18-C2 (Sister using most of the same numbers.) As a classroom demonstration of electrostatic repulsive forces, a plastic cup is hung by a light thread from a support directly above an insulated metal sphere. In our mind we contrive a situation with larger charges than we actually encountered this summer.

Given: The mass of the cup was 2.5 g. Imagine that we could give it a positive charge of 8 µC. Further imagine that the thread is 50 cm long and tied to a support 40 cm above the center of the sphere, and cup is in equilibrium 30 cm horizontally from the center of the sphere.

Find: (a) How great is the electrostatic force between the sphere and the cup?

18.4 mN

(b) What is the charge on the sphere? 

2.3 x 10^-8 C

23-A8   (Reworded and adding some to cover more.) All those neon signs you see hanging in local bars and store windows use a high voltage transformer to produce the thousands of volts it takes to ionize several feet of neon. These signs are actually pretty efficient at producing light. Imagine, for the purposes of this problem, that they are ideal.

Given:  The primary might have 250 turns and draw 60 mA at 120 V, while the secondary has 15,000 turns.

Find (a) What is the voltage applied to the neon sign tube?

5.1 kV

(b) How much current flows through the neon?

1.17 mA

(c)  What is the power rating of this tube?

6 W

25-BI5 (Sister with part added) A little girl asks her favorite uncle why things seen in a magnifying glass held at arm’s length are upside down.  To demonstrate the nature of real images, the nice uncle removes the shade form a table lamp and uses the magnifying glass to form an image of the light bulb on a nearby wall.

Given: The bulb is 21 cm from the lens and the wall is 3 m from the lens.

Find: (a) How large is the image as compared to the size of the light bulb?

1.14 m

(b) What is the focal length of the lens?

21 cm

(c) What is the power of the lens in dipoters?

4.8 m^-1

28-B4 (modified) A space traveler has a twin brother back at home with an identical metabolism. Using some fantastic new advances in propulsion systems, the traveler is able to get up to some substantial fraction of the speed of light. He still judges a day, however, by the beats of his own heart. He starts each day by sending his brother an email.

Given: The traveler is traveling at 2.0 x 10⁸ m/s relative to his stay-at-home brother. One day of his life on the space ship is 86,400 beats of his heart with an average resting metabolism of exactly 1 beat/second.

Find: (a) How far does he travel in one day by his own reckoning?

1.73 x 10¹³ m

(b)   How far is that by his brother’s reckoning?

2.32 x 10¹³ m

(c)    How many beats does his brother’s heart make in one day of the space traveler’s time?

6.43 x 10⁴ beats

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29-B25 (with one number changed)   Electrons in a certain electron microscope are accelerated through a potential difference of 37 kV. Calculate the de Broglie wavelength of these electrons.

6.38 x 10^-12 m

(Hint: The speed of the electrons is small enough to allow use of non-relativistic formulas connecting energy and momentum without serious error.)

32-2 An applet on the Physics Department at the University of Colorado, Boulder website allows you to explore the half-life of various radioactive isotopes. This website suggests thinking in terms an example, which, as it turns out, would be a really bad idea to play with in other than a thought experiment. What they propose thinking about would be a very dangerously radioactive sample of beryllium 11. While most beryllium atoms have 4 protons and 5 neutrons, the atoms in the hypothetical sample have 4 protons and 7 neutrons. No wonder no sample of ¹¹Be will last very long before decaying into boron 11.

Given: The half-life of beryllium 11 is 13.81 seconds. In its example, the website says, “Let's say you start with, oh, 16 grams of ¹¹Be.” Our chemist friends tell us that a mole (a name they give to any sample with 6.03 x 10²³ atoms) of ¹¹Be would have a mass of 11 grams.

Find: (a) How many atoms of ¹¹Be would you start with? (2 points)

8.8 x 10²³ atoms

(b) If you started with no boron, how many atoms of ¹¹B would you have after only one second? (6 points – 1 point for a linear model)

4.5 x 10²² atoms

(c) For two points, name the kind of radiation that would come from this radioactive decay. (2 points)

Beta Rays