated in coil b (Joule heat per unit time) are equal when the time average is taken. Can be shown.

In Question 10, the Joule heat generated by actually substituting the numerical values ​​in the modeled device is calculated.In order to increase the power, coil b was wound 100 times and coil a was wound XNUMX times.It is also a question of how this number of turns works on the Joule heat generated.

◉ Question XNUMX
It is a matter of mechanics dealing with golf competitions.Put the golf ball in the cup with a putter on the green.This is an interesting content for those who have played golf.It seems easy at first glance because it ignores the rolling of the ball and regards it as a mass point, and the movement is along a straight path, but there are slopes with different angles for climbing and descending between the position of the golf ball and the cup. The question has been devised.Question XNUMX is about the coefficient of static friction, and Question XNUMX is about the coefficient of dynamic friction.

Question XNUMX is an application problem of the momentum preservation formula and the rebound coefficient.For QXNUMX, the equation of motion obtained in QXNUMX may be solved, or the law of mechanical energy conservation that takes into consideration the energy consumption due to friction may be applied (the same applies to QXNUMX).The positions of the golf ball and cup are at both ends of a mountain of slopes of different angles.When the positions are exchanged, the head speed required to cross the apex is increased by giving a reason and answering (QXNUMX and QXNUMX).It's an interesting problem.

At the 10th Science Koshien National Convention, Kyoto Prefectural Rakuhoku Senior High School, the representative of Kyoto Prefecture, won the championship.This is good news for an alumnus of my alma mater.
Professor Emeritus, Yokohama National University Ken Sasaki