Physics Puzzles: Mini Puzzles - Birds, Planes and Shadows
July 29th, 2008
| Categories: Mechanics, Physics Puzzles
A few mini-puzzles to keep you busy until I can come up with a suitable “big” question.
- A bird sits in a cage. The bird weights 500 grams and the cage weights 1 kg. The cage is made out of bars. When the bird is perched on a rod connected to the cage, the entire deal weights 1.5kg. However, what will the scale read when the bird is up in the air, flapping its wings?
- The same question, only this time with a sealed cage (no air flow).
- Two identical planes fly up in the sky, one up at 50 meters above the ground, the other 5000 meters above the ground. Which one casts a smaller shadow?
- Take a stroll outside and observe the way sunlight falls on the ground through the trees in a (dense) forest near your home (I hope you have one! If not, let this be an excuse for you to take a day off and watch nature). You’ll notice that the light spots coming through the trees’ branches don’t take on the edgy shapes of the leaves, but rather are round in shape. How is that so?
In case question #1 wasn’t clear enough, here is how the birdcage looks like:
Have fun! 
Ans 1> The bird has no contact with the cage while flying in it. So, the weight of the setup will be that of the cage only. i.e. 1 kg.
Ans 2> If there’s no air flow, the cage is more like a closed vessel. Thus, the weight of the setup will be 1.5 kg.
Ans 3> Obviously, the one nearer to the earth will cast a smaller shadow. i.e. Plane at 50 meter from Earth.
Ans 4> Isn’t it due to Diffraction of light waves?
Hope I’ve got ‘em rite…
Hey Sanket,
1. Pretty much true. It may be just ever-so-slightly above 1 kg, as the air pushed downwards by the bird’s wings may exert a minimal force on the cage’s bottom before getting diffused sideways.
2. True. There must be some force holding the bird up in the air, and since it’s not distance-mediated (like gravity), it must be a contact force. Once we seal off the cage whatever’s holding the cage up must also be holding the bird up. Physically, it’s the air molecules that the bird is pushing down with its wings that hit the cage’s bottom and bounce back that supply that force, and since we’re holding the cage’s bottom up, we must be indirectly countering the molecules’ bounce.
3. Trick question! The light source in this case is the sun, which is “infinitely far” compared to the distance of the planes to the ground. Hence the sun’s rays may be considered to be parallel to each other. As a result, both planes will cast the SAME shadow, regardless of height!
I’m going to leave #4 open for now :).
Ok, I believe a solution for #4 is in order.
Take a box & drill a small hole in one of its sides. Put a candle some distance away from the hole outside the box, and take a look at the light spot created inside the box. What shape will it be? Yep, it won’t assume the hole’s shape, but rather the candle’s shape. This is true whenever the hole is small enough and the source of light is far enough, making the wave nature of light apparent and making geometrical optics invalid.
A similar situation exists with light shining through the leaves: the leaves create small “holes”, and the light source - the sun - is quite far, so the light spots on the ground obtained are really images of “little suns” being projected on the ground.
Regarding number 4, I’ve seen this effect during a partial solar eclipse. The normal bright spots on the ground become crescent-shaped. It’s very cool.