Random Physics Paradox Questions Part

Question #1

A mass is suspended by two identical springs, which are connected in series as shown in the photograph at the left below from a fixed point. Each spring has a parallel string loosely connected from the upper and lower ends to the center as shown in the photograph at the right.

The coupling clip between the two springs can be disconnected such that the mass will then be supported from the fixed point by two parallel spring-string units, one with the spring on top and the string on the bottom, the other with the string on the top and the spring on the bottom.
When the series spring support is disassembled so that the mass is supported by two series spring-string combinations, where will the mass be relative to its initial position as shown in the figure above?

(a) The mass will be at a higher position.
(b) The mass will be at a lower position.
(c) The mass will be at the same vertical position.

Question #2

A (very light) styrofoam block with a (much heavier) aluminum block attached to its top surface, as seen in the photograph at the left below, is placed into a container of water. The combined blocks float with one-half of the styrofoam block immersed in the water, as seen in the photograph at the right below. It's a bit ratty looking, but it works.

Now remove the floating block combination from the water, turn it upside down, and replace it in the water with the aluminum block underneath the styrofoam block. The question is what will happen? Perhaps it might float higher out of the water, so that the black line on the foam block is above the level of the water. On the other hand, perhaps the aluminum block will pull the foam block further into the water, so that the water level will be above the black line, or the blocks may even sink! Or, perhaps it will float with the black line at the water level, as in the original case.
When the inverted block combination is placed in the water (with the styrofoam block on top) where will the water level be relative to the black line in the center of the styrofoam block?

(a) The black line will be above the water level.
(b) The black line will be at the water level, as in the original case.
(c) The black line will be below the water level.
(d) The blocks will sink.

Here is a second question for extra bonus credit: The water level of the container with the blocks in their original configuration is marked by the top of the black tape on both sides of the tank. After the blocks are inverted and replaced in the water, will the water level in the tank be higher, lower, or the same?

Question #3

The question for this week has a somewhat different format from the traditional multiple guess questions previously presented.
Shown below are the front and side views of a three-dimensional object. These drawings are complete and correct mechanical drawings for the object, such as those one might give to a machine shop for its construction. The object is not a solid sphere or a thin spherical shell, and it can be made in a machine shop, as we will see next week.

The question is, what is the third (top) view, and what is the object.
Rather than give you a selection of answers, we give you a selection of clues about the top view:

(a) It might be a circle.
(b) It might be a square.
(c) It might be a square with other lines.
(d) It might be a triangle.
(e) It might be a triangle with other lines.

Question #4

The question for this week is another in the format of last week's question, except this one may be a little easier.
Shown below are the front and side views of a three-dimensional object. These drawings are complete and correct mechanical drawings for the object, such as those one might give to a machine shop for its construction.

The question is, what is the third (top) view, and what is the object.
Rather than give you a selection of answers, we give you a selection of clues about the top view:

(a) It might be a circle.
(b) It might be two squares.
(c) It might be two squares with other lines.
(d) It might be two triangles.
(e) It might be two triangles with other lines.

Question #5

A rectangular frame with a spring hanging from its top segment weighs about 3.5 Newtons, as seen from the reading of the spring scale in the photograph at the left below. If you hang a 500 gram mass on the spring, how much will the scale read? Right! The mass weighs about 5 Newtons, so the scale will read about 8.5 Newtons, as seen in the center picture. Now if you extend the spring so that a small string loop can be connected between hooks on the bottom of the weight and the platform at the bottom of the frame, what will the spring scale read? Right! Its weight does not change, so the spring scale continues to read about 8.5 Newtons. All right, it's not perfect, but it is close enough for this demonstration.

Now suppose that you burn the string, so the mass is free from the constraint holding it to the bottom of the frame. What will the spring scale do instantaneously when the string releases?
The spring scale will:

(a) move to a higher value.
(b) move to a lower value.
(c) remain at the same value.

Question #6

A small hand-cranked generator known as a "Genecon"* has the interesting property (as do all motors and generators) of acting like a motor when provided a source of current. This can be seen on an mpeg video, where one generator drives another, by clicking your mouse on the photograph below. Notice that reversing the direction that you crank the "generator" reverses the direction of the "motor."

Now suppose that the generator is connected to a capacitor rather than to another identical unit, as shown in the photograph below.

Cranking the "generator" charges the capacitor, which will then discharge back into the "motor" when the cranking is stopped and the handle released. What will the genecon do after the capacitor is charged a bit and the crank is released?After the handle is released the handle will:

(a) rotate in the same direction.
(b) rotate in the opposite direction.
(c) remain at rest.

Question #7

A 1.5 volt battery can be used to run a DC motor or to turn on a light bulb, as will be seen on an mpeg video by clicking on the photograph below.

Now suppose that the battery is connected to the motor and the light bulb as a series circuit.
What will happen when the motor and the light bulb are connected in series across the battery?

(a) Both the motor and the light bulb will operate.
(b) Only the motor will operate.
(c) Only the light bulb will operate.
(d) Neither the motor nor the light bulb will operate.

Question #8

Two physical pendula, shown in the photograph at the left below, have the same length but one has a large weight at the end, as shown in the detail photo at the right below.

The two pendula will be raised so that they are oriented in a horizontal position and released simultaneously from rest. What will happen? Will the straight pendulum get to the equilibrium position (vertical orientation, as in the photograph at the left above) first, will the pendulum with the weight get to the vertical orientation first, or will the two pendula reach the vertical orientation at the same time? Which pendulum will win the race?
When the pendula are lifted by 90 degrees and released simultaneously

(a) the straight rod will reach the bottom first.
(b) the rod with the weight on the end will get to the bottom first.
(c) the race will end in a tie.

Question #9

We have seen in the previous question and answer that the rod with an extra weight on the end is a slower pendulum than just a simple uniform rod. The question this week has to do with one of the details surrounding this question, and is perhaps a bit more mathematical than many of the others. Alternatively, this question can be worked out using a simple experiment.

The weight on the pendulum at the left in the above photograph can be moved along the rod and clamped at any desired position. What might the position of the weight be such that the two pendula will fall at the same rate, so when they are released at rest simultaneously from a horizontal position they will reach the vertical (equilibrium) position simultaneously? You may not want to assume that such a position exists, because any amount of weight increases the moment of inertia of the rod.
In order for the race to end in a tie, the weight must be positioned:

(a) at a distance of L/4 from the top of the rod.
(b) at a distance of L/2 from the top of the rod.
(c) at a distance of 2L/3 from the top of the rod.
(d) There is no position for the mass at which the race will be a tie.

Question #10

A beaker of water is in equilibrium with an aluminum mass rigged on a beam as seen in the photograph below. At the left of the photograph are three hooked weights, including two 50g and one 100g masses. Note that in the photograph the hanging weight is in front of the beaker of water and is not touching the beaker or hanging into the water.

Now suppose that the mass on the beam, which has a volume of exactly 50 cubic centimeters, is rotated and placed into the water. This may make the system unbalanced, and require some mass to be put on one of the pans in order to re-establish equilibrium. Or it may not.
Which of the following actions would make the system achieve equilibrium after the 50cc cube hanging from a beam on the left pan is placed into the water on the right pan?

(a) placing 50 grams onto the left pan.
(b) placing 50 grams onto the right pan.
(c) placing 100 grams onto the left pan.
(d) placing 100 grams onto the right pan.
(e) placing 150 grams onto the left pan.
(f) placing 150 grams onto the right pan.
(g) no additional mass is required; the system will remain in equilibrium.

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Thursday, 5 September 2013