I am currently doing a physics project where I am launching a wooden pellet by using a sling into a container full of water. By changing the length the rubber band is stretched, I am measuring the pellet's submergence distance into water.

Question

I know that the velocity of the pellet must increase as the rubber band is stretched to greater distances, but I was wondering if air friction increases as well due to the increase in velocity?

I know friction increases in water when velocity is increased, so will that be relevant to my experiment as well?

What about some of the physics concepts related to my experiment? There is energy transfer from the rubber band to the pellet, and a reaction force from the water as the pellet hits it? Anything else?

Thanks in advance for helping!!

Answer 1

Call the spring constant of your rubber band k (in Newtons/meter for example).
Then the potential energy stored in the stretching is (1/2) k x^2 where x is the distance you stretch it.
When you release, most of that stored potential energy is released to your missile as kinetic energy (1/2)m v^2 where m is the mass in likograms and v is the velocity. Some energy goes into the motion of the band but we assume that the mass of the band is small compared to your missile mass so most goes into the missile.
There is air drag approximately proportional to size and fluid density and velocity squared times a form factor which is small for a streamlined missile and large for a spherical one.
When it hits the water, several things happen:
The water gets accelerated out of the way as the missile hits the water, which requires a de-accelerating force on your missile.
The drag force goes way up because although the missile size and form factor are the same as in air, the density of water is about 800 times as much so the drag is much greater and it will slow down more.
By the way, although most missles are streamlined as I suggested, the problem is that they tend to turn sideways and need fins on the back to go straight, which is why you see fins on arrows and bombs and such. Another way to make a missle go straight is to spin it along the axis of flight, which is how a rifle works wit a spral ridge to spin the bullet as it travels down the barrel.
Hope these few hints help.