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counter intuitive

 
 
Reply Mon 20 Dec, 2004 04:07 am
(1) a two-inch cylindrical hole is cut through the
centre of a sphere. What is the volume remaining
in the sphere?

(2) which way do the great ocean currents flow?

(3) Which way do you turn the handlebars on a
motorcycle to make it go left ?

(4) In what direction do you point your engine if
you're in orbit and you want to fly towards that
space station up ahead ?

(5) If you roll a very basic model car down a ramp,
with the front wheels locked so they can't rotate,
which way will it face when it arrives ?

(6) In what direction does the frictional force on a
car's wheels act?

(7) If you're in a car holding a helium balloon,
which way does it move when you turn a corner?

(8) Which weighs more, a kilogram of gold or a
kilogram of feathers?

(9) You have been assigned to carpet a large,
circular building lobby, with a smaller circular tower,
containing the elevator shafts, in the center. You can
measure across the lobby, but are blocked from
measuring *through* the elevator tower. Determine
how much carpet you need, with a single measurement.


Whim
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DrewDad
 
  1  
Reply Mon 20 Dec, 2004 07:44 am
4. Point your engine away from the mass you are orbiting. The thrust will be toward the center of your orbit, this will (briefly) force you into a lower and faster orbit.
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markr
 
  1  
Reply Mon 20 Dec, 2004 11:49 am
1. The volume that remains is equal to the volume of a sphere with a diameter of 2 inches (PI*4/3 cubic inches).

8. A kilogram is a kilogram.

9. Measure the largest possible chord (it will be tangent to the smaller circle). The length of the chord is the same as the diameter of the circle with the same area as the ring that is to be carpeted.
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markr
 
  1  
Reply Mon 20 Dec, 2004 11:53 am
DrewDad wrote:
4. Point your engine away from the mass you are orbiting. The thrust will be toward the center of your orbit, this will (briefly) force you into a lower and faster orbit.

Isn't the station outside your current orbit (line of sight would be tangent to the current orbit)? If so, wouldn't you point your engine toward the mass you are orbiting?
0 Replies
 
Adrian
 
  1  
Reply Mon 20 Dec, 2004 05:47 pm
(2) All sorts of directions but the primary force for them is created by water sinking. So down....

(3) Depends on your speed....

(6) In the same direction as the car is travelling.
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DrewDad
 
  1  
Reply Mon 20 Dec, 2004 10:21 pm
markr wrote:
DrewDad wrote:
4. Point your engine away from the mass you are orbiting. The thrust will be toward the center of your orbit, this will (briefly) force you into a lower and faster orbit.

Isn't the station outside your current orbit (line of sight would be tangent to the current orbit)? If so, wouldn't you point your engine toward the mass you are orbiting?


I read it that the space station is ahead of you in the same orbit. Thus, you want to catch up.

Actually, the classic maneuver would be to thrust against the direction of your orbit. This drops you to a lower, faster orbit. At the proper time, thrust with your orbit; this would then lift you back into your original orbit.

Thrusting "down" or "up" would actually change your orbit into an elipse. Thrusting "up" would move you away from the center of mass, which is a slower orbit, and the space station would move further ahead of you.
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Adrian
 
  1  
Reply Wed 22 Dec, 2004 09:17 pm
(7) The balloon will move in the same direction as the turn because it has less inertia than the air around it.
0 Replies
 
whimsical
 
  1  
Reply Thu 23 Dec, 2004 07:27 am
Adrian wrote:
(3) Depends on your speed....


Explain why it depends, and answer it for slow and fast speed.
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Tim48185
 
  1  
Reply Mon 3 Jan, 2005 03:57 pm
markr wrote:
8. A kilogram is a kilogram.


That is usually correct, except in this instance. I don't recall the exact amounts, but in this case, the feathers weigh more. Using pounds (the United States units of weight), a pound of feathers weighs 16 ounces. However, a pound of gold weighs less, as gold uses a different measuring scale for pounds, with it being something like 14 ounces (I am not positive on this number though). Regardless, a kilogram of feathers weighs more than a kilogram of gold, although I am not sure of the exact conversion for the gold at this time.
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DrewDad
 
  1  
Reply Mon 3 Jan, 2005 04:20 pm
whimsical wrote:
Adrian wrote:
(3) Depends on your speed....


Explain why it depends, and answer it for slow and fast speed.


From a low speed (stopped to barely moving), the quickest way to turn 90 degrees left is to go 270 degrees right by spinning the rear tire.

From a higher speed, simply turn left.
0 Replies
 
markr
 
  1  
Reply Mon 3 Jan, 2005 05:14 pm
Tim48185 wrote:
markr wrote:
8. A kilogram is a kilogram.


That is usually correct, except in this instance. I don't recall the exact amounts, but in this case, the feathers weigh more. Using pounds (the United States units of weight), a pound of feathers weighs 16 ounces. However, a pound of gold weighs less, as gold uses a different measuring scale for pounds, with it being something like 14 ounces (I am not positive on this number though). Regardless, a kilogram of feathers weighs more than a kilogram of gold, although I am not sure of the exact conversion for the gold at this time.

There are 12 troy ounces to a troy pound and 16 avoirdupois (avdp) ounces to an avdp pound.
The grain is the same in avdp and troy weight.
There are 5760 grains to a troy pound and 7000 grains to an avdp pound.
So, an avdp pound is a bit more than 1.2 times as heavy as a troy pound, and a troy ounce is a bit less than 1.1 times as heavy as an avdp ounce.

However, I've never heard of a troy kilogram; so I'd say a kilogram of feathers weighs the same as a kilogram of gold.
0 Replies
 
raprap
 
  1  
Reply Thu 13 Jan, 2005 05:53 pm
3) Motorcyclists call this countersteering. At speed you steer a motorcycle by changing the camber on the tires (that's why the radial cross section of a motorcycle is round). So if you want to turn left, you push (slightly) on the left handgrip to force the camber to the right. The opposite is true for turning right.

Rap
0 Replies
 
Wolf ODonnell
 
  1  
Reply Fri 11 Feb, 2005 07:13 am
markr wrote:
Tim48185 wrote:
markr wrote:
8. A kilogram is a kilogram.


That is usually correct, except in this instance. I don't recall the exact amounts, but in this case, the feathers weigh more. Using pounds (the United States units of weight), a pound of feathers weighs 16 ounces. However, a pound of gold weighs less, as gold uses a different measuring scale for pounds, with it being something like 14 ounces (I am not positive on this number though). Regardless, a kilogram of feathers weighs more than a kilogram of gold, although I am not sure of the exact conversion for the gold at this time.

There are 12 troy ounces to a troy pound and 16 avoirdupois (avdp) ounces to an avdp pound.
The grain is the same in avdp and troy weight.
There are 5760 grains to a troy pound and 7000 grains to an avdp pound.
So, an avdp pound is a bit more than 1.2 times as heavy as a troy pound, and a troy ounce is a bit less than 1.1 times as heavy as an avdp ounce.

However, I've never heard of a troy kilogram; so I'd say a kilogram of feathers weighs the same as a kilogram of gold.


I'd have to agree with markr. A kilogram is a kilogram, as the definition of that unit is based on a special kilogram weight that's locked up in a vault in Paris.
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