25-Mar-2015: Trajectories

Purpose: The purpose of this lab is to predict the impact location of a ball by applying the concepts of projectile motion.

Materials:

1. A small steel ball with a diameter of approximately 5 cm.
2. Two aluminum "v-channel" to be used as tracks.
3. A wooden board of at least 0.5 m.
4. Two small wooden blocks to hold one of the tracks in place.
5. A ring stand and a clamp to hold one of the tracks in place.
6. Paper and carbon paper to record the impact location of the steel ball.

Process:
     There were two main parts done before we could predict the impact location.

     The first part consisted of setting up the track the ball would take. We taped the two tracks together with one being flat and the other at an incline. Once we secured the tracks, we indicated a point on which we would let the ball roll down each time. We then let the ball roll down and taped the carbon paper in the general area of the impact point.

Securing the tracks with tape. You can see how one track is being supported by the ring stand.

The final set up in order to determine the launching speed of the steel ball.

     The second part consisted of figuring out the launching speed of the ball. We let the steel ball roll down the tracks five times. We then measured the height of the table which was 88.1 cm. We measured the distance from the table to the impact points. We measured five different distances: 61.7 cm, 61.7 cm, 61.8 cm, 61.9 cm, and 61.9 cm. We averaged the measured distance and used 61.8 for our calculations.

      We know that there is no initial velocity in the y-axis and the only force acting on the ball is the force of gravity. Using Δy = -0.5(g)(t^2), therefore 0.881 = 0.5 (9.8)( t^2) we determined the time it took for the fall to reach the floor was approximately 0.424 seconds. 

We were then able to calculate the initial velocity in the x-axis. We used Δx = (Vox)(t), therefore 0.618 = (Vox)(0.424) and determined the launching speed was approximately 1.46 m/s.

Our calculations to find the launch speed.

Conclusion: