Ruler Collision Activity Nov.- 18- 2014

Ruler Collision Activity

Objective:

   Derive an expression for finding the final height for an end of a swinging meter stick after an inelastic collision.

Set up:

We used a meter stick with a hole drilled in at the .2 m mark that can freely swing. We then have a clay piece with tape placed where it may collide with the meter stick and will get stuck to it.

Data Collection:

As a change in usual procedure, we performed the lab prior to doing the theoretical calculations. As seen in (fig. 1), we found our maximum height to be .657 m. With that data we measured the height of our zero mark relative to the ground which came to be .5 m, so according to this information the maximum height from our zero in  height is .157 m.

Figure 1. Our video capture set up and one data point at the maximum height after the collision.

To theoretically calculate our maximum height we split this problem into three phases:

I) Energy from GPE to KErot.

       This step was to find our value for omega just before collision.

II) Rotational Collision Lbefore = Lafter 

      This step assumes that the rotational momentum is conserved to find the resulting omega for both the clay and bottom of the meter stick. Since there is a fixed pivot point we do not need to find the new COM and perform the parallel axis theorem.

III) Energy from KErot to GPE since the final rotational velocity is zero

      At this final phase we determine what the final height of the meter stick will be.

In the figure below (fig 2.) we see that our calculated results came to be .131 m which is lower than our actual height by 16.5%.

Figure 2. This is my calculation work of the three phases and overall answer with the actual on the bottom.

Conclusion:
  Our calculated value was significantly lower than the actual which means there must have been a mistake in scaling during the video capture thus causing the data to read higher numbers than it should.