Solving the Flying Pencil Problem - Get Help Now!

[Lookaash]

Homework Statement

Place a pencil on the edge of a table and I hit it. How shall it fly? When will it fly the highest distance?

Homework Equations

Definetely F=m*a and for the flight x = 1/2 a t^2

The Attempt at a Solution

Well there are several hidden factors that are making the problem difficult. One is that when I hit the pencil, I continue on my path, so it is just not an impulse. Another is the width of the table - the pencil jumps of it.

Basically, the only thing I know for sure is that if I place the pencil on a table that has no width and in a way that the center of mass is directly above edge of the table, then if I hit it very near of the center of gravity, it will just rotate and will not fly at all.

I know that the length of the flight depends on how far is the center of mass from the edge of the table and also on where and how I hit it. Hitting it further from the center of mass should give it bigger impulse, but I think it turns into more rotation and not so much into tangential velocity. But on the other hand hitting it nearly the center of mass gives it greater rotation too, because the hitting object will change the pencil's angle more quickly. I am getting really confused... Is there anyone who can help me?

 

[Zoe-b]

I did the very same experiment for coursework a while back =] although I'm afraid I can't be a great deal of help since I didn't manage to get to grips with the maths properly.

I looked at it from an experimental point of view- I did some experiments where the pencil was on a fixed axis, and measured the angular velocity of the pencil after it was hit, in an attempt to work out the amount of energy given to the pencil... If you then measured the angular velocity when the pencil was in flight presumably you could work out how much of the energy is transferred for parabolic motion? I don't know.

Another thing to look at is maybe the motion of whatever you use to hit it- for example in my experiment a mass dropped vertically moved sideways after hitting the pencil indicating that horizontal momentum had been transferred to the pencil..

Experimentally, the pencil also sometimes flew backwards, (when its centre of mass was a long way onto the table).. think of hitting a metre ruler when only a few cm hang over the edge- here it would definitely go backwards and not forwards.

So basically I cannot help you with the theory behind it but I do have some pretty screenshots of the experiment itself, which may or may not be of use.

Zoe

 

[Moetasim]

I would suggest approaching this problem by breaking it down into smaller, more manageable parts. First, let's consider the motion of the pencil when it is hit. The force applied by the hitting object will cause the pencil to rotate and also move horizontally. This means that the pencil will have both rotational and translational motion.

Next, we can consider the factors that affect the flight of the pencil, such as the location and angle of the hit, the width of the table, and the position of the center of mass. These factors will affect the initial velocity and trajectory of the pencil, ultimately determining the distance it will travel.

To accurately solve this problem, we would need to use mathematical equations and principles such as torque, rotational motion, and projectile motion. Additionally, we would need to take into account the properties of the pencil itself, such as its mass and shape.

I would also recommend conducting experiments to gather data and analyze the results. By varying the factors mentioned above, we can determine the optimal conditions for achieving the highest flight distance.

In summary, solving the Flying Pencil Problem requires a combination of theoretical analysis and experimentation. It is a complex problem that cannot be solved with a simple formula, but with careful consideration of all the relevant factors, we can arrive at a solution.