Physics Quiz/Trivia: Understanding Data and the Importance of Proper Analysis

[ZapperZ]

As promised, here are the questions (and answers) to the Physics Quiz/Trivia that took place in our Chat room on March 24, 2013.

List of winners/participants can be found here:

https://www.physicsforums.com/showthread.php?t=680662

I will be posting the questions and answers in stages, since some of them require LaTex formatting and will take a bit of an effort to format them here. The thread will be locked until all the questions have been posted. After that, it will be opened and you may post your comments/questions then.

Zz.

 

[ZapperZ]

1. Einstein published 3 landmark papers in his miraculous year of 1905. The special theory of relativity and the photoelectric effect were 2 of them. What was the third?

Ans: Brownian Motion

2. http://i115.photobucket.com/albums/n320/zapperz/PF Trivia/2ships_zpsca4e5216.jpg

Ans: 3. Ship B.

The parabolic trajectory means that air resistance can be ignored. The time of motion is solely dictated by the vertical height of the projectile. Thus, the shorter height will fall back to the ground first.

3. An infinite, planar, uniform charge distribution produces an electric field of magnitude 5 V/m at a distance of 1 meter from the charge surface. What is the magnitude of the electric field 2 meters from the charge surface?

Ans: 5 V/m

The magnitude of an electric field from such a geometry does not depend on distance from the infinite planar source.

4. A frog in a hemispherical pod finds that he just floats without sinking into a sea of blue-green ooze with density 1.35 g/cm3. If the pod has radius 6cm and negligible mass, what is the mass of the frog? (2 points)

The principle involved here of course is buoyancy, which says that when an object floats, the magnitude of the buoyant force is equal to the magnitude of its weight. Here, the magnitude of the buoyant force is due to the weight of the displaced liquid. The volume of the displaced liquid is equal to the volume of the half sphere. Using simple algebra, we get the mass of the frog to be ~610 g.

5. Which one of these does not belong with the others: A neutrino, a muon, a proton, an alpha particle, a Li3+.

Ans: neutrino. It is the only neutral particle.

6. What is the name given to the highest energy of the occupied state at T=0 of a metal's conduction electrons?

Ans: Fermi energy

 

[ZapperZ]

7. When one learns how to play tennis, and learns how to serve, one is usually taught to make sure one's ball toss isn't too high. One reason given is that under windy conditions, a ball that is tossed too high will be more susceptible to be affected by the wind than a ball tossed lower. However, one also doesn't want to toss the ball too low, or else one will not get the racket back in time and to generate the needed body motion to hit the serve with some force.

Now, ignoring the biomechanics of the body in generating an effective serve and simply considering the mechanics of a vertical ball toss alone where in the trajectory of the tossed ball is it the most ideal location to strike the ball, and why? (2 points - you must answer both correctly to receive the 2 points).

Ans: At or near the apex of the trajectory. At this location, the ball is moving the slowest (instantaneously motionless at the apex), and thus, this is the region where the ball spends the longest amount of time. There is a greater likelihood (and making it easier) to hit the ball at the racket's sweetspot.

 

[ZapperZ]

8. See attachment.

 

[ZapperZ]

9. In the photoelectric effect, what is the name given to the smallest amount of energy to liberate an electron from the metal's surface?

Ans: Work function.

10. What is the total resistor value between points A and B in this little electric circuit, given that R1 = R2 = R3 = 1 Ohm?

Ans: 1/3 Ohm. All 3 resistors are in parallel to each other.

11. He3 becomes a superfluid at a significantly lower temperature than He4. What is the most significant difference between He3 and He4 that contributes to such a different property?

Ans: He3 is a fermion while He4 is a boson. It is significantly more difficult to make fermions to become a superfluid which often requires 2 fermions to form a pair first.

12. What is the common use of a nude ion gauge?

Ans: As a vacuum pressure gauge.

 

[ZapperZ]

13. A mass-spring system has a frequency of oscillation of 5 Hz on earth. What is it frequency of oscillation when it is brought to the surface of the moon? A) less than 5 Hz; b) 5 Hz; c) more than 5 Hz; d) it won't oscillate; e) not enough information.

Ans: 5 Hz. The only thing that has changed in the equilibrium length of the spring.

14. Two events "occur" at the same place in the laboratory frame of reference and are separated in time by 3 seconds. What is the spatial distance between these events in a rocket frame moving with respect to the laboratory frame, in which the events are separated in time by 5 seconds? (3 points)

Ans: 12e8 m

15. What common "particle" is composed of "udd" quarks?

Ans: Neutron

16. A carbon is a carbon, of course, of course. But is it really? A diamond is one of the hardest substance known. It also has many other physical properties that makes it unique. Its close cousin, graphite, just on properties alone, appears to be on a complete opposite of the spectrum. Pure graphite is brittle, dark in color, and certainly nowhere near the hardest material known. Yet, both of these materials are made up of carbon atoms! What is the major reason for such different properties in these two materials?

Ans: The arrangement of the carbon atoms.

 

[ZapperZ]

17. While moving down the river, a motor boat passes a raft at a certain point A. In T = 60 minutes after that the boat turns around. After a while the boat and the raft meet again at a distance of L = 6.0 km below the A point. What would the speed of the water current? (assume that the boat moves with a constant speed in both directions, the turn is instantaneous, and the raft moves at the same speed as the water current). (3 points)

Ans: 3 km/h

18. Which one does not belong with the others: Pion, Kaon, Upsilon, Muon, J/Psi, Rho?

Ans: Muon. It is the only lepton. The others are mesons.

19. A block and a sphere, both having mass M, are at the top of an inclined plane. The mass slides down with no friction while the sphere rolls down without slipping. At the bottom of the inclined plane, which object has the higher translational speed? a) block, b) sphere, c) both have same speed, d) not enough information.

Ans: (a) block. The sphere's initial energy goes into not just the translational energy, but also into rotational energy. So its translational energy (and thus translational speed) will be smaller.

20. A 20 g particle moves in simple harmonic motion with a frequency of 3 oscillations per second and an amplitude of 5cm. Through what TOTAL DISTANCE does the particle move during one cycle of its motion? [Total distance is not the total displacement]

Ans: An "amplitude" is measured from the "center" of the oscillation, i.e. from the equilibrium point. So therefore, a particles goes up (5 cm), then it goes down to the equilibrium point (5 cm), then goes through the equilibrium point to the maximum displacement below (5 cm), and then goes back up to the equilibrium point (5 cm). The total distance traveled in one cycle is 5 cm x 4 = 20 cm.

 

[ZapperZ]

21. In the figure, the rectangle at the corner measures 4 cm by 8 cm. What is the radius of the circle?

Ans: Using Pythagoras' Theorem (see figure), we can write

(r-a)^2 + (r-b)^2 = r^2

Since a=4 cm and b=8 cm, we can expand this equation and arrive at a quadratic expression of

r^2 - 24r + 80 = 0

Upon factoring, we get

(r-20)(r-4) = 0

This gives us two solutions, r=20, 4 cm

The radius has to be 20 cm. For r=4, r-b=4-8=-4 cm, which is unphysical.

22. What is the lowest energy eigenvalue of a quantum harmonic oscillator?

1/2 hbar*omega.

23. You are in an elevator when the cable snaps. You and the elevator are plunging to the ground. A popular myth says that if you proceed to jump right before the moment of impact, you could survive the elevator crash. What is the most significant problem with such a myth?

Ans: Unless you are already in a crouching position when the cable snaps, you are now floating in the elevator and has no ability to push against the floor with your legs.

24. You are an astronaut, and you observe a small planet to be spherical. After landing on the planet, you set off, walking straight ahead, and find yourself returning to your spaceship from the opposite side after completing a lap of 25 km. You hold a hammer and a falcon feather at a height of 1.4 m, release them, and observe them to fall together to the surface in 29.2 s. What is the mass of the planet? (2 points)

There are two sets of independent information given above. The first is the circumference of the planet (25 km), which tells you its radius. The second is the value of g on the surface of the planet (the fact that both objects fall at the same time means that there is no significant air resistance/drag on the objects, so that the rate of fall is a true reflection of g).

With these two values, one can use the Newton universal gravitational law to calculate the mass of the planet, which is 7.8 x 10^14 kg.

 

[ZapperZ]

25. A student is given a circuit containing a variable power supply, a resistor, and an ammeter all in series, and a voltmeter attached across the resistor. The student is then asked to determine, as accurately as possible, the resistance of the resistor.

Knowing that Ohm's Law stated that V=IR, the student made a series of measurement of potential difference (V) versus current (I) on the resistor. The student end up with this data set:

Using Ohm's Law, he knows that the slope or gradent of PD versus I will give him the resistance of the resistor. He then enters these numbers into his data analysis program, runs a linear line fit routine, and it spits out the value of the slope that he wants, which is ~0.4 Ohm.

Sounds alright, doesn't it? However, there is one MAJOR problem with this. Can you describe what it is? You may assume that the voltmeter, ammeter, and power supply are "ideal", meaning they do not contribute to the accuracy or inaccuracy of the measured values.

A quick glance at the plotted data reveals that it is not a straight line. Fitting a straight-line to those data does not make an accurate representation of the behavior of the data. So the data analysis is faulty.

The End.

Zz.

 

[lightarrow]

Using Ohm's Law, he knows that the slope or gradent of PD versus I will give him the resistance of the resistor. He then enters these numbers into his data analysis program, runs a linear line fit routine, and it spits out the value of the slope that he wants, which is ~0.4 Ohm.

Sounds alright, doesn't it? However, there is one MAJOR problem with this. Can you describe what it is? You may assume that the voltmeter, ammeter, and power supply are "ideal", meaning they do not contribute to the accuracy or inaccuracy of the measured values.

A quick glance at the plotted data reveals that it is not a straight line. Fitting a straight-line to those data does not make an accurate representation of the behavior of the data. So the data analysis is faulty.

It's faulty because he is using Ohm's law which is not valid in this case, do you agree?

 

[Borek]

14. Two events "occur" at the same place in the laboratory frame of reference and are separated in time by 3 seconds. What is the spatial distance between these events in a rocket frame moving with respect to the laboratory frame, in which the events are separated in time by 5 seconds? (3 points)

Ans: 12e8 m

I would love to see it calculated. Not because I doubt the result, but it is so alien to me I just have no idea how to approach it.

 

[jbriggs444]

I would love to see it calculated. Not because I doubt the result, but it is so alien to me I just have no idea how to approach it.

In special relativity, the separation between two events is given by a formula very like the pythagorean theorem. But instead of time adding, it subtracts. So you take the square root of the square of the spatial distance minus the square of the distance in time.

This separation is "invariant". That is, it will be the same number no matter what frame of reference you use to calculate it.

From the lab frame we have that the separation between the two events is the sqrt(distance²-time²). Distance is zero, so this is just sqrt(-9). The fact that the result is the square root of a negative number means that the interval is "time-like". It is 3 seconds. [Which was somewhat obvious by inspection]

From the rocket frame we have that the the interval is sqrt(distance²-time²) = sqrt(distance²-25). From above, we know that this result is 3 seconds.

Solve for distance.

sqrt(-9) = sqrt(distance²-25)
-9 = distance² - 25
16 = distance²
distance = 4

This result is in units of seconds. The above was simplified by using units in which the speed of light is equal to 1. So the distance is 4 light seconds. Multiply by the speed of light and you have 12e8 meters.

 

[ZapperZ]

It's faulty because he is using Ohm's law which is not valid in this case, do you agree?

Sure, but that's essentially what I wrote. Ohm's Law, i.e. V=IR, assumes that for a constant R, V is proportional to I and thus, you get a linear relationship between the two. This linear relationship is no longer valid if one plots the data. So using that equation isn't accurate, and forcing the fit to this equation is not an accurate representation of what the data look like.

There is a long story associated with this, and why I asked this question. When I was a lab TA during my graduate school years, we had a typical lab on finding the spring constant using a set of weights. One time, I added a second spring that was deformed to each group's equipment and required that they try to find the spring constant of that as well. Well guess what? Most of the students in the class simply dumped the data into the linear regression program, let it spew a result, and that's that, regardless of the fact that if they examine the plot, they would see that the relationship between F (applied mass on the spring) and x (extension of the spring) was no longer linear! Only a few of the students actually commented in their report on this.

The moral of the story here is that the software you use can do many things, and it WILL spit out a number for you. However, it doesn't mean that that number has any meaning or is a valid result based on the relationship shown in the data.

Zz.

 

[Borek]

In special relativity, the separation between two events is given by a formula very like the pythagorean theorem. But instead of time adding, it subtracts. So you take the square root of the square of the spatial distance minus the square of the distance in time.

(...)

Many thanks.

 

[lightarrow]

Sure, but that's essentially what I wrote. Ohm's Law, i.e. V=IR, assumes that for a constant R, V is proportional to I and thus, you get a linear relationship between the two. This linear relationship is no longer valid if one plots the data. So using that equation isn't accurate, and forcing the fit to this equation is not an accurate representation of what the data look like.

There is a long story associated with this, and why I asked this question. When I was a lab TA during my graduate school years, we had a typical lab on finding the spring constant using a set of weights. One time, I added a second spring that was deformed to each group's equipment and required that they try to find the spring constant of that as well. Well guess what? Most of the students in the class simply dumped the data into the linear regression program, let it spew a result, and that's that, regardless of the fact that if they examine the plot, they would see that the relationship between F (applied mass on the spring) and x (extension of the spring) was no longer linear! Only a few of the students actually commented in their report on this.

The moral of the story here is that the software you use can do many things, and it WILL spit out a number for you. However, it doesn't mean that that number has any meaning or is a valid result based on the relationship shown in the data.

Zz.

Yes, to make physics also means to understand what we are doing.
Thank you.

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lightarrow