Projectile Gun Semester Project: Shooting a Box on an Inclined Plane

[estoydemoda]

Our semester project in ap physics was shooting a projectile with a projectile gun at an angle at a cm^3 box traveling up (or down) an inclined plane.

Our teacher chose the angle of our gun, the angle of the incline, the mass in the box and countermass (attached to a pully at the top of the inclined plane).

Our job was to do the calculations to where to put the inclined plane to make the projectile hit the box.

Beforehand, we needed to know the velocity of the projectile once it leaves the shaft and the coefficient of friction between the box and the plane.

To make sure that our box went in a straight path, we made it a railing system out of parts of a model train set. Our problem was that when we were testing for our coefficient, it wasn't constant. After trying many different times and with different weights and angles we still couldn't get a constant coefficient. My partner, bored in statistics class, graphed our coefficients in comparison to their velocities and to our surprise they were linear. We performed linear regression and found a line that would give us our coefficient depending on the velocity if there were no friction.
We were a little uneasy about using it at first but we were able to predict some times to the nearest milisecond with it so we went with it and we hit.

Once we made the line we looked a little more carefully at the box and realized it was vibrating like mad, and it probably caused the normal force to change, but since we were getting consistent results by considering it a changing coefficient, we just went with that.

Does anybody have any input to what what has happened?

oh and by the way, according to the regression line the coefficient was going up with higher velocities

 

[abercrombiems02]

Well, you results do verify why coefficients of kinetic friction are less and those of static friction. Essentially when any two objects slidge over each other, they virbrate but with very small amplitudes. The amplitude and frequencies of these amplitudes determine the coefficient of friction. If you can see your box vibrate these amplitudes are very large and will impact the coefficient of friction. As the frequency increases this coefficient should approach a constant. Remember that frequency and velocity are directly proportional if we treat the box like a wave. The best way to obtain a constant coefficient would be to use a large counterweight such that your coefficient would be constant or to improve the design of the incline such that the object slid. When an object slides the amplitude of vibrations is very small and neglegible, which is why the coefficient of friction is a coefficient and not a function. Remember the placement of the rope on the block induces a moment on the block which causes and uneven force distribution over the bottome surface.