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Critical Thinking Questions in Physics Part 1
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by Hasan Fakhruddin
The Indiana Academy for Science, Mathematics, and Humanities BSU
Muncie, Indiana
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Mechanics and Electricity and Magnetism
1. Does This Make Any Cent? $1 = 100¢ = 10¢ x 10¢
= $(1/10) x $(1/10)
= $(1/100)
= 1¢ Answer: There is incorrect use of units. In the second step, the effective unit of ¢2 is not the same as $ on the left side. Again, the unit of $2 in step 3 is changed to $ in the fourth step.
2. The Eiffel Tower has a mass of 10,000,000 kg. A 100:1 scale model of the tower made from the same material will have a mass of
(A) 100,000 kg
(B) 10,000 kg
(C) 1,000 kg
(D) 100 kg
(E) 10 kg
(F) 1 kg
Answer: (E) 10 kg
Some students may jump to the answer of 100,000 kg, thinking the model will weigh 1/100 of the actual tower. However, if the height of the model is 1/100 of the height of the tower, all its dimensions are 1/100. Hence the model is (1/100) x (1/100) x (1/100) = 1 millionth of the volume of the actual tower (no matter what shape the tower is). Hence, if the model is made of the same material as the tower, its mass would be 1 millionth the mass of the tower, i.e., 10 kg.
3. The paths crossed for three men -- A, B, and C -- walking through woods. It was a cold night. They decided to light a fire and rest by it for the night. They set out to bring some firewood. A came back with 5 logs of wood, B brought 3 logs, but C came back empty-handed. C requested that they let him rest by the fire and promised to pay them some money in the morning. In the morning C paid them $8. How should A and B split the money fairly?
(A) A $7; B $1
(B) A $6; B $2
(C) A $5; B $3
(D) A $4; B $4
(E) None of these
Answer: (A) A $7; B $1
One has to realize that all three men are equally benefited by the fire from the 8 logs of wood. Each man used 8/3 logs of wood through the night. Therefore, A contributed 5 - 8/3 = 7/3 logs of wood.
B contributed 3 - 8/3 = 1/3 log of wood. Hence they must share $8 in proportion to 7/3:1/3 or 7:1.
4. Scaling a Wall. An insect is climbing up a 30 ft. vertical wall. Starting from the bottom, the insect climbs up 3 ft. during the day and slips down 2 ft. during the night. In how many days will the insect reach the top of the wall?
(A) 31 days
(B) 30 days
(C) 29 days
(D) 28 days
(E) 27 days
(F) Never
Answer: (D) 28 days
Some students may jump to the answer of 30 days, arguing that the insect gains 1 ft. in height per day. However, in 27 days it will have climbed 27 ft., and on the 28th day it will cover the remaining 3 ft. to reach the top.
5. Where on Earth Is This Person? A person somewhere on the earth travels 10 mi. south, then 10 mi. east, and then 10 mi. north. He is back at his starting point. Which place on the earth is he?
There is one solution at the north pole, and there are infinite solutions at the south pole, as illustrated by the diagrams below.
6. Hiker Up and Down the Hill. A hiker started to climb up the hill at 6:00 a.m. and either kept climbing up or rested at some place(s). He reached the top at 6:00 p.m. He rested there for the next 12 hours. Next day at 6:00 a.m., he began to travel down the same path. He either moved downward or rested at some place(s). For the up and down trips, how many times was he at the same place at the same time?
(A) Never
(B) At least once
(C) Once and only once
(D) At most once
(E) Only twice
(F) None of these
Answer: (C) Once and only once
Method 1: Draw the x vs. t graph for the hiker, with t ranging from 6:00 a.m. to 6:00 p.m. for the two days. The graphs for the two trips will intersect for only one value of x.
Method 2: Imagine that as the hiker starts to ascend, there is a "virtual hiker" who starts the descent at 6:00 a.m. It is easy to see that the two "hikers" will meet once and only once.
7. Playful Dog and the Master. Mr. Fiz is returning home at a speed of 2 mph with his dog Ix. He unleashes Ix when they are still 3 miles from his house. Ix happily begins running back and forth between the house and his master with a constant speed of 3 mph. Ix does not waste any time while turning around. By the time Mr. Fiz reaches home, how many miles has Ix run?
(A) 3.5 miles
(B) 4.0 miles
(C) 4.5 miles
(D) 3.333...miles
(E) 3.555...miles
(F) None of these
Answer: (C) 4.5 miles
Some students may try to form a summation series for the distances traveled by the dog for the trips between the house and the master. It gets very complicated.
The simple solution: Mr. Fiz takes 1½ h to reach home. Therefore, the dog has been running for 1½ h. With the speed of 3 mph, the dog has thus traveled a distance of (3 mph) x (1½ h) = 4.5 miles.
8. Average Round-Trip Speed. A person travels from city A to city B with a speed of 40 mph and returns with a speed of 60 mph. What is his average round-trip speed?
(A) 100 mph
(B) 50 mph
(C) 48 mph
(D) 10 mph
(E) None of these
Answer: (C) 48 mph
The answer does not depend on the distance between the cities A and B. Assume the distance to be x, with round-trip distance 2x. The time taken from A to B is 
h, and the time for the return trip is 
h. For the speeds of 40 mph and 60 mph, the round-trip time is 
h and 
h. The average speed is defined as Vavg = total distance ÷ total time.
This becomes an exercise in the arithmetic of fractions. The answer turns out to be 48 mph, independent of x.
Students are very likely to jump to the answer of 50 mph, as it is the average of the given speeds. However, that is not the way average speed is defined!
9. Two Trains. Two trains are moving toward each other with speeds of 17 mph and 43 mph. How far apart are they 1 minute before they pass each other?
(A) 60 miles
(B) 30 miles
(C) 6 miles
(D) 3 miles
(E) 2 miles
(F) 1 mile
Answer: (F) 1 mile
There is no need to do tedious calculation if we realize that each train is approaching the other at a relative speed of (17 mph + 43 mph) = 60 mph = 1 mile/min. Hence 1 minute before collision they are 1 mile apart.
10. And The Winner Is... Two marbles roll along two horizontal tracks. One track has a dip, and the other has a bump of the same shape. Which marble wins?
Answer: The marble on the track with the dip wins. On the straight parts of the tracks, the two marbles have the same speed. However, at every point of the dip the marble has greater speed than the other marble at the corresponding point of the hump. Thus the marble on the track with a dip wins. This argument assumes that the marbles always remain in contact with the tracks.
11. Time of Flight of Three Projectiles. Three projectiles are launched from the same point over a level ground with speeds VA, VB, and VC. They all attain the same maximum height. Which of the following is true about their times of flight?
(A) tA = tB = tC
(B) tA > tB > tC
(C) tA < tB < tC
(D) None of these
Answer: (A) tA = tB = tC
The three projectiles have equal maximum heights, hence they have equal initial vertical components for their speeds. Thus they all take equal times to reach the maximum height and return back to the ground.
Students may think that since the projectiles travel different distances along their trajectories they have different travel times.
12. Initial Speeds of Three Projectiles. Three projectiles are launched from the same point over a level ground with speeds VA, VB, and VC. They all attain the same maximum height. Which of the following is true about their initial speeds?
(A) VA = VB = VC
(B) VA > VB > VC
(C) VA < VB < VC
(D) None of these
Answer: (C) VA < VB < VC
The three projectiles have equal initial velocities and equal times of flight. However, for their horizontal ranges, XA < XB < XC. The horizontal range is caused by the horizontal components of their speeds in the same time. Hence vAx < vBx < vCx. This implies that vA < vB < vC.
13. Speed of a Projectile and the Angle of Launch. A ball is launched from the same height repeatedly with the same speed Vo but in different directions A, B, and C as shown below. It reaches the ground with speeds VA, VB, and VC respectively. Which of the following is true about these speeds?
(A) VA = VB = VC
(B) VA > VB > VC
(C) VA < VB < VC
(D) None of these
Correct Answer: (A)VA= VB = VC
In each instance, the ball starts with the same speed, hence the same kinetic energy. When the ball hits the ground, it has lost the same amount of gravitational potential energy and hence gained the same amount of kinetic energy. Thus, in each instance, the ball hits the ground with the same speed.
Here students might think that direction of the initial velocity may affect the speed of impact on the ground.
14. The Breakaway Drop. A drum is spinning at constant speed with its axis vertical. A drop of water at a point P on its surface detaches and flies off.
Looking from the top, what is the most likely path followed by the drop?
Answer: (B)
The water drop P is initially in uniform circular motion. Hence at any moment its velocity is tangential to the drum surface. When it detaches from the drum, there is no more centripetal force causing it to go in a circular path, hence it travels tangentially off from the surface.
In a three-dimensional picture, the drop will follow a parabolic path to the ground.
15. Weight of the Flies. The weight of a closed jar is W while the flies inside it are flying around. What will be the weight of the jar if the flies settle down inside the jar?
(A) Equal to W
(B) Less than W
(C) Less than W
Answer: (A) Equal to W
When the flies are flying, they are pushing down on air, which in turn is pushing down on the jar. In fact, the jar is supporting the flies even when they are flying around.
If the jar were placed on a sensitive scale, the reading would fluctuate about W and average out at W over a long interval of time.
16. Weight of Gas. A closed jar containing a gas is weighed. Do the molecules of the gas contribute to the measured weight?
(A) Yes, fully
(B) Yes, but partially
(C) No
Answer: (A) Yes, fully
This may appear to be similar to the question 15 in which the jar contains flies. However, in this case we are considering whether the weight of the gas itself contributes to the weight of the whole system. One approach to this problem is to consider the vertical velocities of the molecules. As a molecule moves down, its velocity is increasing due to the acceleration due to gravity. When the molecule collides with the bottom of the container, it imparts a force in excess of its weight; the excess force is just right to compensate for the time the molecule was not in contact with the jar.
Again, on a microscopic scale, if the jar were placed on a sensitive scale, the reading in the scale would vary around W but average out to W over a long enough interval of time.
17. Weighing In Weightlessness. How do astronauts weigh themselves in the state of weightlessness?
Answer: The weight of astronauts in a close orbit around the earth is about 90 percent of their weight on the surface of the earth. However, they feel weightless because they are effectively in a free fall and hence have no normal force from a surface acting on them. The normal force gives people a feeling of their weight. If a person stands on a weighing scale to find her weight, the scale reads the normal force it applies to support that person. Hence a weighing scale would show zero weight for an astronaut if she "stands" on such a scale in a satellite. However, astronauts can find their mass (inertia) using the fact that the period of oscillations of a spring-mass system depends on the mass attached to it and not on the gravity. A machine designed by NASA on this principle is called Body Mass Measuring Device (BMMD).
18. Floating Ice in a Non-inertial Frame. A person carrying a cup of water with floating ice steps into an elevator. If the elevator accelerates upward, the ice will
(A) Float higher
(B) Sink deeper
(C) Stay at the same level
Answer: (C) Stay at the same level
The upward accelerating frame is equivalent to an inertial frame with a higher value of gravitational acceleration given by g' = g + a. The buoyancy force on the ice is due to the pressure of water, which is proportional to gravity g'. The weight of the block is mg'. Hence both the weight of the block and the buoyancy force increase by the same factor when the elevator accelerates upward (and decrease by the same factor when the elevator accelerates downward). Therefore the ice floats at the same level, and the level of water in the cup does not change.
19. Tail Propeller of a Chopper. Why does a helicopter have a second propeller near its tail?
Answer: As the main (horizontal) propeller rotates one way, the rest of the helicopter tends to rotate in the opposite direction due to the law of conservation of angular momentum. The rotation of the main body of the helicopter can be prevented by another propeller near the tail of the helicopter.
20. Three Switches and a Lamp. There are three switches A, B, and C in a room. Two of them are dummy switches, and the third is the switch for a desk lamp in another room. You are allowed to turn the three switches on and off as you like. You then go into the room with the desk lamp only once, and you are able to tell which of the switches is the right switch for the lamp. How can you do this?
| If the lamp is on | If the lamp is off | | It is B. | | If the bulb is warm to touch | If the bulb is cool to touch | | It is A. | It is C. |
Answer: Turn switch A on. Leave it on for a few minutes. Turn A off and B on. Go to the desk lamp.
21. Induced Current. A boy carries a metal rod PQ horizontally on a pickup truck traveling on a straight horizontal road. An emf is induced in the rod due to the earth's magnetic field, making the end P positive (+) and the end Q negative (-). The ends of the rod are now connected by a wire. In which direction will the induced current, if any, flow in the rod?
(A) P to Q
(B) Q to P
(C) No current will flow through the rod.
Answer: (C) No current will flow through the rod.
The rod and the wire form a closed loop. There is no change in the magnetic flux through the loop as the truck moves along a straight line. Hence, by Faraday's law, there is no induced emf or induced current in the loop.
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