Rain drops falling in tube without hitting walls of tube.

In summary, the correct orientation for the tube on the cart is to be inclined forwards at an angle of theta= arctan(V(of cart)/V(of rain drop)). This will ensure that rain drops, falling vertically, will miss hitting the walls of the tube while the cart is in uniform motion on a horizontal plane. The equation for this orientation can be derived by considering the velocity of the cart and the velocity of the rain drops.
  • #1
teddyayalew
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Homework Statement


A tube is mounted on a flat cart which is in uniform motion on a horizontal plan. How must the tube be orientated on the car in order for rain drops, falling vertically, to miss hitting the walls when falling inside the tube? The motion of the rain drops is assumed uniform.


Homework Equations





The Attempt at a Solution


The answer is " The tube must be inclined forwards from the vertical with respect to the path of the cart at an angle :
theta= arctan(V(of cart)/V(of rain drop))

I had the hunch that it had to be leaned forward but I don't know how to arrive at this algebraic expression.
 
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  • #2
I tried to draw a diagram but couldn't come up with an equation. Can someone explain how to arrive at the above expression?
 

1. How do rain drops fall in a tube without hitting the walls?

When rain falls from the sky, it is subject to air resistance which causes it to spread out and fall in a random pattern. In a tube, the walls of the tube create a boundary that prevents the rain drops from spreading out, causing them to fall in a straight line and not hit the walls.

2. What causes the rain drops to fall in a tube without hitting the walls?

The rain drops are subject to gravity, which pulls them towards the center of the Earth. In a tube, this force is strong enough to overcome the air resistance, causing the drops to fall in a straight line.

3. Is there any other force at play in this phenomenon?

In addition to gravity, there may also be air currents or wind that can affect the path of the rain drops. However, these forces are usually not strong enough to cause the drops to deviate from their straight path in the tube.

4. Can this phenomenon be observed in other types of tubes?

Yes, this phenomenon can be observed in any type of tube that is long and narrow enough to create a boundary for the rain drops. This includes pipes, straws, and even tall glasses.

5. How does the size of the tube affect the path of the rain drops?

The size of the tube has a direct impact on the path of the rain drops. A smaller tube will have a more pronounced effect on the drops, causing them to fall in a tighter and more defined path. A larger tube may allow for more deviation in the path of the drops.

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